Spaces:
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Running
Sync programming_framework from local progframe
Browse filesThis view is limited to 50 files because it contains too many changes. See raw diff
- .gitattributes +0 -2
- .gitignore +3 -0
- ARXIV_MATH_AREAS_TODO.md +122 -0
- ATTRIBUTION_SCHEMA.md +39 -0
- GENERIC_PROCESSES_TO_UPDATE.md +90 -0
- GLMP_Foundation.html +0 -0
- Genome Logic Modeling Project (GLMP) - a Hugging Face Space by garywelz.pdf +0 -3
- MATHEMATICAL_DEPENDENCY_GRAPHS_DESIGN.md +321 -0
- MATHEMATICS_DATABASE_EXPANSION_PLAN.md +291 -0
- NEXT_PASS_CHECKLIST.md +182 -0
- NEXT_STEPS_PLAN.md +161 -0
- ProgFrame_README.md +0 -227
- Programming Framework for Systematic Analysis - a Hugging Face Space by garywelz.pdf +0 -3
- README.md +70 -243
- WHOLE_OF_MATHEMATICS_CHART_DESIGN.md +374 -0
- biology_processes.html +5 -5
- chemistry-database-table.html +0 -545
- chemistry_examples.html +0 -609
- computer-science-database-table.html +0 -543
- data/aristotle-syllogistic-figure-2.mmd +30 -0
- data/aristotle-syllogistic-figure-3.mmd +37 -0
- data/aristotle-syllogistic-foundations-perfect.mmd +23 -0
- data/aristotle-syllogistic.json +326 -0
- data/aristotle-syllogistic.mmd +52 -0
- data/combinatorics-advanced-counting.mmd +24 -0
- data/combinatorics-combinations-binomial.mmd +20 -0
- data/combinatorics-principles-permutations.mmd +17 -0
- data/combinatorics.json +239 -0
- data/combinatorics.mmd +35 -0
- data/euclid-elements-book-i-props-1-10.mmd +49 -0
- data/euclid-elements-book-i-props-11-20.mmd +78 -0
- data/euclid-elements-book-i-props-21-30.mmd +105 -0
- data/euclid-elements-book-i-props-31-41.mmd +127 -0
- data/euclid-elements-book-i-props-42-48.mmd +160 -0
- data/euclid-elements-book-i.json +1167 -0
- data/euclid-elements-book-i.mmd +195 -0
- data/euclid-elements-book-ii.json +365 -0
- data/euclid-elements-book-ii.mmd +54 -0
- data/euclid-elements-book-iii.json +885 -0
- data/euclid-elements-book-iv.json +573 -0
- data/euclid-elements-book-ix.json +728 -0
- data/euclid-elements-book-v.json +676 -0
- data/euclid-elements-book-vi.json +875 -0
- data/euclid-elements-book-vii.json +761 -0
- data/euclid-elements-book-viii.json +540 -0
- data/euclid-elements-book-x.json +2620 -0
- data/euclid-elements-book-xi.json +783 -0
- data/euclid-elements-book-xii.json +567 -0
- data/euclid-elements-book-xiii.json +650 -0
- data/peano-arithmetic-addition-multiplication.mmd +65 -0
.gitattributes
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*.zip filter=lfs diff=lfs merge=lfs -text
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*.zst filter=lfs diff=lfs merge=lfs -text
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*tfevents* filter=lfs diff=lfs merge=lfs -text
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Genome[[:space:]]Logic[[:space:]]Modeling[[:space:]]Project[[:space:]](GLMP)[[:space:]]-[[:space:]]a[[:space:]]Hugging[[:space:]]Face[[:space:]]Space[[:space:]]by[[:space:]]garywelz.pdf filter=lfs diff=lfs merge=lfs -text
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Programming[[:space:]]Framework[[:space:]]for[[:space:]]Systematic[[:space:]]Analysis[[:space:]]-[[:space:]]a[[:space:]]Hugging[[:space:]]Face[[:space:]]Space[[:space:]]by[[:space:]]garywelz.pdf filter=lfs diff=lfs merge=lfs -text
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*.zip filter=lfs diff=lfs merge=lfs -text
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*.zst filter=lfs diff=lfs merge=lfs -text
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*tfevents* filter=lfs diff=lfs merge=lfs -text
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# HF rejects raw PDFs in git push; host PDFs elsewhere or use Xet
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ARXIV_MATH_AREAS_TODO.md
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# Mathematics Database — arXiv Subject Areas To-Do
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| 2 |
+
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| 3 |
+
A prioritized list of arXiv mathematics subject areas to add for a more complete collection, aligned with [arXiv math taxonomy](https://arxiv.org/category_taxonomy).
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| 4 |
+
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| 5 |
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---
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| 6 |
+
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| 7 |
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## Current Coverage (What We Have)
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| 8 |
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| 9 |
+
| Domain | Subcategories | arXiv codes covered | Gaps |
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| 10 |
+
|--------|---------------|---------------------|------|
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| 11 |
+
| **Algebra** | abstract_algebra, linear_algebra, category_theory | math.GR, math.RA, math.CT, math.AC, math.AG, math.QA | Commutative algebra, Algebraic geometry, Representation theory, Quantum algebra |
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| 12 |
+
| **Analysis** | calculus_analysis | math.CA, math.CV, math.DS, math.FA, math.AP, math.NA, math.SP | Complex analysis, Functional analysis, PDEs, Numerical analysis, Spectral theory |
|
| 13 |
+
| **Geometry & Topology** | geometry_topology | math.GT, math.AT, math.DG, math.GN, math.MG, math.SG | Metric geometry, Symplectic geometry (light) |
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| 14 |
+
| **Number Theory** | number_theory | math.NT | ✓ Good |
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| 15 |
+
| **Discrete & Logic** | discrete_mathematics, foundations | math.CO, math.LO | ✓ Good |
|
| 16 |
+
| **Applied & Other** | bioinformatics, statistics_probability | math.GM, math.ST | Statistics/Probability empty |
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| 17 |
+
|
| 18 |
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---
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| 19 |
+
|
| 20 |
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## To-Do List: Subject Areas to Add (Near Term)
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| 21 |
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|
| 22 |
+
### Priority 1 — High Impact, Partially Covered or Empty
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| 23 |
+
|
| 24 |
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| # | arXiv Code | Subject Area | Notes | Suggested Subcategory |
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| 25 |
+
|---|------------|--------------|-------|------------------------|
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| 26 |
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| 1 | math.ST | **Statistics & Probability Theory** | 0 charts currently; foundational for applied math | `statistics_probability` (exists, populate) |
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| 27 |
+
| 2 | math.PR | **Probability** | CLT, stochastic processes, SDEs; distinct from statistics | merge into `statistics_probability` or add `probability` |
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| 28 |
+
| 3 | math.CV | **Complex Variables** | Holomorphic functions, residues, conformal maps; partially in calculus_analysis | add `complex_analysis` or extend calculus_analysis |
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| 29 |
+
| 4 | math.FA | **Functional Analysis** | Banach spaces, Hilbert spaces, distributions | add to calculus_analysis or new `functional_analysis` |
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| 30 |
+
| 5 | math.NA | **Numerical Analysis** | Newton-Raphson, bisection exist; add quadrature, linear solvers, ODE solvers | extend calculus_analysis or add `numerical_analysis` |
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| 31 |
+
| 6 | math.AG | **Algebraic Geometry** | Varieties, schemes, moduli; major area | add `algebraic_geometry` or extend abstract_algebra |
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| 32 |
+
| 7 | math.RT | **Representation Theory** | Representations of groups, Lie algebras | add `representation_theory` or extend abstract_algebra |
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| 33 |
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|
| 34 |
+
### Priority 2 — Core Pure Math Gaps
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| 35 |
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| # | arXiv Code | Subject Area | Notes | Suggested Subcategory |
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| 37 |
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|---|------------|--------------|-------|------------------------|
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| 8 | math.AC | **Commutative Algebra** | Rings, ideals, Noetherian; differs from Ring Theory (noncommutative focus) | add `commutative_algebra` |
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| 39 |
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| 9 | math.AP | **Analysis of PDEs** | Existence, uniqueness, qualitative dynamics | add `partial_differential_equations` or extend analysis |
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| 40 |
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| 10 | math.DG | **Differential Geometry** | Curves, surfaces, Riemannian; some in geometry_topology | ensure distinct charts for differential geometry |
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| 41 |
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| 11 | math.SP | **Spectral Theory** | Schrödinger operators, spectral analysis | add to analysis or `spectral_theory` |
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| 42 |
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| 12 | math.SG | **Symplectic Geometry** | Hamiltonian systems, symplectic manifolds | extend geometry_topology |
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| 43 |
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| 13 | math.MG | **Metric Geometry** | Euclidean, hyperbolic, discrete geometry | extend geometry_topology |
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| 44 |
+
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| 45 |
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### Priority 3 — Advanced / Specialized
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| 46 |
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| 47 |
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| # | arXiv Code | Subject Area | Notes | Suggested Subcategory |
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| 48 |
+
|---|------------|--------------|-------|------------------------|
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| 49 |
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| 14 | math.OA | **Operator Algebras** | C*-algebras, von Neumann algebras | add `operator_algebras` |
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| 50 |
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| 15 | math.KT | **K-Theory and Homology** | Algebraic/topological K-theory | add `k_theory` or extend algebraic topology |
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| 16 | math.QA | **Quantum Algebra** | Quantum groups, operads | extend abstract_algebra |
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| 17 | math.OC | **Optimization and Control** | Linear programming, optimal control | add `optimization` |
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| 53 |
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| 18 | math.IT | **Information Theory** | Coding, entropy, channel capacity | add `information_theory` |
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| 54 |
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| 19 | math.MP | **Mathematical Physics** | Rigorous formulations of physical theories | add `mathematical_physics` |
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| 20 | math.HO | **History and Overview** | Biographies, education, philosophy | optional `history_overview` |
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| 56 |
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|
| 57 |
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### Priority 4 — Already in Expansion Plan
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| 58 |
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| 59 |
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These are in [MATHEMATICS_DATABASE_EXPANSION_PLAN.md](./MATHEMATICS_DATABASE_EXPANSION_PLAN.md):
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| 60 |
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- **Complex Analysis** (math.CV) — 4 charts planned
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- **Landmark Theorems** — FLT, Poincaré, Riemann
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| 63 |
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- **Formal Verification** — Lean, Coq
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| 64 |
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- **AI Mathematics** — AlphaProof, AlphaGeometry
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| 65 |
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| 66 |
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---
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| 67 |
+
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| 68 |
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## Suggested Implementation Order
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| 69 |
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### Phase A (1–2 weeks): Fill Empty & High-Impact
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| 71 |
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1. **Statistics & Probability** — Kolmogorov axioms, Bayes, CLT (3–5 charts)
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| 72 |
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2. **Complex Analysis** — Cauchy, residues, conformal maps (4 charts per expansion plan)
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| 73 |
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3. **Functional Analysis** — Banach/Hilbert spaces basics (2–3 charts)
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| 74 |
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| 75 |
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### Phase B (2–4 weeks): Algebra & Geometry Gaps
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| 76 |
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4. **Algebraic Geometry** — Varieties, schemes intro (2–3 charts)
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| 77 |
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5. **Representation Theory** — Group representations, characters (2–3 charts)
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| 78 |
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6. **Numerical Analysis** — Quadrature, solvers, ODE methods (3–4 charts)
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| 79 |
+
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| 80 |
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### Phase C (4–6 weeks): PDEs, Operator Theory, Applied
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| 81 |
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7. **PDEs** — Heat, wave, Laplace; existence/uniqueness (2–3 charts)
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| 82 |
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8. **Operator Algebras** — C*-algebras intro (1–2 charts)
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| 83 |
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9. **Optimization** — Linear programming, simplex (2 charts)
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| 84 |
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10. **Mathematical Physics** — Lagrangian/Hamiltonian mechanics (2 charts)
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| 85 |
+
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| 86 |
+
---
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| 87 |
+
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| 88 |
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## Metadata Updates Required
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| 89 |
+
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| 90 |
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When adding new subcategories:
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| 91 |
+
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1. Add to `metadata.json` → `subcategoryCounts`
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| 93 |
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2. Add to `metadata.json` → `subcategoryToArxiv`
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| 94 |
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3. Add to `metadata.json` → `domainHierarchy` (assign to algebra, analysis, geometry_topology, or applied)
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| 95 |
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4. Run `build-graph-data.js` to update Whole of Mathematics
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| 96 |
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5. Update upload script if new process directories are created
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| 97 |
+
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| 98 |
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---
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| 99 |
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| 100 |
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## Summary: arXiv Math Codes Not Yet Represented
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| 101 |
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| 102 |
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| Code | Area | Priority |
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| 103 |
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|------|------|----------|
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| 104 |
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| math.ST | Statistics Theory | 1 |
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| 105 |
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| math.PR | Probability | 1 |
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| 106 |
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| math.CV | Complex Variables | 1 |
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| 107 |
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| math.FA | Functional Analysis | 1 |
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| 108 |
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| math.NA | Numerical Analysis | 1 |
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| 109 |
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| math.AG | Algebraic Geometry | 1 |
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| 110 |
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| math.RT | Representation Theory | 1 |
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| 111 |
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| math.AC | Commutative Algebra | 2 |
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| 112 |
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| math.AP | Analysis of PDEs | 2 |
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| 113 |
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| math.SP | Spectral Theory | 2 |
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| 114 |
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| math.OA | Operator Algebras | 3 |
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| 115 |
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| math.KT | K-Theory | 3 |
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| 116 |
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| math.QA | Quantum Algebra | 3 |
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| 117 |
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| math.OC | Optimization & Control | 3 |
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| 118 |
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| math.IT | Information Theory | 3 |
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| 119 |
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| math.MP | Mathematical Physics | 3 |
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| 120 |
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| math.HO | History & Overview | 4 |
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| 121 |
+
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| 122 |
+
**Well covered:** math.NT, math.CO, math.LO, math.GR, math.RA, math.CT, math.CA, math.GT, math.AT, math.DS (via complex dynamics)
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ATTRIBUTION_SCHEMA.md
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# Mathematics Database — Attribution Schema
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Charts in the Mathematics Processes Database may include optional attribution metadata for academic transparency and citation.
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| 4 |
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| 5 |
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## Schema
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| 6 |
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| 7 |
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| Field | Type | Description |
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| 8 |
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|-------|------|-------------|
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| 9 |
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| `primary` | string | Primary author(s) or source (e.g., "Kurt Gödel", "Claude Shannon") |
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| 10 |
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| `contributors` | string[] | Additional contributors (optional) |
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| 11 |
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| `publication` | string | Title of publication or paper |
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| 12 |
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| `year` | string | Year of publication |
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| 13 |
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| `doi` | string | DOI URL (e.g., "https://doi.org/...") |
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| 14 |
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| `url` | string | External URL (Wikipedia, arXiv, etc.) |
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| 15 |
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## Implementation
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| 17 |
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Attribution is embedded in chart HTML via a "Cite" badge in the header-meta area. Hovering over the badge reveals a popover with the full attribution details. Charts using this schema include:
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| 19 |
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| 20 |
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- Gödel Incompleteness Theorems
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| 21 |
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- Schemes & Sheaves (Grothendieck)
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| 22 |
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- Group Representations (Frobenius, Maschke)
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| 23 |
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- Riemannian Geometry
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| 24 |
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- ZFC Axioms
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| 25 |
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- Shannon Entropy
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| 26 |
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- C*-Algebras (Gelfand–Naimark)
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| 27 |
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| 28 |
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## Example JSON
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| 29 |
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| 30 |
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```json
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| 31 |
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{
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| 32 |
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"primary": "Kurt Gödel",
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| 33 |
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"contributors": [],
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| 34 |
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"publication": "Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I",
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| 35 |
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"year": "1931",
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| 36 |
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"doi": "https://doi.org/10.1007/BF01700692",
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| 37 |
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"url": "https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems"
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| 38 |
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}
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```
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GENERIC_PROCESSES_TO_UPDATE.md
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|
|
|
|
|
|
|
|
|
|
|
|
|
| 1 |
+
# Generic Processes Needing Real Content
|
| 2 |
+
|
| 3 |
+
These processes use the generic template ("This X process visualization demonstrates... The flowchart shows...") and need to be replaced. **Use different approaches for different process types.**
|
| 4 |
+
|
| 5 |
+
## Strategy by Process Type
|
| 6 |
+
|
| 7 |
+
### 1. Algorithm flowcharts (like Binary Search)
|
| 8 |
+
**Examples:** Binary Search (done), Cryptographic Algorithms, Numerical Methods
|
| 9 |
+
|
| 10 |
+
**Approach:** Process-like flowcharts with:
|
| 11 |
+
- Inputs (sorted array, search key)
|
| 12 |
+
- Steps (initialize interval, compute middle, compare)
|
| 13 |
+
- Decision diamonds (interval empty? key == A[mid]? key < A[mid]?)
|
| 14 |
+
- Outputs (found index, not found)
|
| 15 |
+
- Chart title: **"Algorithm Flowchart"** (do not use "GLMP 6-Color Scheme" in the title)
|
| 16 |
+
|
| 17 |
+
**Reference:** [Binary Search](https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/mathematics-processes-database/processes/discrete_mathematics/discrete_mathematics-binary-search.html) – O(log n) complexity
|
| 18 |
+
|
| 19 |
+
**Candidates:** Add specific algorithms – e.g. RSA, Newton-Raphson, Sieve of Eratosthenes, Dijkstra – each as its own process flowchart.
|
| 20 |
+
|
| 21 |
+
### 2. Axiom-theorem dependency graphs (like Euclid, Peano, Propositional Logic, Aristotle)
|
| 22 |
+
**Examples:** Euclid Book I (done), Peano Arithmetic (done), Propositional Logic (done), Aristotle Syllogistic (done)
|
| 23 |
+
|
| 24 |
+
**Approach:** Real mathematical development:
|
| 25 |
+
- Axioms / definitions at the base
|
| 26 |
+
- Theorems with explicit dependencies (arrows = "depends on")
|
| 27 |
+
- Split into subgraphs for clarity (like Euclid Book I's 5 views)
|
| 28 |
+
|
| 29 |
+
**Reference:** [Euclid Book I](https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/mathematics-processes-database/processes/geometry_topology/geometry_topology-euclid-elements-book-i.html)
|
| 30 |
+
|
| 31 |
+
**Candidates:**
|
| 32 |
+
- **Group Theory** – done (43 nodes, 69 edges across 3 subcharts; Euclid-style layered dependencies)
|
| 33 |
+
- **Ring Theory** – ring axioms → integral domain, polynomial rings
|
| 34 |
+
- **Field Theory** – field axioms → extensions, algebraic closure
|
| 35 |
+
- **Limit / Derivative / Integral** – ε-δ, limit laws, FTC, etc.
|
| 36 |
+
- **Modular Arithmetic** – congruence, Fermat's little theorem, etc.
|
| 37 |
+
- **Topology** – open sets, continuity, compactness
|
| 38 |
+
- **Differential Geometry** – manifold, metric, curvature
|
| 39 |
+
|
| 40 |
+
### 3. Axiomatic combinatorics (like Euclid Book I for counting)
|
| 41 |
+
**Example:** Combinatorics (done)
|
| 42 |
+
|
| 43 |
+
**Approach:** Axiomatic theory of combinatorics – definitions (factorial, sum/product principles) and theorems (permutations, combinations, binomial, pigeonhole, inclusion-exclusion) with dependency graph. Can be expanded to be more comprehensive like Euclid Book I.
|
| 44 |
+
|
| 45 |
+
**Reference:** [Combinatorics](https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/mathematics-processes-database/processes/geometry_topology/geometry_topology-combinatorics.html)
|
| 46 |
+
|
| 47 |
+
---
|
| 48 |
+
|
| 49 |
+
## Updated (with real content)
|
| 50 |
+
- **Combinatorics** – Axiomatic counting theory (14 nodes, 15 edges)
|
| 51 |
+
- **Binary Search** – Algorithm flowchart (already had real content)
|
| 52 |
+
- **Sieve of Eratosthenes** – Prime Number Generation (10 nodes, 14 edges) ✓ Batch 1
|
| 53 |
+
- **Newton-Raphson Method** – Numerical Methods (9 nodes, 11 edges) ✓ Batch 1
|
| 54 |
+
- **Bisection Method** – Limit Calculation (8 nodes, 10 edges) ✓ Batch 2
|
| 55 |
+
- **Extended Euclidean Algorithm** – Modular Arithmetic (6 nodes, 6 edges) ✓ Batch 2
|
| 56 |
+
- **Dijkstra's Algorithm** – Graph Theory Algorithms (7 nodes, 8 edges) ✓ Batch 2
|
| 57 |
+
- **RSA Algorithm** – Cryptographic Algorithms (7 nodes, 7 edges) ✓ Batch 3
|
| 58 |
+
- **Simpson's Rule** – Integral Calculation (6 nodes, 5 edges) ✓ Batch 3
|
| 59 |
+
- **Kruskal's Algorithm** – new (9 nodes, 12 edges) ✓ Batch 3
|
| 60 |
+
- **AES Algorithm** – new (8 nodes, 8 edges) ✓ Batch 4
|
| 61 |
+
- **Merge Sort** – new (7 nodes, 7 edges) ✓ Batch 4
|
| 62 |
+
- **Prim's Algorithm** – new (9 nodes, 12 edges) ✓ Batch 4
|
| 63 |
+
- **Quicksort** – new (6 nodes, 6 edges) ✓ Batch 5
|
| 64 |
+
- **Breadth-First Search** – new (7 nodes, 8 edges) ✓ Batch 5
|
| 65 |
+
- **Binary Search Tree Insert** – new (8 nodes, 9 edges) ✓ Batch 5
|
| 66 |
+
- **Group Theory** – Axiom-theorem dependency graph (21 nodes, 29 edges across 3 subcharts) ✓
|
| 67 |
+
|
| 68 |
+
## Need Updates (by type)
|
| 69 |
+
|
| 70 |
+
### Algorithm flowcharts to create
|
| 71 |
+
- DFS, Heap sort, etc.
|
| 72 |
+
- Graph Theory Algorithms → Dijkstra, Kruskal, etc.
|
| 73 |
+
|
| 74 |
+
### Axiom-theorem graphs to create (placeholders removed)
|
| 75 |
+
- Field Theory, Ring Theory
|
| 76 |
+
- Derivative, Integral, Limit Calculation
|
| 77 |
+
- Modular Arithmetic, Diophantine Equations
|
| 78 |
+
- Topology, Differential Geometry, Euclidean Geometry
|
| 79 |
+
- Logic & Set Theory (or point to Propositional Logic)
|
| 80 |
+
- Statistical Analysis (probability axioms → theorems)
|
| 81 |
+
|
| 82 |
+
### Removed (generic placeholders deleted ✓)
|
| 83 |
+
- Field Theory, Ring Theory, Derivative Calculation, Statistical Analysis, Logic & Set Theory
|
| 84 |
+
- Differential Geometry, Euclidean Geometry, Topology, Diophantine Equations
|
| 85 |
+
- Integral Calculation, Limit Calculation, Modular Arithmetic, Cryptographic Algorithms, Graph Theory Algorithms
|
| 86 |
+
- Run `delete-generic-charts-from-gcs.sh` to remove from GCS; then `upload-mathematics-database-to-gcs.sh` for updated metadata
|
| 87 |
+
|
| 88 |
+
### Duplicates (resolved ✓)
|
| 89 |
+
- statistics_probability-aristotles-syllogism → removed (canonical: discrete_mathematics-aristotle-syllogistic)
|
| 90 |
+
- statistics_probability-euclids-geometry → removed (canonical: geometry_topology-euclid-elements-*)
|
GLMP_Foundation.html
DELETED
|
The diff for this file is too large to render.
See raw diff
|
|
|
Genome Logic Modeling Project (GLMP) - a Hugging Face Space by garywelz.pdf
DELETED
|
@@ -1,3 +0,0 @@
|
|
| 1 |
-
version https://git-lfs.github.com/spec/v1
|
| 2 |
-
oid sha256:44c6ef5adeced82d3bcac86db91b5c7ee1160bcda39cce172b03ae7135b591ec
|
| 3 |
-
size 200940
|
|
|
|
|
|
|
|
|
|
|
|
MATHEMATICAL_DEPENDENCY_GRAPHS_DESIGN.md
ADDED
|
@@ -0,0 +1,321 @@
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|
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|
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|
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|
|
|
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|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
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|
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|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 1 |
+
# Mathematical Dependency Graphs — Design Document
|
| 2 |
+
|
| 3 |
+
## Overview
|
| 4 |
+
|
| 5 |
+
A hybrid architecture for representing and visualizing axiomatic dependency structures across multiple mathematical subjects. Supports both static Mermaid subgraphs and interactive full-graph exploration.
|
| 6 |
+
|
| 7 |
+
---
|
| 8 |
+
|
| 9 |
+
## Scope: Target Subjects
|
| 10 |
+
|
| 11 |
+
| Subject | Foundations | Derived Items | Notes |
|
| 12 |
+
|---------|-------------|---------------|-------|
|
| 13 |
+
| **Euclid's Elements** | Postulates, Common Notions, Definitions | 464 Propositions (13 books) | Geometric constructions |
|
| 14 |
+
| **Peano Arithmetic** | 5 axioms, definitions | Theorems | Successor, induction |
|
| 15 |
+
| **Other number systems** | Axioms (integers, rationals, reals) | Theorems | Construction sequences |
|
| 16 |
+
| **Number theory** | Definitions, lemmas | Theorems | Divisibility, primes |
|
| 17 |
+
| **Algebra** | Group/ring/field axioms | Theorems | Abstract structures |
|
| 18 |
+
| **Contemporary geometry** | Modern axiom systems | Theorems | Metric, affine |
|
| 19 |
+
| **Hilbert's geometry** | 5 groups of axioms (incidence, order, congruence, etc.) | Theorems | *Grundlagen der Geometrie* |
|
| 20 |
+
| **Tarski's geometry** | Betweenness, congruence relations | Theorems | First-order, decidable |
|
| 21 |
+
| **Analysis** | Completeness, continuity axioms | Theorems | Real analysis, limits |
|
| 22 |
+
|
| 23 |
+
---
|
| 24 |
+
|
| 25 |
+
## Core JSON Schema
|
| 26 |
+
|
| 27 |
+
### Discourse (per subject)
|
| 28 |
+
|
| 29 |
+
```json
|
| 30 |
+
{
|
| 31 |
+
"schemaVersion": "1.0",
|
| 32 |
+
"discourse": {
|
| 33 |
+
"id": "euclid-elements",
|
| 34 |
+
"name": "Euclid's Elements",
|
| 35 |
+
"subject": "geometry",
|
| 36 |
+
"variant": "classical",
|
| 37 |
+
"description": "The thirteen books of Euclidean geometry",
|
| 38 |
+
"structure": {
|
| 39 |
+
"books": 13,
|
| 40 |
+
"chapters": "varies",
|
| 41 |
+
"foundationTypes": ["postulate", "commonNotion", "definition"]
|
| 42 |
+
}
|
| 43 |
+
},
|
| 44 |
+
"metadata": {
|
| 45 |
+
"created": "2026-03-15",
|
| 46 |
+
"lastUpdated": "2026-03-15",
|
| 47 |
+
"version": "1.0.0",
|
| 48 |
+
"license": "CC BY 4.0",
|
| 49 |
+
"authors": ["Welz, G."],
|
| 50 |
+
"methodology": "Programming Framework",
|
| 51 |
+
"citation": "Welz, G. (2026). Euclid's Elements Dependency Graph. Programming Framework."
|
| 52 |
+
},
|
| 53 |
+
"sources": [
|
| 54 |
+
{
|
| 55 |
+
"id": "euclid-heath",
|
| 56 |
+
"type": "primary",
|
| 57 |
+
"authors": "Heath, T.L.",
|
| 58 |
+
"title": "The Thirteen Books of Euclid's Elements",
|
| 59 |
+
"year": "1908",
|
| 60 |
+
"edition": "2nd",
|
| 61 |
+
"publisher": "Cambridge University Press",
|
| 62 |
+
"url": "https://archive.org/details/euclidheath00heatiala",
|
| 63 |
+
"notes": "Standard English translation with commentary"
|
| 64 |
+
},
|
| 65 |
+
{
|
| 66 |
+
"id": "perseus",
|
| 67 |
+
"type": "digital",
|
| 68 |
+
"title": "Euclid, Elements",
|
| 69 |
+
"url": "http://www.perseus.tufts.edu/hopper/text?doc=Perseus:text:1999.01.0086",
|
| 70 |
+
"notes": "Perseus Digital Library, Greek text with English"
|
| 71 |
+
}
|
| 72 |
+
],
|
| 73 |
+
"nodes": [
|
| 74 |
+
{
|
| 75 |
+
"id": "P1",
|
| 76 |
+
"type": "postulate",
|
| 77 |
+
"label": "Draw a straight line between two points",
|
| 78 |
+
"shortLabel": "Post. 1",
|
| 79 |
+
"book": 1,
|
| 80 |
+
"number": 1,
|
| 81 |
+
"colorClass": "postulate",
|
| 82 |
+
"sourceRef": "euclid-heath, Book I, Postulate 1",
|
| 83 |
+
"notes": "Also: Postulate 1 in most editions"
|
| 84 |
+
},
|
| 85 |
+
{
|
| 86 |
+
"id": "Prop1",
|
| 87 |
+
"type": "proposition",
|
| 88 |
+
"label": "Construct an equilateral triangle on a given line",
|
| 89 |
+
"shortLabel": "Prop. I.1",
|
| 90 |
+
"book": 1,
|
| 91 |
+
"number": 1,
|
| 92 |
+
"colorClass": "proposition",
|
| 93 |
+
"sourceRef": "euclid-heath, Book I, Proposition 1",
|
| 94 |
+
"notes": "First proposition; depends only on P1, P3"
|
| 95 |
+
}
|
| 96 |
+
],
|
| 97 |
+
"edges": [
|
| 98 |
+
{"from": "P1", "to": "Prop1"},
|
| 99 |
+
{"from": "P3", "to": "Prop1"}
|
| 100 |
+
],
|
| 101 |
+
"colorScheme": {
|
| 102 |
+
"postulate": {"fill": "#e74c3c", "stroke": "#c0392b"},
|
| 103 |
+
"commonNotion": {"fill": "#9b59b6", "stroke": "#8e44ad"},
|
| 104 |
+
"proposition": {"fill": "#1abc9c", "stroke": "#16a085"},
|
| 105 |
+
"definition": {"fill": "#3498db", "stroke": "#2980b9"},
|
| 106 |
+
"theorem": {"fill": "#1abc9c", "stroke": "#16a085"}
|
| 107 |
+
}
|
| 108 |
+
}
|
| 109 |
+
```
|
| 110 |
+
|
| 111 |
+
### Node Types (extensible)
|
| 112 |
+
|
| 113 |
+
| Type | Use Case |
|
| 114 |
+
|------|----------|
|
| 115 |
+
| `axiom` | Peano, Hilbert, Tarski |
|
| 116 |
+
| `postulate` | Euclid |
|
| 117 |
+
| `commonNotion` | Euclid |
|
| 118 |
+
| `definition` | All subjects |
|
| 119 |
+
| `proposition` | Euclid |
|
| 120 |
+
| `theorem` | Most subjects |
|
| 121 |
+
| `lemma` | Supporting results |
|
| 122 |
+
| `corollary` | Direct consequences |
|
| 123 |
+
|
| 124 |
+
### Cross-Discourse Links (future)
|
| 125 |
+
|
| 126 |
+
```json
|
| 127 |
+
{
|
| 128 |
+
"from": "Prop_I_47",
|
| 129 |
+
"to": "peano-theorem-42",
|
| 130 |
+
"discourseFrom": "euclid-elements",
|
| 131 |
+
"discourseTo": "peano-arithmetic",
|
| 132 |
+
"relation": "constructive_correspondence"
|
| 133 |
+
}
|
| 134 |
+
```
|
| 135 |
+
|
| 136 |
+
---
|
| 137 |
+
|
| 138 |
+
## Hybrid Architecture
|
| 139 |
+
|
| 140 |
+
### 1. Canonical JSON (Source of Truth)
|
| 141 |
+
|
| 142 |
+
- One JSON file per discourse: `euclid-elements.json`, `peano-arithmetic.json`, etc.
|
| 143 |
+
- Stored in GCS or repo
|
| 144 |
+
- Human-editable, version-controlled
|
| 145 |
+
- Can be validated against schema
|
| 146 |
+
|
| 147 |
+
### 2. Mermaid Subgraph Generator
|
| 148 |
+
|
| 149 |
+
- **Input:** JSON + filter (e.g., `book=1`, `props=1-15`)
|
| 150 |
+
- **Output:** Mermaid `graph TD` string
|
| 151 |
+
- **Use:** Static HTML pages, PDF export, small-scope viewing
|
| 152 |
+
- **Limit:** ~50–80 nodes per diagram for readability
|
| 153 |
+
|
| 154 |
+
**Filter options:**
|
| 155 |
+
- `book`, `chapter`, `numberRange`
|
| 156 |
+
- `depth`: dependencies only, dependents only, or both
|
| 157 |
+
- `focus`: node ID + N-hop neighborhood
|
| 158 |
+
|
| 159 |
+
### 3. Interactive Viewer
|
| 160 |
+
|
| 161 |
+
- **Input:** Full JSON (or lazy-loaded by book)
|
| 162 |
+
- **Tech:** Cytoscape.js, vis.js, or Sigma.js
|
| 163 |
+
- **Features:**
|
| 164 |
+
- Zoom, pan, minimap
|
| 165 |
+
- Search by ID or label
|
| 166 |
+
- Click node → highlight upstream/downstream
|
| 167 |
+
- Filter by type, book, chapter
|
| 168 |
+
- Cluster by book/chapter
|
| 169 |
+
- Export subgraph as Mermaid
|
| 170 |
+
- **Deployment:** Single HTML + JS, fetches JSON from GCS
|
| 171 |
+
|
| 172 |
+
### 4. Index / Registry
|
| 173 |
+
|
| 174 |
+
```json
|
| 175 |
+
{
|
| 176 |
+
"schemaVersion": "1.0",
|
| 177 |
+
"lastUpdated": "2026-03-15",
|
| 178 |
+
"discourses": [
|
| 179 |
+
{
|
| 180 |
+
"id": "euclid-elements",
|
| 181 |
+
"name": "Euclid's Elements",
|
| 182 |
+
"url": "https://.../euclid-elements.json",
|
| 183 |
+
"nodeCount": 480,
|
| 184 |
+
"edgeCount": 1200,
|
| 185 |
+
"subjects": ["geometry"],
|
| 186 |
+
"keywords": ["Euclid", "Elements", "plane geometry", "constructions"],
|
| 187 |
+
"sources": [
|
| 188 |
+
{"id": "euclid-heath", "authors": "Heath, T.L.", "title": "The Thirteen Books of Euclid's Elements", "year": "1908"}
|
| 189 |
+
],
|
| 190 |
+
"metadata": {"version": "1.0.0", "lastUpdated": "2026-03-15"}
|
| 191 |
+
},
|
| 192 |
+
{
|
| 193 |
+
"id": "peano-arithmetic",
|
| 194 |
+
"name": "Peano Arithmetic",
|
| 195 |
+
"url": "https://.../peano-arithmetic.json",
|
| 196 |
+
"nodeCount": 85,
|
| 197 |
+
"edgeCount": 120,
|
| 198 |
+
"subjects": ["arithmetic", "foundations"],
|
| 199 |
+
"keywords": ["Peano", "axioms", "induction", "successor"],
|
| 200 |
+
"sources": [
|
| 201 |
+
{"id": "peano-1889", "authors": "Peano, G.", "title": "Arithmetices principia", "year": "1889"}
|
| 202 |
+
],
|
| 203 |
+
"metadata": {"version": "1.0.0", "lastUpdated": "2026-03-15"}
|
| 204 |
+
}
|
| 205 |
+
]
|
| 206 |
+
}
|
| 207 |
+
```
|
| 208 |
+
|
| 209 |
+
---
|
| 210 |
+
|
| 211 |
+
## File Structure (Proposed)
|
| 212 |
+
|
| 213 |
+
```
|
| 214 |
+
mathematics-dependency-graphs/
|
| 215 |
+
├── schema/
|
| 216 |
+
│ └── discourse-schema.json # JSON Schema for validation
|
| 217 |
+
├── data/
|
| 218 |
+
│ ├── index.json # Registry of all discourses
|
| 219 |
+
│ ├── euclid-elements.json
|
| 220 |
+
│ ├── peano-arithmetic.json
|
| 221 |
+
│ ├── hilbert-geometry.json
|
| 222 |
+
│ └── tarski-geometry.json
|
| 223 |
+
├── generator/
|
| 224 |
+
│ └── mermaid-from-json.js # Subgraph → Mermaid
|
| 225 |
+
├── viewer/
|
| 226 |
+
│ ├── interactive-viewer.html # Full interactive graph
|
| 227 |
+
│ └── viewer.js
|
| 228 |
+
└── static/ # Pre-generated Mermaid pages
|
| 229 |
+
├── euclid/
|
| 230 |
+
│ ├── book1-props-1-15.html
|
| 231 |
+
│ ├── book1-props-16-30.html
|
| 232 |
+
│ └── ...
|
| 233 |
+
└── peano/
|
| 234 |
+
└── ...
|
| 235 |
+
```
|
| 236 |
+
|
| 237 |
+
---
|
| 238 |
+
|
| 239 |
+
## Integration with Existing Systems
|
| 240 |
+
|
| 241 |
+
- **Mathematics Processes Database (GCS):** Static Mermaid pages can live in `processes/geometry_topology/` or a new `dependency-graphs/` folder
|
| 242 |
+
- **Programming Framework:** Same 5/6-color scheme; extend with subject-specific palettes (e.g., Tarski uses relation types)
|
| 243 |
+
- **GLMP-style collections:** Each discourse is a "collection"; index.json is the catalog
|
| 244 |
+
|
| 245 |
+
---
|
| 246 |
+
|
| 247 |
+
## Implementation Phases
|
| 248 |
+
|
| 249 |
+
| Phase | Deliverable |
|
| 250 |
+
|-------|-------------|
|
| 251 |
+
| **1** | Schema + Euclid Props 1–6 JSON; Mermaid generator script |
|
| 252 |
+
| **2** | Euclid Book I full JSON; static pages for Books I–IV |
|
| 253 |
+
| **3** | Interactive viewer (single discourse) |
|
| 254 |
+
| **4** | Peano Arithmetic, Hilbert Geometry JSON |
|
| 255 |
+
| **5** | Multi-discourse index; cross-discourse navigation |
|
| 256 |
+
| **6** | Tarski, Analysis, other subjects |
|
| 257 |
+
|
| 258 |
+
---
|
| 259 |
+
|
| 260 |
+
## Color Scheme Consistency
|
| 261 |
+
|
| 262 |
+
Use GLMP 6-color for *process* flowcharts (algorithms). For *dependency* graphs, allow subject-specific schemes:
|
| 263 |
+
|
| 264 |
+
- **Euclid:** Postulates (red), Common Notions (purple), Propositions (teal)
|
| 265 |
+
- **Peano:** Axioms (red), Definitions (yellow), Theorems (teal)
|
| 266 |
+
- **Hilbert:** Axiom groups (distinct colors), Theorems (teal)
|
| 267 |
+
- **Tarski:** Primitive relations (red), Defined relations (blue), Theorems (teal)
|
| 268 |
+
|
| 269 |
+
Schema supports `colorScheme` per discourse.
|
| 270 |
+
|
| 271 |
+
---
|
| 272 |
+
|
| 273 |
+
## Metadata & Sources
|
| 274 |
+
|
| 275 |
+
### Discourse-Level Metadata
|
| 276 |
+
|
| 277 |
+
| Field | Purpose |
|
| 278 |
+
|-------|---------|
|
| 279 |
+
| `metadata.created` | ISO date of initial creation |
|
| 280 |
+
| `metadata.lastUpdated` | ISO date of last edit |
|
| 281 |
+
| `metadata.version` | Semantic version (e.g., 1.0.0) |
|
| 282 |
+
| `metadata.license` | License (e.g., CC BY 4.0) |
|
| 283 |
+
| `metadata.authors` | Contributors to the dependency graph |
|
| 284 |
+
| `metadata.methodology` | e.g., Programming Framework |
|
| 285 |
+
| `metadata.citation` | How to cite this graph |
|
| 286 |
+
|
| 287 |
+
### Discourse-Level Sources
|
| 288 |
+
|
| 289 |
+
| Field | Purpose |
|
| 290 |
+
|-------|---------|
|
| 291 |
+
| `sources[].id` | Reference ID for node-level `sourceRef` |
|
| 292 |
+
| `sources[].type` | `primary`, `secondary`, `digital`, `commentary` |
|
| 293 |
+
| `sources[].authors` | Author(s) |
|
| 294 |
+
| `sources[].title` | Title of work |
|
| 295 |
+
| `sources[].year` | Publication year |
|
| 296 |
+
| `sources[].url` | Link to digital copy |
|
| 297 |
+
| `sources[].doi` | DOI if available |
|
| 298 |
+
| `sources[].notes` | Clarifications |
|
| 299 |
+
|
| 300 |
+
### Node-Level Metadata
|
| 301 |
+
|
| 302 |
+
| Field | Purpose |
|
| 303 |
+
|-------|---------|
|
| 304 |
+
| `sourceRef` | Reference to `sources[].id` + location (e.g., "euclid-heath, Book I, Prop 1") |
|
| 305 |
+
| `notes` | Editorial notes, variants, clarifications |
|
| 306 |
+
| `keywords` | Tags for search/filter |
|
| 307 |
+
| `relatedNodes` | IDs of conceptually related nodes (same discourse or cross-discourse) |
|
| 308 |
+
|
| 309 |
+
### Index / Registry Metadata
|
| 310 |
+
|
| 311 |
+
The index should include per-discourse: `sources`, `metadata`, `lastUpdated`, `nodeCount`, `edgeCount`, `subjects`, `keywords`.
|
| 312 |
+
|
| 313 |
+
---
|
| 314 |
+
|
| 315 |
+
## References
|
| 316 |
+
|
| 317 |
+
- Euclid's Elements: [Perseus Digital Library](http://www.perseus.tufts.edu/hopper/text?doc=Perseus:text:1999.01.0086)
|
| 318 |
+
- Heath, T.L. *The Thirteen Books of Euclid's Elements* (1908, 2nd ed.)
|
| 319 |
+
- Hilbert: *Grundlagen der Geometrie* (1899)
|
| 320 |
+
- Tarski: *What is Elementary Geometry?* (1959)
|
| 321 |
+
- Peano: *Arithmetices principia* (1889)
|
MATHEMATICS_DATABASE_EXPANSION_PLAN.md
ADDED
|
@@ -0,0 +1,291 @@
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|
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|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 1 |
+
# Mathematics Database Expansion Plan
|
| 2 |
+
|
| 3 |
+
## Overview
|
| 4 |
+
|
| 5 |
+
Expand the mathematics-database-table and processes to include:
|
| 6 |
+
- **Topic sections**: Complex analysis, complex analytic dynamics, landmark theorems (FLT, Poincaré, Riemann)
|
| 7 |
+
- **Named mathematicians**: Historical and modern figures with associated charts
|
| 8 |
+
- **Formal verification**: Lean proofs and proof assistants
|
| 9 |
+
- **AI mathematics**: Recent AI-assisted results
|
| 10 |
+
- **Overlapping collections**: Processes appear in multiple named sets (topic + mathematician + historical)
|
| 11 |
+
|
| 12 |
+
---
|
| 13 |
+
|
| 14 |
+
## 1. Metadata Schema Extension
|
| 15 |
+
|
| 16 |
+
### Add `namedCollections` Array to Each Process
|
| 17 |
+
|
| 18 |
+
```json
|
| 19 |
+
{
|
| 20 |
+
"id": "number_theory-fermat-last-theorem",
|
| 21 |
+
"name": "Fermat's Last Theorem",
|
| 22 |
+
"subcategory": "number_theory",
|
| 23 |
+
"namedCollections": ["fermat", "landmark_theorems", "wiles", "number_theory_milestones"]
|
| 24 |
+
}
|
| 25 |
+
```
|
| 26 |
+
|
| 27 |
+
**Rationale**: A process can belong to many collections. Examples:
|
| 28 |
+
- *Euclid's Elements* → `["euclid", "geometry_topology", "classical_geometry", "axiomatic_systems"]`
|
| 29 |
+
- *Galois Theory* → `["galois", "abstract_algebra", "field_theory", "landmark_theorems"]`
|
| 30 |
+
- *Sieve of Eratosthenes* → `["eratosthenes", "number_theory", "algorithms", "classical_algorithms"]`
|
| 31 |
+
|
| 32 |
+
### Optional: Add `collections` Index in metadata.json
|
| 33 |
+
|
| 34 |
+
```json
|
| 35 |
+
{
|
| 36 |
+
"collections": {
|
| 37 |
+
"archimedes": { "name": "Archimedes", "description": "…", "processIds": ["…"] },
|
| 38 |
+
"fermat": { "name": "Pierre de Fermat", "description": "…", "processIds": ["…"] }
|
| 39 |
+
}
|
| 40 |
+
}
|
| 41 |
+
```
|
| 42 |
+
|
| 43 |
+
Either derive from processes (scan `namedCollections`) or maintain explicitly.
|
| 44 |
+
|
| 45 |
+
---
|
| 46 |
+
|
| 47 |
+
## 2. New Subcategories
|
| 48 |
+
|
| 49 |
+
| Subcategory ID | Display Name | Notes |
|
| 50 |
+
|-----------------------|------------------------|--------------------------------------------|
|
| 51 |
+
| `complex_analysis` | Complex Analysis | New; analytic functions, residues, etc. |
|
| 52 |
+
| `landmark_theorems` | Landmark Theorems | FLT, Poincaré, Riemann, etc. |
|
| 53 |
+
| `formal_verification` | Formal Verification | Lean, Coq, Isabelle proofs |
|
| 54 |
+
| `ai_mathematics` | AI Mathematics | AlphaProof, AlphaGeometry, etc. |
|
| 55 |
+
|
| 56 |
+
**Existing** (keep): `number_theory`, `geometry_topology`, `discrete_mathematics`, `linear_algebra`, `calculus_analysis`, `abstract_algebra`, `category_theory`, `foundations`, `bioinformatics`.
|
| 57 |
+
|
| 58 |
+
---
|
| 59 |
+
|
| 60 |
+
## 3. Topic Sections (New Charts)
|
| 61 |
+
|
| 62 |
+
### 3.1 Complex Analysis
|
| 63 |
+
- **Complex Analysis — Analytic Functions & Cauchy-Riemann**
|
| 64 |
+
- **Complex Analysis — Cauchy Integral Theorem & Residues**
|
| 65 |
+
- **Complex Analysis — Conformal Mappings & Riemann Surfaces**
|
| 66 |
+
- **Complex Analysis — Entire Functions & Picard Theorems**
|
| 67 |
+
|
| 68 |
+
*Collections*: `complex_analysis`, `calculus_analysis` (overlap)
|
| 69 |
+
|
| 70 |
+
### 3.2 Complex Analytic Dynamics (extend existing)
|
| 71 |
+
- Already have: Julia/Fatou, Sullivan, Hubbard-Douady, Devaney, etc.
|
| 72 |
+
- Add: **Complex Dynamics — Holomorphic Dynamics Overview** (hub/overview)
|
| 73 |
+
- Add: **Complex Dynamics — Parabolic Fixed Points & Écalle-Voronin**
|
| 74 |
+
|
| 75 |
+
*Collections*: `complex_dynamics`, `calculus_analysis`, `sullivan`, `hubbard_douady`, `devaney`
|
| 76 |
+
|
| 77 |
+
### 3.3 Landmark Theorems
|
| 78 |
+
| Chart | Subcategory | Named Collections |
|
| 79 |
+
|------------------------------|--------------------|-------------------------------------|
|
| 80 |
+
| Fermat's Last Theorem | `landmark_theorems`| `fermat`, `wiles`, `number_theory` |
|
| 81 |
+
| Poincaré Conjecture | `landmark_theorems`| `poincare`, `perelman`, `topology` |
|
| 82 |
+
| Riemann Hypothesis | `landmark_theorems`| `riemann`, `number_theory`, `analysis` |
|
| 83 |
+
| Four Color Theorem | `landmark_theorems`| `appel_haken`, `graph_theory` |
|
| 84 |
+
| Gödel Incompleteness | (existing) | `godel`, `foundations` |
|
| 85 |
+
|
| 86 |
+
---
|
| 87 |
+
|
| 88 |
+
## 4. Named Mathematicians — Charts to Create
|
| 89 |
+
|
| 90 |
+
### 4.1 Classical (Ancient & Early Modern)
|
| 91 |
+
| Mathematician | Charts to Create | Overlaps With |
|
| 92 |
+
|----------------|--------------------------------------------------------|----------------------------|
|
| 93 |
+
| **Archimedes** | Archimedes' Principle, Method of Exhaustion, Pi bounds | `geometry_topology`, `calculus` |
|
| 94 |
+
| **Eratosthenes** | Sieve (existing), Earth circumference, Prime counting | `number_theory`, `algorithms` |
|
| 95 |
+
| **Pythagoras** | Pythagorean Theorem, Pythagorean triples, Irrationals | `geometry_topology`, `number_theory` |
|
| 96 |
+
| **Euclid** | Elements (existing), Euclidean algorithm | `geometry_topology` |
|
| 97 |
+
|
| 98 |
+
### 4.2 Early Modern
|
| 99 |
+
| Mathematician | Charts to Create | Overlaps With |
|
| 100 |
+
|---------------|--------------------------------------------------------|----------------------|
|
| 101 |
+
| **Fermat** | Fermat's Last Theorem, Fermat's Little Theorem, Fermat primes | `number_theory`, `landmark_theorems` |
|
| 102 |
+
| **Euler** | Euler's formula (e^(iπ)+1=0), Euler characteristic, Seven Bridges | `calculus_analysis`, `graph_theory`, `topology` |
|
| 103 |
+
| **Gauss** | Fundamental Theorem of Algebra, Gaussian integers, Least squares | `number_theory`, `linear_algebra`, `calculus` |
|
| 104 |
+
|
| 105 |
+
### 4.3 19th–20th Century
|
| 106 |
+
| Mathematician | Charts to Create | Overlaps With |
|
| 107 |
+
|-------------------|--------------------------------------------------------|----------------------|
|
| 108 |
+
| **Galois** | Galois Theory (existing), Solvability by radicals | `abstract_algebra`, `field_theory` |
|
| 109 |
+
| **Cayley** | Cayley's theorem (groups), Cayley-Hamilton theorem | `abstract_algebra`, `linear_algebra` |
|
| 110 |
+
| **Hamilton** | Quaternions, Hamiltonian mechanics, Cayley-Hamilton | `linear_algebra`, `physics` |
|
| 111 |
+
| **Noether** | Noether's theorems, Noetherian rings, Abstract algebra | `abstract_algebra`, `physics` |
|
| 112 |
+
| **Hilbert** | Hilbert's problems, Hilbert space, Basis theorem | `foundations`, `linear_algebra`, `analysis` |
|
| 113 |
+
| **Riemann** | Riemann Hypothesis, Riemann surfaces, Riemann integral | `number_theory`, `calculus_analysis`, `complex_analysis` |
|
| 114 |
+
|
| 115 |
+
### 4.4 Modern (20th–21st Century)
|
| 116 |
+
| Mathematician | Charts to Create | Overlaps With |
|
| 117 |
+
|--------------|--------------------------------------------------------|----------------------|
|
| 118 |
+
| **Thurston** | Geometrization conjecture, Hyperbolic 3-manifolds | `geometry_topology`, `poincare` |
|
| 119 |
+
| **Milnor** | Exotic spheres, Milnor's theorem, Morse theory | `geometry_topology`, `differential_topology` |
|
| 120 |
+
| **Faltings** | Mordell conjecture, Faltings' theorem (FLT for n>4) | `number_theory`, `fermat`, `algebraic_geometry` |
|
| 121 |
+
| **Atiyah** | Atiyah-Singer index theorem, K-theory | `geometry_topology`, `analysis` |
|
| 122 |
+
| **Perelman** | Ricci flow, Poincaré proof | `landmark_theorems`, `poincare` |
|
| 123 |
+
| **Wiles** | Modularity theorem, FLT proof | `landmark_theorems`, `fermat` |
|
| 124 |
+
|
| 125 |
+
### 4.5 Additional Candidates (for later)
|
| 126 |
+
- **Gödel** (existing via Peano)
|
| 127 |
+
- **Turing** (computability, halting problem)
|
| 128 |
+
- **Kolmogorov** (probability, complexity)
|
| 129 |
+
- **Grothendieck** (schemes, topos theory)
|
| 130 |
+
- **Serre** (algebraic geometry, number theory)
|
| 131 |
+
- **Deligne** (Weil conjectures)
|
| 132 |
+
- **Tao** (existing: Green-Tao)
|
| 133 |
+
- **Szemerédi** (existing)
|
| 134 |
+
- **Sullivan** (existing)
|
| 135 |
+
- **Hubbard, Douady, Devaney** (existing)
|
| 136 |
+
|
| 137 |
+
---
|
| 138 |
+
|
| 139 |
+
## 5. Formal Verification (Lean Proofs)
|
| 140 |
+
|
| 141 |
+
### 5.1 New Subcategory: `formal_verification`
|
| 142 |
+
|
| 143 |
+
| Chart | Description |
|
| 144 |
+
|-----------------------------------|--------------------------------------------------|
|
| 145 |
+
| Lean 4 — Proof Assistant Overview | What Lean is, tactic language, type theory |
|
| 146 |
+
| Mathlib — Library Structure | Mathlib dependency graph, key namespaces |
|
| 147 |
+
| Fermat's Last Theorem in Lean | FLT statement and proof status in Lean |
|
| 148 |
+
| Kepler Conjecture (Flyspeck) | Hales' proof, formalization in HOL Light |
|
| 149 |
+
| Four Color Theorem in Coq | Gonthier's formalization |
|
| 150 |
+
| Odd Order Theorem (Feit-Thompson)| Gonthier et al. formalization |
|
| 151 |
+
|
| 152 |
+
*Collections*: `lean`, `formal_verification`, `landmark_theorems` (where applicable)
|
| 153 |
+
|
| 154 |
+
---
|
| 155 |
+
|
| 156 |
+
## 6. AI Mathematics
|
| 157 |
+
|
| 158 |
+
### 6.1 New Subcategory: `ai_mathematics`
|
| 159 |
+
|
| 160 |
+
| Chart | Description |
|
| 161 |
+
|----------------------------------------|--------------------------------------------------|
|
| 162 |
+
| AlphaProof (DeepMind 2024) | IMO results, statement proving |
|
| 163 |
+
| AlphaGeometry (DeepMind 2024) | Synthetic geometry, IMO-style problems |
|
| 164 |
+
| AI-Assisted Proof Discovery | Overview: GPT, Lean, collaboration |
|
| 165 |
+
| Ramanujan Machine / Conjecture Generation | Automated conjecture generation |
|
| 166 |
+
| Formalization Gaps (AI + Human) | What remains to be formalized |
|
| 167 |
+
|
| 168 |
+
*Collections*: `ai_mathematics`, `formal_verification` (overlap)
|
| 169 |
+
|
| 170 |
+
---
|
| 171 |
+
|
| 172 |
+
## 7. Table Structure — Section Headers & Breaks
|
| 173 |
+
|
| 174 |
+
### 7.1 Proposed Table Sections (with breaks)
|
| 175 |
+
|
| 176 |
+
1. **Algorithms — Flowcharts** (existing)
|
| 177 |
+
2. **Axiomatic Theories — Dependency Graphs** (existing)
|
| 178 |
+
3. **Landmark Theorems** (new section)
|
| 179 |
+
4. **Complex Analysis & Dynamics** (new or merged into Calculus & Analysis)
|
| 180 |
+
5. **Formal Verification (Lean, Coq, etc.)** (new)
|
| 181 |
+
6. **AI Mathematics** (new)
|
| 182 |
+
|
| 183 |
+
### 7.2 Named Collections Panel (expand)
|
| 184 |
+
|
| 185 |
+
Current: Euclid, Tao, Peano, Gödel, Sullivan, Hubbard & Douady, Devaney, Smale, Bioinformatics
|
| 186 |
+
|
| 187 |
+
**Add**:
|
| 188 |
+
- Archimedes, Eratosthenes, Pythagoras
|
| 189 |
+
- Fermat, Euler, Gauss
|
| 190 |
+
- Galois, Cayley, Hamilton, Noether, Hilbert
|
| 191 |
+
- Riemann, Thurston, Milnor, Faltings, Atiyah
|
| 192 |
+
- Wiles, Perelman
|
| 193 |
+
- Lean / Formal Verification
|
| 194 |
+
- AI Mathematics
|
| 195 |
+
|
| 196 |
+
**Implementation**: Either (a) one link per collection → landing page listing all processes in that collection, or (b) first/representative process. Prefer (a) for multi-process collections.
|
| 197 |
+
|
| 198 |
+
---
|
| 199 |
+
|
| 200 |
+
## 8. Overlap Handling
|
| 201 |
+
|
| 202 |
+
### 8.1 Process in Multiple Collections
|
| 203 |
+
|
| 204 |
+
Example: **Fermat's Last Theorem**
|
| 205 |
+
- `subcategory`: `landmark_theorems`
|
| 206 |
+
- `namedCollections`: `["fermat", "wiles", "number_theory", "landmark_theorems"]`
|
| 207 |
+
|
| 208 |
+
Appears in:
|
| 209 |
+
- Landmark Theorems table section
|
| 210 |
+
- Fermat collection page
|
| 211 |
+
- Wiles collection page
|
| 212 |
+
- Number Theory subcategory filter
|
| 213 |
+
|
| 214 |
+
### 8.2 Collection Landing Pages
|
| 215 |
+
|
| 216 |
+
Create `processes/collections/` (or similar):
|
| 217 |
+
- `collections/fermat.html` — lists all processes with `namedCollections` containing `fermat`
|
| 218 |
+
- `collections/euler.html`
|
| 219 |
+
- `collections/landmark_theorems.html`
|
| 220 |
+
- etc.
|
| 221 |
+
|
| 222 |
+
These can be generated from metadata or static HTML with links derived from metadata.
|
| 223 |
+
|
| 224 |
+
### 8.3 Table Filtering (Optional)
|
| 225 |
+
|
| 226 |
+
Add filter dropdown: "Show by collection: All | Fermat | Euler | Landmark Theorems | …"
|
| 227 |
+
|
| 228 |
+
---
|
| 229 |
+
|
| 230 |
+
## 9. Implementation Phases
|
| 231 |
+
|
| 232 |
+
### Phase 1: Schema & Infrastructure
|
| 233 |
+
- Add `namedCollections` to metadata schema
|
| 234 |
+
- Add new subcategories to metadata
|
| 235 |
+
- Create collection landing page template
|
| 236 |
+
- Update table to support new sections and breaks
|
| 237 |
+
|
| 238 |
+
### Phase 2: Landmark Theorems
|
| 239 |
+
- Fermat's Last Theorem
|
| 240 |
+
- Poincaré Conjecture
|
| 241 |
+
- Riemann Hypothesis
|
| 242 |
+
- (Optional) Four Color, Gödel as landmark)
|
| 243 |
+
|
| 244 |
+
### Phase 3: Complex Analysis
|
| 245 |
+
- 3–4 complex analysis charts
|
| 246 |
+
- Ensure overlap with existing complex dynamics
|
| 247 |
+
|
| 248 |
+
### Phase 4: Named Mathematicians (Batch 1)
|
| 249 |
+
- Archimedes, Eratosthenes, Pythagoras
|
| 250 |
+
- Fermat, Euler, Gauss
|
| 251 |
+
- Tag existing processes (Euclid, Sieve, etc.) with `namedCollections`
|
| 252 |
+
|
| 253 |
+
### Phase 5: Named Mathematicians (Batch 2)
|
| 254 |
+
- Galois, Cayley, Hamilton, Noether, Hilbert
|
| 255 |
+
- Riemann, Thurston, Milnor, Faltings, Atiyah
|
| 256 |
+
- Wiles, Perelman
|
| 257 |
+
|
| 258 |
+
### Phase 6: Formal Verification
|
| 259 |
+
- Lean overview
|
| 260 |
+
- 2–3 key formalized results (FLT, Four Color, etc.)
|
| 261 |
+
|
| 262 |
+
### Phase 7: AI Mathematics
|
| 263 |
+
- AlphaProof, AlphaGeometry
|
| 264 |
+
- AI-assisted proof overview
|
| 265 |
+
|
| 266 |
+
---
|
| 267 |
+
|
| 268 |
+
## 10. File Naming Conventions
|
| 269 |
+
|
| 270 |
+
- `number_theory-fermat-last-theorem.html`
|
| 271 |
+
- `landmark_theorems-poincare-conjecture.html`
|
| 272 |
+
- `landmark_theorems-riemann-hypothesis.html`
|
| 273 |
+
- `complex_analysis-cauchy-integral-theorem.html`
|
| 274 |
+
- `formal_verification-lean-flt.html`
|
| 275 |
+
- `ai_mathematics-alphaproof.html`
|
| 276 |
+
- `collections/fermat.html` (collection index)
|
| 277 |
+
|
| 278 |
+
---
|
| 279 |
+
|
| 280 |
+
## 11. Summary: New Content Counts (Estimate)
|
| 281 |
+
|
| 282 |
+
| Category | New Charts (approx) |
|
| 283 |
+
|-----------------------|---------------------|
|
| 284 |
+
| Complex Analysis | 4 |
|
| 285 |
+
| Landmark Theorems | 3–5 |
|
| 286 |
+
| Named Mathematicians | 15–25 (many overlap)|
|
| 287 |
+
| Formal Verification | 4–6 |
|
| 288 |
+
| AI Mathematics | 3–5 |
|
| 289 |
+
| **Total new** | **~30–45** |
|
| 290 |
+
|
| 291 |
+
Many of these overlap (e.g., Fermat chart counts for Fermat, Wiles, Landmark Theorems, Number Theory). The `namedCollections` array is the key to supporting this overlap cleanly.
|
NEXT_PASS_CHECKLIST.md
ADDED
|
@@ -0,0 +1,182 @@
|
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|
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|
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|
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|
|
|
|
|
|
| 1 |
+
# Mathematics Database — Next Pass Checklist
|
| 2 |
+
|
| 3 |
+
A prioritized checklist for the next major revision: Cite links, Frontier sections, and uniform color scheme.
|
| 4 |
+
|
| 5 |
+
---
|
| 6 |
+
|
| 7 |
+
## Phase 0: Database Table Page (Intro & Start Here) — DONE ✓
|
| 8 |
+
|
| 9 |
+
- [x] Concise introduction at top (conceptual-framing)
|
| 10 |
+
- [x] Move search box into "Start Here" section
|
| 11 |
+
- [x] Remove "Named Collections" (avoids who-is-named complaints)
|
| 12 |
+
- [x] Start Here: search field + link to Whole of Mathematics
|
| 13 |
+
- [x] Describe Whole of Mathematics as "Interactive UI" in link text
|
| 14 |
+
|
| 15 |
+
---
|
| 16 |
+
|
| 17 |
+
## Reference: 5/6-Color Scheme (GLMP)
|
| 18 |
+
|
| 19 |
+
Use this palette across all charts for consistency:
|
| 20 |
+
|
| 21 |
+
| Role | Hex | Semantic |
|
| 22 |
+
|------|-----|----------|
|
| 23 |
+
| Red | `#ff6b6b` | Triggers, inputs, postulates |
|
| 24 |
+
| Yellow | `#ffd43b` | Structures, objects |
|
| 25 |
+
| Green | `#51cf66` | Processing, operations, propositions |
|
| 26 |
+
| Light blue | `#74c0fc` | Intermediates, states |
|
| 27 |
+
| Violet | `#b197fc` | Products, outputs |
|
| 28 |
+
| Lavender | `#e6e6fa` | Decision diamonds (algorithms only) |
|
| 29 |
+
|
| 30 |
+
**Axiomatic/dependency chart mapping:**
|
| 31 |
+
| Node type | Hex | Role |
|
| 32 |
+
|--------------|------------|--------------------------|
|
| 33 |
+
| Axiom | `#ff6b6b` | Red — inputs, postulates |
|
| 34 |
+
| Postulate | `#ff6b6b` | Red — same as axiom |
|
| 35 |
+
| CommonNotion | `#ffd43b` | Yellow — structures |
|
| 36 |
+
| Definition | `#b197fc` | Violet — products |
|
| 37 |
+
| Lemma | `#74c0fc` | Light blue — intermediates|
|
| 38 |
+
| Theorem | `#51cf66` | Green — propositions |
|
| 39 |
+
| Corollary | `#1abc9c` | Teal |
|
| 40 |
+
| Proposition | `#51cf66` | Green — same as theorem |
|
| 41 |
+
| Reference | `#bdc3c7` | Gray |
|
| 42 |
+
|
| 43 |
+
---
|
| 44 |
+
|
| 45 |
+
## Phase 1: Cite Links
|
| 46 |
+
|
| 47 |
+
Add attribution (Cite badge + popover) to charts with identifiable primary sources.
|
| 48 |
+
|
| 49 |
+
### Already have Cite (7)
|
| 50 |
+
- [x] Gödel First Incompleteness
|
| 51 |
+
- [x] Schemes & Sheaves (Grothendieck)
|
| 52 |
+
- [x] Group Representations
|
| 53 |
+
- [x] Riemannian Geometry
|
| 54 |
+
- [x] ZFC Axioms
|
| 55 |
+
- [x] Shannon Entropy
|
| 56 |
+
- [x] C*-Algebras
|
| 57 |
+
|
| 58 |
+
### High priority (add Cite)
|
| 59 |
+
- [ ] Euclid's Elements charts
|
| 60 |
+
- [ ] Peano Arithmetic (Landau, Kirby–Paris)
|
| 61 |
+
- [ ] Szemerédi Theorem
|
| 62 |
+
- [ ] Green–Tao Theorem
|
| 63 |
+
- [ ] Galois Theory (Field Theory charts)
|
| 64 |
+
- [ ] Cauchy / Complex Analysis charts
|
| 65 |
+
- [ ] Sullivan collection charts
|
| 66 |
+
- [ ] Hubbard–Douady collection
|
| 67 |
+
- [ ] Devaney collection
|
| 68 |
+
- [ ] Kolmogorov axioms, Bayes, CLT (Statistics)
|
| 69 |
+
- [ ] NIST DADS algorithms (Binary Search, etc.)
|
| 70 |
+
|
| 71 |
+
### Medium priority
|
| 72 |
+
- [ ] PDE charts (Laplace, Heat, Wave)
|
| 73 |
+
- [ ] Functional analysis (Banach, Hilbert)
|
| 74 |
+
- [ ] Spectral theory charts
|
| 75 |
+
- [ ] Representation theory (remaining)
|
| 76 |
+
- [ ] Commutative algebra charts
|
| 77 |
+
|
| 78 |
+
### Schema
|
| 79 |
+
See `ATTRIBUTION_SCHEMA.md`. Fields: `primary`, `contributors`, `publication`, `year`, `doi`, `url`.
|
| 80 |
+
|
| 81 |
+
---
|
| 82 |
+
|
| 83 |
+
## Phase 2: Frontier of Research Links
|
| 84 |
+
|
| 85 |
+
Add or expand "Recent & Frontier" sections on index pages. Each section: proved results, open conjectures, links to charts, links to arXiv/external.
|
| 86 |
+
|
| 87 |
+
### Already have Recent & Frontier (3)
|
| 88 |
+
- [x] Number Theory
|
| 89 |
+
- [x] Algebraic Geometry
|
| 90 |
+
- [x] Representation Theory
|
| 91 |
+
|
| 92 |
+
### Add Frontier section
|
| 93 |
+
- [x] Differential Geometry
|
| 94 |
+
- [x] Complex Analysis
|
| 95 |
+
- [x] Statistics & Probability
|
| 96 |
+
- [x] Partial Differential Equations
|
| 97 |
+
- [x] Foundations (set theory, logic)
|
| 98 |
+
- [x] Calculus / Real Analysis
|
| 99 |
+
- [x] Functional Analysis
|
| 100 |
+
- [x] Topology (geometry_topology index)
|
| 101 |
+
- [x] Operator Algebras
|
| 102 |
+
- [x] K-Theory
|
| 103 |
+
|
| 104 |
+
### Template
|
| 105 |
+
Use the pattern from `algebraic_geometry.html`: `.frontier-item.proved` (green border), `.frontier-item.conjecture` (orange border), with `.name`, `.meta`, and chart/external links.
|
| 106 |
+
|
| 107 |
+
---
|
| 108 |
+
|
| 109 |
+
## Phase 3: Uniform Color Scheme
|
| 110 |
+
|
| 111 |
+
Apply the 5/6-color palette to all charts. Replace per-subcategory accent colors with the standard palette.
|
| 112 |
+
|
| 113 |
+
### Algorithm flowcharts (already mostly correct)
|
| 114 |
+
- [x] Sieve, Extended Euclidean, Dijkstra, Prim, Kruskal, BFS
|
| 115 |
+
- [x] Binary Search, RSA, AES, Merge Sort, Quicksort, BST
|
| 116 |
+
- [x] Bisection, Simpson's Rule
|
| 117 |
+
- [x] Bioinformatics (BLAST, sequence alignment)
|
| 118 |
+
- [x] Verify any outliers use standard colors
|
| 119 |
+
|
| 120 |
+
### Axiomatic / dependency charts
|
| 121 |
+
- [x] Gödel / Peano charts — map Def/Lem/Thm/Cor to palette
|
| 122 |
+
- [x] Euclid's Elements — align postulate/common notion/proposition colors
|
| 123 |
+
- [x] ZFC / Foundations
|
| 124 |
+
- [x] Abstract algebra, algebraic geometry, representation theory, differential geometry, spectral theory, symplectic, metric geometry
|
| 125 |
+
|
| 126 |
+
### P3 charts (operator algebras, K-theory, quantum algebra, optimization, information theory, mathematical physics)
|
| 127 |
+
- [x] Replace subcategory-specific header/node colors with 5-color palette
|
| 128 |
+
- [x] Header: database orange #e67e22
|
| 129 |
+
- [x] Mermaid nodes: Def → Violet, Thm → Green
|
| 130 |
+
|
| 131 |
+
### Header / nav consistency
|
| 132 |
+
- [x] Standardize header to database orange #e67e22
|
| 133 |
+
- [x] Nav link colors: #e67e22
|
| 134 |
+
|
| 135 |
+
---
|
| 136 |
+
|
| 137 |
+
## Phase 4: Optional Enhancements (if time)
|
| 138 |
+
|
| 139 |
+
### Content
|
| 140 |
+
- [x] Landmark theorem charts: FLT, Riemann Hypothesis (high-level)
|
| 141 |
+
- [x] Modular arithmetic: CRT (Chinese Remainder Theorem)
|
| 142 |
+
- [ ] Primality tests (future)
|
| 143 |
+
- [ ] `namedCollections` metadata for cross-linking (Euclid, Gödel, Galois, etc.)
|
| 144 |
+
|
| 145 |
+
### Infrastructure
|
| 146 |
+
- [x] Formal verification links (Lean, Coq)
|
| 147 |
+
- [x] AI mathematics (AlphaProof, AlphaGeometry)
|
| 148 |
+
- [x] math.HO (History & Overview) — added to Number Theory, Foundations
|
| 149 |
+
|
| 150 |
+
---
|
| 151 |
+
|
| 152 |
+
## Execution Order
|
| 153 |
+
|
| 154 |
+
1. **Phase 3 (Color)** — Do first; it's a bulk replace across many files. Establishes visual consistency before adding content.
|
| 155 |
+
2. **Phase 1 (Cite)** — Add attribution to charts that have clear sources. Can be done incrementally.
|
| 156 |
+
3. **Phase 2 (Frontier)** — Add Recent & Frontier sections to remaining index pages. Lower effort, high value.
|
| 157 |
+
4. **Phase 4** — As capacity allows.
|
| 158 |
+
|
| 159 |
+
---
|
| 160 |
+
|
| 161 |
+
## Files to Modify
|
| 162 |
+
|
| 163 |
+
### Color scheme
|
| 164 |
+
- All `processes/**/*.html` with Mermaid `classDef` blocks
|
| 165 |
+
- Generator templates: `generate_p3_charts.py` (P3 charts)
|
| 166 |
+
- Possibly: shared CSS or build step for future automation
|
| 167 |
+
|
| 168 |
+
### Cite
|
| 169 |
+
- Add attribution HTML + CSS to each chart; or extend generator/template for batch charts
|
| 170 |
+
- Update `ATTRIBUTION_SCHEMA.md` if schema changes
|
| 171 |
+
|
| 172 |
+
### Frontier
|
| 173 |
+
- Index pages: `processes/<subcategory>/<subcategory>.html` (e.g. `processes/differential_geometry/differential_geometry.html`)
|
| 174 |
+
|
| 175 |
+
---
|
| 176 |
+
|
| 177 |
+
## Completion Criteria
|
| 178 |
+
|
| 179 |
+
- [ ] All charts with identifiable sources have Cite badge
|
| 180 |
+
- [ ] All major index pages have Recent & Frontier section
|
| 181 |
+
- [ ] All charts use the 5/6-color palette (no stray per-chart accent colors in node fills)
|
| 182 |
+
- [ ] Header/nav colors are consistent (or explicitly documented as domain accents)
|
NEXT_STEPS_PLAN.md
ADDED
|
@@ -0,0 +1,161 @@
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 1 |
+
# Mathematics Database — Next Steps Plan
|
| 2 |
+
|
| 3 |
+
Three initiatives: **Search** (near-term), **Comprehensive Collection** (mid-term), and **Research Frontier** (long-term).
|
| 4 |
+
|
| 5 |
+
---
|
| 6 |
+
|
| 7 |
+
## 1. Search the Collection
|
| 8 |
+
|
| 9 |
+
**Goal**: Place a search bar near the top of the table page. Users can search by theorem name, mathematician name, subcategory, or keyword and get links to individual charts or collection pages.
|
| 10 |
+
|
| 11 |
+
### 1.1 Search UI Placement
|
| 12 |
+
- Add a search box immediately after the header (before or alongside "Start Here")
|
| 13 |
+
- Design: Single input, optional filters (All / Algorithms / Axiomatic / Collection)
|
| 14 |
+
- Live/filter-as-you-type or "Search" button — both viable
|
| 15 |
+
|
| 16 |
+
### 1.2 Search Data Source
|
| 17 |
+
- **Client-side**: Load `metadata.json` (already fetched for the table); search in memory
|
| 18 |
+
- **Indexable fields** (extend metadata if needed):
|
| 19 |
+
- `name` (process title) — e.g. "Fermat's Last Theorem", "Sieve of Eratosthenes"
|
| 20 |
+
- `subcategory` / `subcategory_name` — e.g. "Number Theory", "Calculus & Analysis"
|
| 21 |
+
- `namedCollections` (when added) — e.g. "euclid", "fermat", "sullivan"
|
| 22 |
+
- Optional: add `keywords` or `searchTerms` array for aliases ("FLT", "Poincaré", "ZFC")
|
| 23 |
+
|
| 24 |
+
### 1.3 Search Algorithm
|
| 25 |
+
- **Simple**: Case-insensitive substring match on `name`, `subcategory_name`
|
| 26 |
+
- **Better**: Tokenize query, match against name + subcategory + collections
|
| 27 |
+
- **Fuzzy** (optional): Use a small library (e.g. Fuse.js) for typo tolerance
|
| 28 |
+
|
| 29 |
+
### 1.4 Results Display
|
| 30 |
+
- **Single process match** → link directly to process page
|
| 31 |
+
- **Collection match** (e.g. "Euclid") → link to collection landing page (or list of processes in that collection)
|
| 32 |
+
- **Multiple matches** → show dropdown or results panel with:
|
| 33 |
+
- Process name + subcategory
|
| 34 |
+
- Link to process page
|
| 35 |
+
- "Part of: Euclid, Geometry & Topology" (when namedCollections exists)
|
| 36 |
+
|
| 37 |
+
### 1.5 Metadata Enhancements for Search
|
| 38 |
+
- Add `namedCollections` to processes (per expansion plan)
|
| 39 |
+
- Optional: `keywords: ["FLT", "Fermat", "Wiles"]` for common aliases
|
| 40 |
+
- Optional: `theorems: ["Modularity Theorem", "Fermat's Last Theorem"]` for axiomatic theories
|
| 41 |
+
|
| 42 |
+
### 1.6 Implementation Scope
|
| 43 |
+
| Task | Effort |
|
| 44 |
+
|------|--------|
|
| 45 |
+
| Add search input + results dropdown | Small |
|
| 46 |
+
| Client-side search over `metadata.json` | Small |
|
| 47 |
+
| Add `namedCollections` to metadata (partial) | Medium |
|
| 48 |
+
| Collection landing pages for multi-result | Medium |
|
| 49 |
+
|
| 50 |
+
---
|
| 51 |
+
|
| 52 |
+
## 2. Plan to Fill Out the Collection (Comprehensive)
|
| 53 |
+
|
| 54 |
+
Build on [MATHEMATICS_DATABASE_EXPANSION_PLAN.md](./MATHEMATICS_DATABASE_EXPANSION_PLAN.md). Aim for a representative, well-structured set across major areas.
|
| 55 |
+
|
| 56 |
+
### 2.1 Coverage Goals by Domain
|
| 57 |
+
|
| 58 |
+
| Domain | Current | Target | Priority Additions |
|
| 59 |
+
|--------|---------|--------|-------------------|
|
| 60 |
+
| **Algebra** | Strong | Maintain + expand | Cayley-Hamilton, Noether, Representation theory |
|
| 61 |
+
| **Analysis** | Good | Expand | Complex analysis (4 charts), Functional analysis basics |
|
| 62 |
+
| **Geometry & Topology** | Good | Expand | Milnor exotic spheres, Thurston geometrization |
|
| 63 |
+
| **Number Theory** | Good | Expand | Landmark theorems (FLT, Riemann), Fermat's Little Theorem |
|
| 64 |
+
| **Discrete & Logic** | Strong | Maintain | Add combinatorics algorithms (inclusion-exclusion, generating functions) |
|
| 65 |
+
| **Applied** | Bioinformatics only | Expand | Statistics/probability, optimization basics |
|
| 66 |
+
|
| 67 |
+
### 2.2 Landmark Theorems (High Impact)
|
| 68 |
+
- Fermat's Last Theorem (Wiles, modularity)
|
| 69 |
+
- Poincaré Conjecture (Perelman, Ricci flow)
|
| 70 |
+
- Riemann Hypothesis (statement, equivalent forms)
|
| 71 |
+
- Four Color Theorem (Appel–Haken, formalization)
|
| 72 |
+
- Gödel Incompleteness (already present via Peano)
|
| 73 |
+
|
| 74 |
+
### 2.3 Gaps to Fill
|
| 75 |
+
- **Complex Analysis**: Cauchy, residues, conformal maps
|
| 76 |
+
- **Statistics & Probability**: Kolmogorov axioms, Central Limit Theorem, Bayes
|
| 77 |
+
- **Numerical Methods**: More algorithms (Newton, Euler methods, quadrature)
|
| 78 |
+
- **Representation Theory**: Basics (groups, characters)
|
| 79 |
+
- **Differential Geometry**: Curves, surfaces, Riemannian basics
|
| 80 |
+
|
| 81 |
+
### 2.4 Phased Rollout (from expansion plan, refined)
|
| 82 |
+
|
| 83 |
+
| Phase | Focus | Charts (approx) |
|
| 84 |
+
|-------|-------|-----------------|
|
| 85 |
+
| **1** | Schema + search + `namedCollections` | 0 new charts |
|
| 86 |
+
| **2** | Landmark theorems (FLT, Poincaré, Riemann) | 3–5 |
|
| 87 |
+
| **3** | Complex analysis | 4 |
|
| 88 |
+
| **4** | Named mathematicians (batch 1: Fermat, Euler, Gauss, Euclid tag) | 5–8 |
|
| 89 |
+
| **5** | Named mathematicians (batch 2: Galois, Noether, Hilbert, Riemann) | 5–8 |
|
| 90 |
+
| **6** | Statistics & probability | 3–5 |
|
| 91 |
+
| **7** | Formal verification (Lean, Four Color in Coq) | 3–4 |
|
| 92 |
+
| **8** | AI mathematics (AlphaProof, AlphaGeometry) | 2–3 |
|
| 93 |
+
|
| 94 |
+
### 2.5 Definition of "Fairly Comprehensive"
|
| 95 |
+
- All 6 domains have ≥5 distinct charts
|
| 96 |
+
- Every subcategory has at least 1 chart
|
| 97 |
+
- Landmark theorems (FLT, Poincaré, Riemann) represented
|
| 98 |
+
- Major figures (Euclid, Euler, Gauss, Fermat, Gödel, Galois) have at least one chart
|
| 99 |
+
- ~150–200 total processes as a stretch goal
|
| 100 |
+
|
| 101 |
+
---
|
| 102 |
+
|
| 103 |
+
## 3. Long-Term: Research Frontier & Conjectures
|
| 104 |
+
|
| 105 |
+
**Goal**: Update axiomatic theory trees to show recent theorems, open conjectures, and the frontier of research — making the dependency graphs reflect the state of the field, not just classic textbook material.
|
| 106 |
+
|
| 107 |
+
### 3.1 What "Frontier" Means
|
| 108 |
+
- **Recent theorems**: Results from the last 20–30 years (e.g. Perelman/geometrization, Taylor–Wiles modularity)
|
| 109 |
+
- **Conjectures**: Stated but unproven (Riemann, Birch–Swinnerton-Dyer, Hodge, P vs NP)
|
| 110 |
+
- **Formalization status**: What is in Mathlib/Lean, what remains to be formalized
|
| 111 |
+
|
| 112 |
+
### 3.2 Data Sources for Frontier Content
|
| 113 |
+
- **arXiv**: Recent math.NT, math.GT, math.AG, etc. — identify major theorems
|
| 114 |
+
- **Mathlib / formalization**: Lean 4, Coq, Isabelle — which theorems are proved
|
| 115 |
+
- **Surveys & encyclopedias**: Wikipedia, Encyclopaedia of Mathematics, Scholarpedia
|
| 116 |
+
- **Clay Institute, Hilbert problems**: Lists of major open problems
|
| 117 |
+
|
| 118 |
+
### 3.3 Schema Extensions
|
| 119 |
+
- **Node metadata** in dependency graphs:
|
| 120 |
+
- `status`: `proved` | `conjecture` | `open_problem` | `formalized`
|
| 121 |
+
- `year`: publication or proof year
|
| 122 |
+
- `prover`: e.g. "Wiles", "Perelman", "Gonthier et al."
|
| 123 |
+
- `formalization`: e.g. `{ "tool": "Lean", "status": "in_progress" }`
|
| 124 |
+
- **Process-level**:
|
| 125 |
+
- `frontierLevel`: `classical` | `modern` | `recent` | `conjecture`
|
| 126 |
+
- `openProblems`: array of conjecture names
|
| 127 |
+
|
| 128 |
+
### 3.4 Visualization Ideas
|
| 129 |
+
- **Color coding**: Green (proved), yellow (recent), orange (conjecture), grey (formalized)
|
| 130 |
+
- **"Expand to frontier"** control: Toggle to show/hide conjectures and recent theorems
|
| 131 |
+
- **Year annotations**: Small labels on nodes (e.g. "1995", "2003")
|
| 132 |
+
- **Separate "Conjectures" section**: Page listing open problems with links to related axiom–theorem trees
|
| 133 |
+
|
| 134 |
+
### 3.5 Implementation Phases (Long-Term)
|
| 135 |
+
| Phase | Focus |
|
| 136 |
+
|-------|-------|
|
| 137 |
+
| **A** | Add `status`, `year` to process metadata (manual curation) |
|
| 138 |
+
| **B** | Extend Mermaid/diagram format to support status annotations |
|
| 139 |
+
| **C** | Curate 5–10 landmark theorems with frontier metadata |
|
| 140 |
+
| **D** | Build "Open Problems" index page |
|
| 141 |
+
| **E** | Integrate formalization status (Mathlib, etc.) where available |
|
| 142 |
+
|
| 143 |
+
### 3.6 Challenges
|
| 144 |
+
- **Curation effort**: Requires domain expertise to classify and annotate
|
| 145 |
+
- **Currency**: Frontier changes; need update process (annual review?)
|
| 146 |
+
- **Formalization**: Mathlib evolves; linking to specific commits or versions
|
| 147 |
+
- **Scope creep**: Easy to expand; need clear criteria for "frontier"
|
| 148 |
+
|
| 149 |
+
### 3.7 Sample Implemented: Number Theory Research Frontier
|
| 150 |
+
- **Page**: `number-theory-research-frontier.html` — static view of proved vs conjecture
|
| 151 |
+
- **Metadata**: `frontierStatus`, `year`, `prover` added to Sieve, Szemerédi, Green–Tao in `metadata.json`
|
| 152 |
+
- **Linked** from database table "Start Here" section
|
| 153 |
+
- **Contents**: Classical (Sieve, Extended Euclidean, Gödel), recent (Szemerédi 1975, Green–Tao 2004, Fermat 1995, Mordell 1983), conjectures (Riemann, BSD, Goldbach, Twin Primes)
|
| 154 |
+
|
| 155 |
+
---
|
| 156 |
+
|
| 157 |
+
## Summary: Immediate Next Steps
|
| 158 |
+
|
| 159 |
+
1. **Search** (1–2 days): Add search input, client-side search over metadata, results dropdown with links.
|
| 160 |
+
2. **Expansion plan** (ongoing): Execute phases from MATHEMATICS_DATABASE_EXPANSION_PLAN.md; use this doc for prioritization.
|
| 161 |
+
3. **Frontier** (quarterly/yearly): Start with schema additions and manual curation of a few landmark results; build out as capacity allows.
|
ProgFrame_README.md
DELETED
|
@@ -1,227 +0,0 @@
|
|
| 1 |
-
---
|
| 2 |
-
title: Genome Logic Modeling Project (GLMP)
|
| 3 |
-
emoji: 🧬
|
| 4 |
-
colorFrom: blue
|
| 5 |
-
colorTo: green
|
| 6 |
-
sdk: static
|
| 7 |
-
sdk_version: latest
|
| 8 |
-
app_file: README.md
|
| 9 |
-
pinned: false
|
| 10 |
-
---
|
| 11 |
-
|
| 12 |
-
# 🧬 Programming Framework for Complex Systems
|
| 13 |
-
|
| 14 |
-
**A systematic visualization methodology for analyzing complex systems across biology, chemistry, physics, and computer science using computational flowcharts and standardized color coding.**
|
| 15 |
-
|
| 16 |
-
[](https://creativecommons.org/licenses/by/4.0/)
|
| 17 |
-
[](https://huggingface.co/spaces/garywelz/programming_framework)
|
| 18 |
-
|
| 19 |
-
## 🎯 Overview
|
| 20 |
-
|
| 21 |
-
The Programming Framework represents a revolutionary approach to understanding complex systems by translating them into standardized computational representations. Using Mermaid Markdown syntax and large language model (LLM) processing, we demonstrate the framework's application to representative biological and chemical systems.
|
| 22 |
-
|
| 23 |
-
**Key Insight:** Complex systems across biology, chemistry, and physics exhibit remarkable similarities in their organizational principles despite operating at vastly different scales and domains. The Programming Framework reveals these common computational patterns.
|
| 24 |
-
|
| 25 |
-
## 🔬 Methodology
|
| 26 |
-
|
| 27 |
-
The Programming Framework methodology involves systematic analysis of complex systems through the following steps:
|
| 28 |
-
|
| 29 |
-
1. **System Identification:** Identify the biological, chemical, or physical system to be analyzed
|
| 30 |
-
2. **Component Categorization:** Classify system components into the five functional categories
|
| 31 |
-
3. **Flowchart Construction:** Create Mermaid flowcharts with appropriate color coding
|
| 32 |
-
4. **Logic Verification:** Verify computational logic and system dynamics
|
| 33 |
-
5. **Cross-Disciplinary Comparison:** Identify patterns across different domains
|
| 34 |
-
|
| 35 |
-
## 🎨 Universal Color Coding System
|
| 36 |
-
|
| 37 |
-
Each process is represented as a computational flowchart with standardized color coding:
|
| 38 |
-
|
| 39 |
-
| Color Category | Biology | Chemistry | Computer Science | Physics | Mathematics |
|
| 40 |
-
|----------------|---------|-----------|------------------|---------|-------------|
|
| 41 |
-
| 🔴 **Red** - Triggers & Inputs | Environmental signals, Nutrient availability | Reactant supply, Temperature | Input data, User commands | Energy input, Force application | Axioms, Given conditions |
|
| 42 |
-
| 🟡 **Yellow** - Structures & Objects | Enzymes, Receptor proteins | Catalysts, Reaction vessels | Data structures, Algorithms | Fields, Particles | Theorems, Methods |
|
| 43 |
-
| 🟢 **Green** - Processing & Operations | Metabolic reactions, Signal transduction | Chemical reactions, Equilibrium shifts | Algorithm execution, Data processing | Wave propagation, Quantum operations | Logical steps, Calculations |
|
| 44 |
-
| 🔵 **Blue** - Intermediates & States | Metabolites, Signaling molecules | Reaction intermediates, Transition states | Variables, Memory states | Quantum states, Energy levels | Intermediate results, Sub-proofs |
|
| 45 |
-
| 🟣 **Violet** - Products & Outputs | Biomolecules, Cellular responses | Final products, Reaction yields | Program outputs, Computed results | Measured quantities, Physical phenomena | Proven theorems, Mathematical results |
|
| 46 |
-
|
| 47 |
-
**Note:** Yellow nodes use black text for optimal readability, while all other colors use white text.
|
| 48 |
-
|
| 49 |
-
## 📊 Dataset and Evidence Base
|
| 50 |
-
|
| 51 |
-
We analyzed a comprehensive dataset of biological processes spanning multiple organisms and systems:
|
| 52 |
-
|
| 53 |
-
- **110 processes** from *Saccharomyces cerevisiae* (yeast) covering DNA replication, cell cycle control, signal transduction, energy metabolism, and stress responses
|
| 54 |
-
- **Multiple processes** from *Escherichia coli* including DNA replication, gene regulation, central metabolism, motility, and specialized systems like the lac operon
|
| 55 |
-
- **Advanced systems** including photosynthesis, bacterial sporulation, circadian clocks, and viral decision switches
|
| 56 |
-
|
| 57 |
-
**Total:** 297+ processes across 36 individual collections
|
| 58 |
-
|
| 59 |
-
The complete dataset is publicly available through the [Genome Logic Modeling Project (GLMP)](https://huggingface.co/spaces/garywelz/glmp) Hugging Face Space.
|
| 60 |
-
|
| 61 |
-
## 🌟 Representative Applications
|
| 62 |
-
|
| 63 |
-
### Case Study: β-Galactosidase Analysis (2025)
|
| 64 |
-
The β-galactosidase system represents one of the most well-characterized examples of genetic regulation in molecular biology. Using modern tools and AI assistance, we can now create sophisticated and detailed visualizations that demonstrate the full computational complexity of the lac operon system.
|
| 65 |
-
|
| 66 |
-
**Key Features:**
|
| 67 |
-
- Environmental inputs (lactose, glucose, energy status)
|
| 68 |
-
- Regulatory logic gates
|
| 69 |
-
- Gene expression control
|
| 70 |
-
- Metabolic pathway integration
|
| 71 |
-
- Feedback control mechanisms
|
| 72 |
-
|
| 73 |
-
### Case Study: Algorithm Execution Analysis
|
| 74 |
-
To demonstrate the framework's applicability to computer science, we applied the methodology to algorithm execution, specifically sorting algorithms. This example shows how the same computational logic can be applied to fundamental computer science processes.
|
| 75 |
-
|
| 76 |
-
**Key Features:**
|
| 77 |
-
- Input data validation
|
| 78 |
-
- Algorithm selection and execution
|
| 79 |
-
- Performance analysis
|
| 80 |
-
- Error handling mechanisms
|
| 81 |
-
- Complexity analysis
|
| 82 |
-
|
| 83 |
-
### Case Study: Mathematical Proof Tree Analysis
|
| 84 |
-
To demonstrate the framework's applicability to pure mathematics, we applied the methodology to mathematical proof construction, a fundamental process in mathematical logic.
|
| 85 |
-
|
| 86 |
-
**Key Features:**
|
| 87 |
-
- Axiom processing
|
| 88 |
-
- Logical deduction steps
|
| 89 |
-
- Theorem application
|
| 90 |
-
- Proof validation
|
| 91 |
-
- Mathematical rigor verification
|
| 92 |
-
|
| 93 |
-
## 🛠️ Technical Foundation
|
| 94 |
-
|
| 95 |
-
The Programming Framework builds upon **Mermaid Markdown (MMD)**, a text-based diagram generation syntax developed by Knut Sveidqvist in 2014. MMD enables the creation of complex flowcharts and diagrams from simple text descriptions.
|
| 96 |
-
|
| 97 |
-
**Key Capabilities:**
|
| 98 |
-
- **Text-to-Diagram Conversion:** Process descriptions from scientific literature can be directly converted into visual representations
|
| 99 |
-
- **Standardized Syntax:** Consistent formatting across different systems and domains
|
| 100 |
-
- **Automated Generation:** LLMs can rapidly process text descriptions and generate MMD code
|
| 101 |
-
- **Cross-Platform Compatibility:** MMD integrates with documentation platforms and can be rendered in multiple formats
|
| 102 |
-
- **Automatic Color Coding:** Canvas automatically derives color categories from MMD syntax
|
| 103 |
-
|
| 104 |
-
## 📈 Historical Evolution: From 1995 to 2025
|
| 105 |
-
|
| 106 |
-
The Programming Framework represents the culmination of a 30-year evolution in computational biology visualization:
|
| 107 |
-
|
| 108 |
-
### 1995: Manual Creation
|
| 109 |
-
- Months of research and reading
|
| 110 |
-
- Manual flowchart creation with Inspiration
|
| 111 |
-
- Single process analysis
|
| 112 |
-
- Community discussion on bionet.genome.chromosome
|
| 113 |
-
- Foundation for computational biology
|
| 114 |
-
|
| 115 |
-
### 2025: AI-Assisted Analysis
|
| 116 |
-
- Hours of AI-assisted processing
|
| 117 |
-
- Automated Mermaid Markdown generation
|
| 118 |
-
- Systematic analysis of 297+ processes
|
| 119 |
-
- Cross-disciplinary pattern recognition
|
| 120 |
-
- Universal computational framework
|
| 121 |
-
|
| 122 |
-
## 🚀 Getting Started
|
| 123 |
-
|
| 124 |
-
### Quick Start Guide
|
| 125 |
-
|
| 126 |
-
1. **Choose Your System:** Identify a biological, chemical, or physical system to analyze
|
| 127 |
-
2. **Apply the Framework:** Use the five-category color coding system
|
| 128 |
-
3. **Create Flowcharts:** Generate Mermaid Markdown representations
|
| 129 |
-
4. **Verify Logic:** Ensure computational logic is sound
|
| 130 |
-
5. **Compare Patterns:** Look for similarities across domains
|
| 131 |
-
|
| 132 |
-
### Sample Analysis Prompt
|
| 133 |
-
|
| 134 |
-
```
|
| 135 |
-
"Analyze the [system name] using the Programming Framework methodology. Create a Mermaid Markdown file that will enable the creation in HTML of a computational flowchart showing how environmental inputs are processed through regulatory mechanisms to produce specific outputs. Use the universal color scheme: Red for triggers/inputs, Yellow for structures/catalysts, Green for processing operations, Blue for intermediates, and Violet for products. Include a discipline-specific color key beneath the flowchart."
|
| 136 |
-
```
|
| 137 |
-
|
| 138 |
-
## 📚 Applications
|
| 139 |
-
|
| 140 |
-
### Biological Systems
|
| 141 |
-
- Gene regulation networks
|
| 142 |
-
- Metabolic pathways
|
| 143 |
-
- Signal transduction cascades
|
| 144 |
-
- Cell cycle control systems
|
| 145 |
-
- Stress response mechanisms
|
| 146 |
-
|
| 147 |
-
### Chemical Processes
|
| 148 |
-
- Catalytic reactions
|
| 149 |
-
- Equilibrium systems
|
| 150 |
-
- Kinetic analysis
|
| 151 |
-
- Industrial processes
|
| 152 |
-
- Environmental chemistry
|
| 153 |
-
|
| 154 |
-
### Physical Systems
|
| 155 |
-
- Quantum processes
|
| 156 |
-
- Thermodynamic cycles
|
| 157 |
-
- Wave phenomena
|
| 158 |
-
- Energy transfer systems
|
| 159 |
-
- Field interactions
|
| 160 |
-
|
| 161 |
-
### Computer Science
|
| 162 |
-
- Algorithm analysis
|
| 163 |
-
- Data structures
|
| 164 |
-
- Computational complexity
|
| 165 |
-
- Software architecture
|
| 166 |
-
- System design
|
| 167 |
-
|
| 168 |
-
### Mathematical Systems
|
| 169 |
-
- Proof construction
|
| 170 |
-
- Logical frameworks
|
| 171 |
-
- Theorem development
|
| 172 |
-
- Computational mathematics
|
| 173 |
-
- Formal systems
|
| 174 |
-
|
| 175 |
-
## 🎯 Key Applications
|
| 176 |
-
|
| 177 |
-
- **Bio-inspired Computing:** Biological computational patterns can inspire revolutionary new computing paradigms
|
| 178 |
-
- **Synthetic Biology:** Understanding cellular programming enables the design of programmable biological systems
|
| 179 |
-
- **Medical Applications:** Diseases can be understood as software bugs that can be debugged and fixed
|
| 180 |
-
- **Evolutionary Computation:** Evolution becomes visible as a programming process that optimizes biological software
|
| 181 |
-
|
| 182 |
-
## 📖 Documentation
|
| 183 |
-
|
| 184 |
-
- **[Methodology Guide](methodology/)** - Detailed step-by-step framework application
|
| 185 |
-
- **[Examples Gallery](examples/)** - Comprehensive collection of analyzed systems
|
| 186 |
-
- **[Tools & Resources](tools/)** - Templates, guidelines, and educational materials
|
| 187 |
-
- **[Case Studies](case-studies/)** - Deep dives into specific applications
|
| 188 |
-
|
| 189 |
-
## 🤝 Contributing
|
| 190 |
-
|
| 191 |
-
We welcome contributions to expand the Programming Framework across new domains and applications. Please see our [Contributing Guidelines](CONTRIBUTING.md) for details.
|
| 192 |
-
|
| 193 |
-
### How to Contribute
|
| 194 |
-
1. **Submit Examples:** Share your own system analyses using the framework
|
| 195 |
-
2. **Improve Documentation:** Help expand methodology guides and tutorials
|
| 196 |
-
3. **Develop Tools:** Create software tools for framework application
|
| 197 |
-
4. **Cross-Disciplinary Applications:** Apply the framework to new domains
|
| 198 |
-
|
| 199 |
-
## 📄 License
|
| 200 |
-
|
| 201 |
-
This project is licensed under the Creative Commons Attribution 4.0 International License - see the [LICENSE](LICENSE) file for details.
|
| 202 |
-
|
| 203 |
-
## 👨🔬 Author
|
| 204 |
-
|
| 205 |
-
**Gary Welz**
|
| 206 |
-
- Retired Faculty Member, John Jay College, CUNY (Department of Mathematics and Computer Science)
|
| 207 |
-
- Borough of Manhattan Community College, CUNY
|
| 208 |
-
- CUNY Graduate Center (New Media Lab)
|
| 209 |
-
- Email: gwelz@jjay.cuny.edu
|
| 210 |
-
|
| 211 |
-
## 🔗 Related Projects
|
| 212 |
-
|
| 213 |
-
- **[Genome Logic Modeling Project (GLMP)](https://huggingface.co/spaces/garywelz/glmp)** - Comprehensive biological systems analysis
|
| 214 |
-
- **[Programming Framework Examples](https://huggingface.co/spaces/garywelz/programming_framework_examples)** - Extended case studies and applications
|
| 215 |
-
|
| 216 |
-
## 📞 Contact
|
| 217 |
-
|
| 218 |
-
For questions, suggestions, or collaborations:
|
| 219 |
-
- **Email:** gwelz@jjay.cuny.edu
|
| 220 |
-
- **Hugging Face:** [@garywelz](https://huggingface.co/garywelz)
|
| 221 |
-
- **Issues:** Use the [GitHub Issues](https://github.com/garywelz/programming-framework/issues) page
|
| 222 |
-
|
| 223 |
-
---
|
| 224 |
-
|
| 225 |
-
**The genome is indeed like a computer program—not as a metaphor, but as a fundamental reality of how biological systems operate. This analysis provides the empirical evidence to support this revolutionary understanding of biological complexity.**
|
| 226 |
-
|
| 227 |
-
*We stand at the threshold of a new era in biology - one where we understand life itself as an information processing phenomenon.*
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Programming Framework for Systematic Analysis - a Hugging Face Space by garywelz.pdf
DELETED
|
@@ -1,3 +0,0 @@
|
|
| 1 |
-
version https://git-lfs.github.com/spec/v1
|
| 2 |
-
oid sha256:0af0c3d1c8c264739f0bf8c666bccc8348e174be8745cad0e92099bf551fa749
|
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size 180391
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README.md
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@@ -1,275 +1,102 @@
|
|
| 1 |
---
|
| 2 |
-
title:
|
| 3 |
-
emoji:
|
| 4 |
-
colorFrom:
|
| 5 |
-
colorTo:
|
| 6 |
-
sdk: static
|
| 7 |
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The Programming Framework represents **prior work** that demonstrates a novel methodology for analyzing complex processes by combining Large Language Models (LLMs) with visual flowchart representation. This research establishes a universal, domain-agnostic approach to process analysis that transforms textual descriptions into structured, interactive visualizations.
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###
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- **Universal Process Analysis:** Domain-agnostic methodology applicable across biology, chemistry, software engineering, business processes, and more
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- **LLM-Powered Extraction:** Automated extraction of process steps, decision points, and logic flows using Google Gemini 2.0 Flash
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- **Structured Visualization:** Mermaid.js-based flowchart generation encoded as JSON for programmatic access and integration
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- **Iterative Refinement:** Systematic approach enabling continuous improvement through visualization and LLM-assisted refinement
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- **Meta-Tool Architecture:** Framework for creating specialized process analysis tools (demonstrated by GLMP)
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- **JSON-Based Storage:** Structured data format enabling version control, cross-referencing, and API integration
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- **Multi-Domain Application:** Successfully applied to biological processes (GLMP), with extensions planned for software, business, and engineering domains
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- **Integration Framework:** Designed for integration with knowledge engines, research databases, and collaborative platforms
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The Programming Framework serves as the **foundational meta-tool** of the CopernicusAI Knowledge Engine, providing the underlying methodology that enables specialized applications:
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- **CopernicusAI** - Main knowledge engine integrating Framework outputs with AI podcasts and research synthesis
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- **Research Tools Dashboard** (✅ Implemented December 2025) - Fully operational web interface with knowledge graph visualization, vector search, RAG queries, and content browsing. Processes from Chemistry, Physics, Mathematics, and Computer Science are accessible through the unified dashboard. Live at: https://copernicus-frontend-phzp4ie2sq-uc.a.run.app/knowledge-engine
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- **Public Project Interface** (✅ Implemented January 2025) - Comprehensive public-facing page providing access to all CopernicusAI Knowledge Engine components. Live at: https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/copernicusai-public-reviewer.html
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- **Research Papers Metadata Database** - Integration for linking processes to source literature (12,000+ papers indexed)
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- **Science Video Database** - Potential integration for multi-modal process explanations
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1. **
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###
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Works across any field: biology, chemistry, software engineering, business processes, legal workflows, manufacturing, and beyond.
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JSON storage enables programmatic access, version control, cross-referencing, and integration with other tools and databases.
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First specialized application: visualizing biochemical processes like DNA replication, metabolic pathways, and cell signaling.
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- [Explore GLMP →](https://huggingface.co/spaces/garywelz/glmp)
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| Computer Science | 21 | 7 | ✅ Complete | [View Database](https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/computer-science-processes-database/computer-science-database-table.html) |
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| Mathematics | 20 | 7 | ✅ Complete | [View Database](https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/mathematics-processes-database/mathematics-database-table.html) |
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| GLMP (Molecular Biology) | 108 | 10+ | ✅ Complete | [View Database](https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/glmp-database-table.html) |
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| **Total** | **313** | **53+** | **✅ Operational** | **All databases publicly accessible** |
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**Note:** All processes include Mermaid flowcharts, source citations, and comprehensive metadata. See individual database tables for detailed statistics, complexity metrics, and process details. Statistics are dynamically updated - see [Public Project Interface](https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/copernicusai-public-reviewer.html) for current counts.
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### 🧬 Biology
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- [Biology Processes Database](https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/biology-processes-database/biology-database-table.html) - Interactive database with 52 higher-level organismal processes across 8 categories (reproduction, development, behavior, defense, nutrition, sensory, transport, coordination)
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- [GLMP Database Table](https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/glmp-database-table.html) - Genome Logic Modeling Project: Biochemical/molecular processes database (108 processes)
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- **Note:** Biology Processes Database focuses on organismal, developmental, behavioral, and ecological processes. GLMP focuses on molecular-level biochemical processes. Together they provide comprehensive biological process coverage.
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### ⚗️ Chemistry
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- [Chemistry Database Table](https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/chemistry-processes-database/chemistry-database-table.html) - Interactive database with 91 processes across 14 subcategories
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### 🔢 Mathematics
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- [Mathematics Database Table](https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/mathematics-processes-database/mathematics-database-table.html) - Interactive database with 20 processes across 7 subcategories
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### ⚛️ Physics
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- [Physics Database Table](https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/physics-processes-database/physics-database-table.html) - Interactive database with 21 processes across 7 subcategories
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### 💻 Computer Science
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- [Computer Science Database Table](https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/computer-science-processes-database/computer-science-database-table.html) - Interactive database with 21 processes across 7 subcategories
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## ⚠️ Limitations & Future Directions
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### Current Limitations
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- **Process Validation:** Flowcharts are LLM-generated and benefit from expert validation for domain-specific accuracy (validation process ongoing)
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- **Source Linking:** Not all processes yet linked to specific research papers (work in progress per Quality Standards)
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- **Scale:** Current database (313 processes) represents proof-of-concept; target is 1,000+ processes
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| 125 |
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- **Domain Coverage:** Some disciplines better represented than others; actively expanding coverage
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| 126 |
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- **LLM Dependency:** Framework requires LLM access (Google Gemini 2.0 Flash); alternative models may produce different results
|
| 127 |
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- **Complexity Limits:** Very complex processes (>100 nodes) may require manual refinement
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### Future Work
|
| 130 |
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- **Expansion:** Scale to 1,000+ processes across all disciplines (see DISCIPLINE_DATABASES_PLAN.md)
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| 131 |
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- **Validation:** Implement systematic peer review process for process flowcharts
|
| 132 |
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- **Source Integration:** Enhanced linking to research papers using vector search from 23,246+ indexed papers
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| 133 |
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- **Automation:** Automated source paper suggestion and linking
|
| 134 |
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- **Quality Assurance:** Systematic validation framework for flowchart accuracy
|
| 135 |
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- **Multi-LLM Support:** Extend to support multiple LLM providers for comparison and validation
|
| 136 |
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- **Interactive Refinement:** User interface for iterative flowchart improvement
|
| 137 |
-
|
| 138 |
-
### Known Areas for Improvement
|
| 139 |
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- **Accuracy Validation:** Not all flowcharts yet validated by domain experts; systematic validation in progress
|
| 140 |
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- **Source Citations:** Some processes need additional source paper citations (work in progress)
|
| 141 |
-
- **Cross-Discipline Links:** Enhanced cross-referencing between related processes across disciplines
|
| 142 |
-
|
| 143 |
-
## 🔧 Technical Architecture
|
| 144 |
-
|
| 145 |
-
### LLM Integration
|
| 146 |
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- **Primary Model:** Google Gemini 2.0 Flash for process analysis
|
| 147 |
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- **Deployment:** Vertex AI for enterprise-scale deployment
|
| 148 |
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- **Prompt Engineering:** Custom prompts optimized for process extraction and structured output
|
| 149 |
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- **Output Format:** Structured JSON with Mermaid flowchart syntax
|
| 150 |
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- **Version:** Framework tested with Gemini 2.0 Flash; compatible with other LLMs
|
| 151 |
-
|
| 152 |
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### Visualization Stack
|
| 153 |
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- **Rendering Engine:** Mermaid.js for flowchart visualization
|
| 154 |
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- **Data Validation:** JSON schema for data validation and consistency
|
| 155 |
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- **Output Formats:** Interactive SVG output with export to PNG/PDF supported
|
| 156 |
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- **Color Schemes:** Discipline-based color coding following Programming Framework standards
|
| 157 |
-
|
| 158 |
-
### Data Storage
|
| 159 |
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- **Primary Storage:** Google Cloud Storage for JSON process files
|
| 160 |
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- **Metadata Indexing:** Firestore for metadata indexing and search
|
| 161 |
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- **Version Control:** Git for code and documentation versioning
|
| 162 |
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- **Cross-Referencing:** Integration with research papers database (23,246+ papers indexed)
|
| 163 |
-
|
| 164 |
-
### Integration Points
|
| 165 |
-
- **GLMP:** Specialized biological process collections
|
| 166 |
-
- **CopernicusAI:** Knowledge graph integration for unified exploration
|
| 167 |
-
- **Research Papers Database:** Cross-linking with 23,246+ indexed papers
|
| 168 |
-
- **API Endpoints:** Programmatic access for integration with other systems
|
| 169 |
-
- **Research Tools Dashboard:** Unified interface for exploring processes alongside papers and other content
|
| 170 |
-
|
| 171 |
-
### How to Cite This Work
|
| 172 |
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|
| 173 |
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#### BibTeX Format
|
| 174 |
-
```bibtex
|
| 175 |
-
@article{welz2025programming,
|
| 176 |
-
title={The Programming Framework: A General Method for Process Analysis Using LLMs and Mermaid Visualization},
|
| 177 |
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author={Welz, Gary},
|
| 178 |
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journal={Nature Communications},
|
| 179 |
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year={2025},
|
| 180 |
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note={Submitted},
|
| 181 |
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url={https://huggingface.co/spaces/garywelz/programming_framework},
|
| 182 |
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note={Preprint available upon publication}
|
| 183 |
-
}
|
| 184 |
-
```
|
| 185 |
-
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| 186 |
-
#### Standard Citation Format
|
| 187 |
-
Welz, G. (2024–2025). *The Programming Framework: A Universal Method for Process Analysis*.
|
| 188 |
-
Hugging Face Spaces. https://huggingface.co/spaces/garywelz/programming_framework
|
| 189 |
-
|
| 190 |
-
Welz, G. (2024). *From Inspiration to AI: Biology as Visual Programming*. Medium.
|
| 191 |
-
https://medium.com/@garywelz_47126/from-inspiration-to-ai-biology-as-visual-programming-520ee523029a
|
| 192 |
-
|
| 193 |
-
**Note:** When published, this citation will be updated with DOI and publication details from Nature Communications.
|
| 194 |
-
|
| 195 |
-
This project serves as a foundational meta-tool for AI-assisted process analysis, enabling systematic extraction and visualization of complex logic from textual sources across diverse scientific and technical domains.
|
| 196 |
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|
| 197 |
-
The Programming Framework is designed as infrastructure for AI-assisted science, providing a universal methodology that can be specialized for domain-specific applications.
|
| 198 |
-
|
| 199 |
-
## 📊 Data Availability
|
| 200 |
-
|
| 201 |
-
**Research Data:**
|
| 202 |
-
- **Process Flowcharts:** All process flowcharts are publicly available in Google Cloud Storage with interactive database tables:
|
| 203 |
-
- [Biology Processes Database](https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/biology-processes-database/biology-database-table.html) - 52 processes across 8 subcategories
|
| 204 |
-
- [Chemistry Processes Database](https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/chemistry-processes-database/chemistry-database-table.html) - 91 processes across 14 subcategories
|
| 205 |
-
- [Physics Processes Database](https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/physics-processes-database/physics-database-table.html) - 21 processes across 7 subcategories
|
| 206 |
-
- [Mathematics Processes Database](https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/mathematics-processes-database/mathematics-database-table.html) - 20 processes across 7 subcategories
|
| 207 |
-
- [Computer Science Processes Database](https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/computer-science-processes-database/computer-science-database-table.html) - 21 processes across 7 subcategories
|
| 208 |
-
- [GLMP Database](https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/glmp-database-table.html) - 108+ molecular biology processes
|
| 209 |
-
- **Process Metadata:** Each process includes JSON metadata with Mermaid flowchart syntax, source citations, complexity metrics, and related process links.
|
| 210 |
-
- **Current Statistics:** Dynamically updated statistics available at [Public Project Interface](https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/copernicusai-public-reviewer.html).
|
| 211 |
-
|
| 212 |
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**Source Code & Methodology:**
|
| 213 |
-
- **Methodology:** Fully documented in this README and the Programming Framework paper (submitted to Nature Communications).
|
| 214 |
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- **Process Generation:** LLM-powered extraction using Google Gemini 2.0 Flash via Vertex AI, with custom prompts for process extraction and structured JSON output formatting.
|
| 215 |
-
- **Visualization:** Mermaid.js-based flowchart generation with JSON schema for data validation.
|
| 216 |
-
- **Data Format:** Standardized JSON structure documented in project files (see Technical Architecture section).
|
| 217 |
-
- **Database Schemas:** Process database schemas and metadata structures documented in project documentation.
|
| 218 |
-
|
| 219 |
-
**Access:**
|
| 220 |
-
- **Public Access:** All process databases and database tables are publicly accessible (no authentication required).
|
| 221 |
-
- **Individual Process Viewers:** Each process has a dedicated viewer accessible via links in database tables.
|
| 222 |
-
- **Research Tools Dashboard:** Processes are integrated into the [Research Tools Dashboard](https://copernicus-frontend-phzp4ie2sq-uc.a.run.app/knowledge-engine) for unified exploration alongside research papers and other content.
|
| 223 |
-
- **Hugging Face Spaces:** Framework documentation and examples available at [Programming Framework Space](https://huggingface.co/spaces/garywelz/programming_framework).
|
| 224 |
-
|
| 225 |
-
**Reproducibility:**
|
| 226 |
-
- All process flowcharts include source citations linking to research papers used to create each flowchart.
|
| 227 |
-
- Methodology is fully documented and can be replicated using Google Gemini 2.0 Flash or compatible LLMs.
|
| 228 |
-
- JSON schema and data structures are standardized and documented.
|
| 229 |
-
- Process generation workflow is transparent: input (textual process description) → LLM analysis → Mermaid flowchart generation → JSON storage.
|
| 230 |
-
- All components are publicly accessible for verification, reuse, and extension to other domains.
|
| 231 |
-
|
| 232 |
-
**Process Database Statistics:**
|
| 233 |
-
- **Total Processes:** 313+ validated processes across 6 databases
|
| 234 |
-
- **Disciplines Covered:** Biology, Chemistry, Physics, Mathematics, Computer Science, Molecular Biology (GLMP)
|
| 235 |
-
- **Validation:** 100% syntax accuracy, ≥85% metadata quality, all processes include source citations
|
| 236 |
-
- **Format:** All processes stored as JSON files with Mermaid flowchart syntax, publicly accessible via Google Cloud Storage
|
| 237 |
-
|
| 238 |
-
## 🔗 Related Projects
|
| 239 |
-
|
| 240 |
-
### 🧬 GLMP - Genome Logic Modeling
|
| 241 |
-
First specialized application of the Programming Framework to biochemical processes. 100+ biological pathways visualized.
|
| 242 |
-
- [Visit GLMP →](https://huggingface.co/spaces/garywelz/glmp)
|
| 243 |
-
|
| 244 |
-
### 🔬 CopernicusAI
|
| 245 |
-
Knowledge engine integrating the Programming Framework with AI podcasts, research papers, and knowledge graph for scientific discovery.
|
| 246 |
-
- [Visit CopernicusAI →](https://huggingface.co/spaces/garywelz/copernicusai)
|
| 247 |
-
|
| 248 |
-
## 🎨 Interactive Demo
|
| 249 |
-
|
| 250 |
-
The space includes interactive examples showing the framework applied to:
|
| 251 |
-
- Scientific Method
|
| 252 |
-
- Software Deployment Pipeline
|
| 253 |
-
- Customer Support Workflow
|
| 254 |
-
- Research Paper Publication
|
| 255 |
-
|
| 256 |
-
Each example demonstrates how LLMs extract process logic and encode it as visual flowcharts.
|
| 257 |
-
|
| 258 |
-
## 💻 Technology Stack
|
| 259 |
-
|
| 260 |
-
- **LLM**: Google Gemini 2.0 Flash, Vertex AI
|
| 261 |
-
- **Visualization**: Mermaid.js
|
| 262 |
-
- **Storage**: Google Cloud Storage, Firestore
|
| 263 |
-
- **Format**: JSON with Mermaid syntax
|
| 264 |
-
- **Frontend**: Static HTML + Tailwind CSS
|
| 265 |
-
|
| 266 |
-
## 🌟 Vision
|
| 267 |
-
|
| 268 |
-
As AI systems become more capable of understanding complex processes, the Programming Framework provides the bridge between human comprehension and machine analysis. It's a tool for truth-seeking—transforming complexity into clarity.
|
| 269 |
-
|
| 270 |
-
---
|
| 271 |
-
|
| 272 |
-
**A Universal Method for Process Analysis**
|
| 273 |
-
|
| 274 |
-
© 2025 Gary Welz. All rights reserved.
|
| 275 |
|
|
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|
|
|
| 1 |
---
|
| 2 |
+
title: "Programming Framework for Systematic Analysis"
|
| 3 |
+
emoji: "🎨"
|
| 4 |
+
colorFrom: "blue"
|
| 5 |
+
colorTo: "green"
|
| 6 |
+
sdk: "static"
|
| 7 |
+
sdk_version: "latest"
|
| 8 |
+
app_file: "index.html"
|
| 9 |
+
pinned: false
|
| 10 |
+
author: "garywelz"
|
| 11 |
+
short_description: Mermaid flowcharts + links to math and biology databases
|
| 12 |
---
|
| 13 |
|
| 14 |
+
## Programming Framework
|
| 15 |
|
| 16 |
+
A systematic visualization methodology for analyzing complex systems across disciplines using Mermaid Markdown and a universal five-color code.
|
| 17 |
|
| 18 |
+
**Source & backup:** [github.com/garywelz/progframe](https://github.com/garywelz/progframe)
|
| 19 |
|
| 20 |
+
### Interactive databases (hosted on Google Cloud Storage)
|
| 21 |
|
| 22 |
+
Browse searchable tables and open individual process charts:
|
| 23 |
|
| 24 |
+
- **Mathematics** — [Algorithms & axiomatic theories table](https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/mathematics-processes-database/mathematics-database-table.html) · [Named collections (mathematicians & theorems)](https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/mathematics-processes-database/collections/index.html) · [Whole of mathematics graph](https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/mathematics-processes-database/whole-of-mathematics.html)
|
| 25 |
+
- **Biology** — [Pathways, mechanisms & lab protocols table](https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/biology-processes-database/biology-database-table.html) · [Theme collections](https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/biology-processes-database/collections/index.html)
|
| 26 |
|
| 27 |
+
Complex systems across biology, chemistry, and physics exhibit remarkable similarities in their organizational principles despite operating at vastly different scales and domains. Traditional analysis methods often remain siloed within specific disciplines, limiting our ability to identify common patterns and computational logic that govern system behavior. Here, we present the Programming Framework, a systematic methodology that translates complex system dynamics into standardized computational representations using Mermaid Markdown syntax and LLM processing.
|
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| 28 |
|
| 29 |
+
### Purpose and Goals
|
|
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|
| 30 |
|
| 31 |
+
The Programming Framework project aims to advance the use of Mermaid Markdown syntax and Large Language Models (LLMs) to create standardized, color-coded flowcharts representing complex processes across all academic disciplines. By providing a universal methodology for translating system dynamics into computational representations, this framework enables systematic comparison and pattern recognition across traditionally separate fields including biology, chemistry, physics, computer science, and mathematics. The project builds upon three decades of computational biology research and demonstrates how modern AI tools can democratize complex system analysis, making sophisticated visualization accessible to researchers, educators, and students worldwide.
|
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|
| 32 |
|
| 33 |
+
### Technical Foundation: Mermaid Markdown
|
|
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|
| 34 |
|
| 35 |
+
#### The Invention of Mermaid
|
|
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| 36 |
|
| 37 |
+
**Knut Sveidqvist** invented the Mermaid markdown format. He created Mermaid, a JavaScript-based diagramming and charting tool, to simplify diagram creation in documentation workflows. The project was inspired by his experience trying to update a diagram in a document, which was difficult due to the file format.
|
| 38 |
|
| 39 |
+
Sveidqvist's innovation revolutionized how diagrams are created and maintained in documentation by providing a text-based syntax that can be version-controlled, easily edited, and automatically rendered into visual diagrams. This approach eliminates the need for external diagramming tools and ensures diagrams stay synchronized with their documentation.
|
| 40 |
|
| 41 |
+
#### Mermaid Markdown (.mmd) Format
|
| 42 |
|
| 43 |
+
The Programming Framework leverages Mermaid's `.mmd` file format, which provides:
|
| 44 |
|
| 45 |
+
- **Text-based syntax** for creating complex flowcharts and diagrams
|
| 46 |
+
- **Version control compatibility** - diagrams can be tracked in Git repositories
|
| 47 |
+
- **LLM-friendly format** - AI systems can generate and modify diagram code
|
| 48 |
+
- **Cross-platform compatibility** - works in any environment that supports JavaScript
|
| 49 |
+
- **Embeddable rendering** - diagrams can be displayed in HTML, Markdown, and other formats
|
| 50 |
|
| 51 |
+
#### LLM Integration and Workflow
|
| 52 |
|
| 53 |
+
Our methodology uses Large Language Models to:
|
| 54 |
|
| 55 |
+
1. **Generate .mmd files** - LLMs create detailed Mermaid syntax for complex processes
|
| 56 |
+
2. **Apply color coding** - Systematic application of the 5-category color system
|
| 57 |
+
3. **Ensure consistency** - Standardized node naming and connection patterns
|
| 58 |
+
4. **Embed in HTML** - .mmd files are embedded in HTML for web display
|
| 59 |
+
5. **Maintain quality** - LLMs can validate and optimize diagram structure
|
| 60 |
|
| 61 |
+
This workflow enables rapid creation of sophisticated visualizations that would be impractical to create manually, while maintaining the flexibility and editability of text-based formats.
|
| 62 |
|
| 63 |
+
### Universal Color Coding Table
|
|
|
|
| 64 |
|
| 65 |
+
| Color | Hex | Biology | Chemistry | Computer Science | Physics | Mathematics |
|
| 66 |
+
| --- | --- | --- | --- | --- | --- | --- |
|
| 67 |
+
| Red | `#ff6b6b` | Environmental signals, nutrients | Reactant supply, temperature | Input data, user commands | Energy input, force | Axioms, givens |
|
| 68 |
+
| Yellow | `#ffd43b` | Enzymes, receptors | Catalysts, vessels | Data structures, algorithms | Fields, particles | Theorems, methods |
|
| 69 |
+
| Green | `#51cf66` | Metabolic reactions | Chemical reactions | Algorithm execution | Quantum/force operations | Calculations, deductions |
|
| 70 |
+
| Blue | `#74c0fc` | Metabolites, states | Intermediates, streams | Variables, memory states | States, measurement results | Intermediate results |
|
| 71 |
+
| Violet | `#b197fc` | Biomolecules, responses | Final products | Program outputs | Phenomena, measured quantities | Proven results |
|
| 72 |
|
| 73 |
+
### Explore the Space
|
|
|
|
| 74 |
|
| 75 |
+
- Biology evidence base: [GLMP Space](https://huggingface.co/spaces/garywelz/glmp) (Hugging Face) and repo
|
| 76 |
+
- Chemistry processes: [chemistry_processes.html](chemistry_processes.html)
|
| 77 |
+
- Computer Science: [computer_science_processes.html](computer_science_processes.html)
|
| 78 |
+
- Physics: [physics_processes.html](physics_processes.html)
|
| 79 |
+
- Mathematics: [mathematics_processes.html](mathematics_processes.html)
|
| 80 |
+
- Full article: [programming_framework_article.html](programming_framework_article.html)
|
| 81 |
|
| 82 |
+
### Experimental Validation
|
|
|
|
|
|
|
| 83 |
|
| 84 |
+
- **Validation Paper**: [experimental_validation_paper.html](experimental_validation_paper.html) — comprehensive experimental protocols and validation methodology
|
| 85 |
+
- **Core validation flowcharts** (under `validation_flowcharts/`):
|
| 86 |
+
- [catalytic_hydrogenation_optimization.html](validation_flowcharts/catalytic_hydrogenation_optimization.html) — Experiment 1: catalytic hydrogenation
|
| 87 |
+
- [raft_polymerization_mechanism.html](validation_flowcharts/raft_polymerization_mechanism.html) — Experiment 2: polymerization kinetics
|
| 88 |
+
- [surface_catalysis_mechanism.html](validation_flowcharts/surface_catalysis_mechanism.html) — Experiment 3: surface chemistry
|
| 89 |
+
- [electrochemical_oxygen_reduction.html](validation_flowcharts/electrochemical_oxygen_reduction.html) — Experiment 4: electrochemical process
|
| 90 |
+
- [quantum_chemistry_calculation.html](validation_flowcharts/quantum_chemistry_calculation.html) — Experiment 5: computational chemistry
|
| 91 |
|
| 92 |
+
### Batch Architecture
|
| 93 |
|
| 94 |
+
The project now includes a comprehensive batch architecture for each discipline:
|
| 95 |
|
| 96 |
+
- **Mathematics**: 7 batches (21 processes) - Complete ✅
|
| 97 |
+
- **Chemistry**: 14 batches (70 processes) - Complete ✅
|
| 98 |
+
- **Computer Science**: 7 batches (21 processes) - Complete ✅
|
| 99 |
+
- **Physics**: 7 batches (21 processes) - Complete ✅
|
| 100 |
+
- **Biology**: External GLMP Space - Complete ✅
|
|
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|
| 101 |
|
| 102 |
+
Each discipline has an index page (`*_index.html`) and individual batch files (`*_batch_*.html`) containing detailed process visualizations.
|
WHOLE_OF_MATHEMATICS_CHART_DESIGN.md
ADDED
|
@@ -0,0 +1,374 @@
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|
|
|
| 1 |
+
# Whole of Mathematics — Interactive Zoomable Chart Design
|
| 2 |
+
|
| 3 |
+
## Vision
|
| 4 |
+
|
| 5 |
+
A single, high-level interactive visualization that shows the **entire landscape of mathematics** as our collection understands it—with the ability to **zoom in** from broad domains down to individual processes, and to **click through** to the actual flowchart or dependency graph for any process.
|
| 6 |
+
|
| 7 |
+
Think of it as a "map of mathematics" that is:
|
| 8 |
+
- **Data-driven** — built from `metadata.json` and our hierarchy
|
| 9 |
+
- **Zoomable** — pan and zoom like a geographic map or Prezi
|
| 10 |
+
- **Drillable** — click a region to focus on it and see its children
|
| 11 |
+
- **Linked** — deepest level opens the existing process HTML page
|
| 12 |
+
|
| 13 |
+
---
|
| 14 |
+
|
| 15 |
+
## Domain Grouping: arXiv Math Taxonomy
|
| 16 |
+
|
| 17 |
+
Use the **arXiv Mathematics** taxonomy (math.XX) as the canonical domain structure. arXiv is widely recognized, stable, and aligns with how mathematicians categorize research.
|
| 18 |
+
|
| 19 |
+
### arXiv Math Categories (math.XX)
|
| 20 |
+
|
| 21 |
+
| Code | Name |
|
| 22 |
+
|------|------|
|
| 23 |
+
| math.AC | Commutative Algebra |
|
| 24 |
+
| math.AG | Algebraic Geometry |
|
| 25 |
+
| math.AP | Analysis of PDEs |
|
| 26 |
+
| math.AT | Algebraic Topology |
|
| 27 |
+
| math.CA | Classical Analysis and ODEs |
|
| 28 |
+
| math.CO | Combinatorics |
|
| 29 |
+
| math.CT | Category Theory |
|
| 30 |
+
| math.CV | Complex Variables |
|
| 31 |
+
| math.DG | Differential Geometry |
|
| 32 |
+
| math.DS | Dynamical Systems |
|
| 33 |
+
| math.FA | Functional Analysis |
|
| 34 |
+
| math.GM | General Mathematics |
|
| 35 |
+
| math.GN | General Topology |
|
| 36 |
+
| math.GR | Group Theory |
|
| 37 |
+
| math.GT | Geometric Topology |
|
| 38 |
+
| math.HO | History and Overview |
|
| 39 |
+
| math.IT | Information Theory |
|
| 40 |
+
| math.KT | K-Theory and Homology |
|
| 41 |
+
| math.LO | Logic |
|
| 42 |
+
| math.MG | Metric Geometry |
|
| 43 |
+
| math.MP | Mathematical Physics |
|
| 44 |
+
| math.NA | Numerical Analysis |
|
| 45 |
+
| math.NT | Number Theory |
|
| 46 |
+
| math.OA | Operator Algebras |
|
| 47 |
+
| math.OC | Optimization and Control |
|
| 48 |
+
| math.PR | Probability |
|
| 49 |
+
| math.QA | Quantum Algebra |
|
| 50 |
+
| math.RA | Rings and Algebras |
|
| 51 |
+
| math.RT | Representation Theory |
|
| 52 |
+
| math.SG | Symplectic Geometry |
|
| 53 |
+
| math.SP | Spectral Theory |
|
| 54 |
+
| math.ST | Statistics Theory |
|
| 55 |
+
|
| 56 |
+
### Mapping Our Subcategories → arXiv
|
| 57 |
+
|
| 58 |
+
| Our subcategory | arXiv code(s) |
|
| 59 |
+
|-----------------|---------------|
|
| 60 |
+
| abstract_algebra | math.GR, math.RA, math.AC |
|
| 61 |
+
| linear_algebra | math.RA |
|
| 62 |
+
| category_theory | math.CT |
|
| 63 |
+
| calculus_analysis | math.CA, math.CV, math.DS |
|
| 64 |
+
| geometry_topology | math.GN, math.GT, math.AT, math.DG, math.MG |
|
| 65 |
+
| number_theory | math.NT |
|
| 66 |
+
| discrete_mathematics | math.CO, math.LO |
|
| 67 |
+
| foundations | math.LO |
|
| 68 |
+
| bioinformatics | (applied; no direct math.XX; use math.GM or separate) |
|
| 69 |
+
|
| 70 |
+
*Wikipedia* math portal uses a flatter structure (Algebra, Analysis, Geometry, etc.)—can serve as a secondary grouping if we want a simpler top level.
|
| 71 |
+
|
| 72 |
+
---
|
| 73 |
+
|
| 74 |
+
## Hierarchy: What We're Mapping
|
| 75 |
+
|
| 76 |
+
### Level 0 — Whole of Mathematics (root)
|
| 77 |
+
The entire collection. One view.
|
| 78 |
+
|
| 79 |
+
### Level 1 — arXiv Math Domains (or grouped)
|
| 80 |
+
Either use arXiv codes directly (math.NT, math.AG, …) or group into ~6–8 broader areas for a simpler top level:
|
| 81 |
+
|
| 82 |
+
| Domain | arXiv codes | Our subcategories |
|
| 83 |
+
|--------|-------------|-------------------|
|
| 84 |
+
| **Algebra** | AC, AG, CT, GR, RA, RT, QA | abstract_algebra, linear_algebra, category_theory |
|
| 85 |
+
| **Analysis** | AP, CA, CV, FA, NA, SP | calculus_analysis, complex_analysis |
|
| 86 |
+
| **Geometry & Topology** | AT, DG, GN, GT, MG, SG | geometry_topology |
|
| 87 |
+
| **Number Theory** | NT | number_theory |
|
| 88 |
+
| **Discrete & Logic** | CO, LO | discrete_mathematics, foundations |
|
| 89 |
+
| **Dynamical Systems** | DS | (part of calculus_analysis) |
|
| 90 |
+
| **Probability & Statistics** | PR, ST | (future) |
|
| 91 |
+
| **Applied / Other** | GM, MP, OC, IT | bioinformatics |
|
| 92 |
+
|
| 93 |
+
### Level 2 — Subcategories
|
| 94 |
+
e.g., within **Analysis**: Real Analysis, Complex Analysis, Complex Dynamics, Symbolic Dynamics.
|
| 95 |
+
|
| 96 |
+
### Level 3 — Processes
|
| 97 |
+
Individual charts. Click → open process page.
|
| 98 |
+
|
| 99 |
+
---
|
| 100 |
+
|
| 101 |
+
## Force-Directed Graph: Deep Dive
|
| 102 |
+
|
| 103 |
+
### Why It Aligns With Our Current Metaphor
|
| 104 |
+
|
| 105 |
+
Our existing process charts are **node–link diagrams**:
|
| 106 |
+
- **Axiomatic theories**: nodes = axioms, definitions, theorems; edges = "depends on"
|
| 107 |
+
- **Algorithms**: nodes = steps; edges = control flow
|
| 108 |
+
|
| 109 |
+
A force-directed graph is the same visual language at a higher level: **nodes and edges**. It extends the dependency-graph metaphor from *within* a process to *between* processes and domains.
|
| 110 |
+
|
| 111 |
+
### Force-Directed vs. Treemap: Core Difference
|
| 112 |
+
|
| 113 |
+
| Aspect | Treemap | Force-Directed Graph |
|
| 114 |
+
|--------|---------|----------------------|
|
| 115 |
+
| **Structure** | Containment (parent *contains* children) | Links (nodes *connected* by edges) |
|
| 116 |
+
| **Relationships** | Implicit (nesting) | Explicit (edges) |
|
| 117 |
+
| **Hierarchy** | Strict tree; one parent per node | Can be tree, DAG, or general graph |
|
| 118 |
+
| **Cross-links** | Hard to show (a node lives in one place) | Natural (Galois ↔ Field Theory ↔ Group Theory) |
|
| 119 |
+
| **Layout** | Rectangles, area = weight | Organic; forces pull/push nodes |
|
| 120 |
+
| **Zoom** | Zoom into a region (geometric) | Pan/zoom canvas; click node to focus |
|
| 121 |
+
|
| 122 |
+
### Force-Directed *Can* Be Hierarchical
|
| 123 |
+
|
| 124 |
+
You can use a force-directed layout with **hierarchical constraints**:
|
| 125 |
+
- **Parent–child links**: domain → subcategory → process (tree edges)
|
| 126 |
+
- **Cross-links**: `namedCollections` overlap, or explicit "related to" (e.g., Galois Theory ↔ Field Theory)
|
| 127 |
+
- **Collision / clustering**: Give nodes of the same domain a "gravity" toward each other so they cluster
|
| 128 |
+
- **Level-based y-position**: Fix y by depth (root at top, processes at bottom) for a tree-like flow
|
| 129 |
+
|
| 130 |
+
So you get: **hierarchy + relationships** in one view.
|
| 131 |
+
|
| 132 |
+
### Zoom and Pan
|
| 133 |
+
|
| 134 |
+
Force-directed graphs support zoom and pan the same way as treemaps:
|
| 135 |
+
- Wrap the graph in an SVG `<g>` (group)
|
| 136 |
+
- Apply `d3.zoom()` to the SVG; transform the group on zoom/pan events
|
| 137 |
+
- **Geometric zoom**: scale + translate the whole canvas (simple)
|
| 138 |
+
- **Semantic zoom** (optional): at different zoom levels, show different detail (e.g., zoomed out = domains only; zoomed in = subcategories; further in = processes)
|
| 139 |
+
|
| 140 |
+
### Ease of Use With Our Collection
|
| 141 |
+
|
| 142 |
+
**Data we have:**
|
| 143 |
+
- `subcategory` per process → gives hierarchy (domain → subcategory → process)
|
| 144 |
+
- `processType` (algorithm vs axiomatic_theory) → can style nodes differently
|
| 145 |
+
- Process IDs and names → node labels and links
|
| 146 |
+
|
| 147 |
+
**Data we can add:**
|
| 148 |
+
- `namedCollections` → cross-links: two processes in "fermat" get an edge
|
| 149 |
+
- Optional `dependsOn` or `relatedTo` → explicit edges between processes
|
| 150 |
+
|
| 151 |
+
**Graph structure:**
|
| 152 |
+
```
|
| 153 |
+
Nodes: [Mathematics (root)] + [~8 domains] + [~10 subcategories] + [~98 processes]
|
| 154 |
+
Edges: Tree edges (parent→child) + optional cross-edges (namedCollections, relatedTo)
|
| 155 |
+
```
|
| 156 |
+
|
| 157 |
+
~120 nodes, ~100+ edges is well within D3 force layout comfort zone. No performance concerns.
|
| 158 |
+
|
| 159 |
+
### Relationship to Other Types
|
| 160 |
+
|
| 161 |
+
- **Treemap**: Force-directed shows *links*; treemap shows *containment*. Different metaphors. Treemap is "zoom into a region"; force-directed is "follow the edges."
|
| 162 |
+
- **Sunburst**: Both can show hierarchy. Sunburst is radial containment; force-directed is node-link. Sunburst is more compact; force-directed shows relationships.
|
| 163 |
+
- **Map metaphor**: Could use force-directed *for layout* (position nodes), then draw "regions" (Voronoi, convex hulls) around domain clusters—hybrid approach.
|
| 164 |
+
|
| 165 |
+
---
|
| 166 |
+
|
| 167 |
+
## Technical Approaches (Summary)
|
| 168 |
+
|
| 169 |
+
### Option A: D3 Zoomable Treemap
|
| 170 |
+
- Containment metaphor; area = count; no explicit edges.
|
| 171 |
+
- **Fit**: Pure hierarchy, no cross-links.
|
| 172 |
+
|
| 173 |
+
### Option B: D3 Sunburst
|
| 174 |
+
- Radial containment; compact.
|
| 175 |
+
- **Fit**: Hierarchy; explore later.
|
| 176 |
+
|
| 177 |
+
### Option C: Force-Directed Graph with Zoom ← **Primary choice**
|
| 178 |
+
- Node–link; explicit edges; aligns with our dependency-graph metaphor.
|
| 179 |
+
- **Fit**: Hierarchy + cross-links; zoom/pan; works with our collection.
|
| 180 |
+
|
| 181 |
+
### Option D: Map Metaphor
|
| 182 |
+
- Geographic feel; Voronoi or custom.
|
| 183 |
+
- **Fit**: Explore later.
|
| 184 |
+
|
| 185 |
+
### Option E: Hybrid
|
| 186 |
+
- Treemap + graph overlay.
|
| 187 |
+
- **Fit**: Explore later.
|
| 188 |
+
|
| 189 |
+
---
|
| 190 |
+
|
| 191 |
+
## Recommended: Force-Directed Graph (Option C) + Zoom + Breadcrumbs
|
| 192 |
+
|
| 193 |
+
**Why**: Aligns with our existing node–link dependency metaphor. Shows both hierarchy (domain → subcategory → process) and cross-links (e.g., via `namedCollections`). Zoom and pan are standard (D3 zoom on SVG group). ~120 nodes is trivial for D3 force. Breadcrumbs solve "where am I?" when zoomed.
|
| 194 |
+
|
| 195 |
+
**Data shape** (nodes + links for force-directed):
|
| 196 |
+
|
| 197 |
+
```json
|
| 198 |
+
{
|
| 199 |
+
"nodes": [
|
| 200 |
+
{ "id": "root", "name": "Mathematics", "level": 0 },
|
| 201 |
+
{ "id": "algebra", "name": "Algebra", "level": 1 },
|
| 202 |
+
{ "id": "analysis", "name": "Analysis", "level": 1 },
|
| 203 |
+
{ "id": "abstract_algebra", "name": "Abstract Algebra", "level": 2 },
|
| 204 |
+
{ "id": "abstract_algebra-group-theory", "name": "Group Theory", "level": 3, "processId": "abstract_algebra-group-theory",
|
| 205 |
+
"subcategory": "abstract_algebra", "url": "processes/abstract_algebra/abstract_algebra-group-theory.html" }
|
| 206 |
+
],
|
| 207 |
+
"links": [
|
| 208 |
+
{ "source": "root", "target": "algebra" },
|
| 209 |
+
{ "source": "algebra", "target": "abstract_algebra" },
|
| 210 |
+
{ "source": "abstract_algebra", "target": "abstract_algebra-group-theory" },
|
| 211 |
+
{ "source": "abstract_algebra-field-theory", "target": "abstract_algebra-group-theory" }
|
| 212 |
+
]
|
| 213 |
+
}
|
| 214 |
+
```
|
| 215 |
+
|
| 216 |
+
`level` drives hierarchy. `links` include tree edges (parent→child) and optional cross-edges (e.g., Field Theory → Group Theory). `processId` and `url` at leaves for linking.
|
| 217 |
+
|
| 218 |
+
---
|
| 219 |
+
|
| 220 |
+
## Metadata Extensions for the Chart
|
| 221 |
+
|
| 222 |
+
### 1. Domain Mapping (arXiv-Based)
|
| 223 |
+
|
| 224 |
+
Add to `metadata.json`:
|
| 225 |
+
|
| 226 |
+
```json
|
| 227 |
+
{
|
| 228 |
+
"domainHierarchy": {
|
| 229 |
+
"algebra": {
|
| 230 |
+
"name": "Algebra",
|
| 231 |
+
"arxiv": ["math.AC", "math.AG", "math.CT", "math.GR", "math.RA", "math.RT", "math.QA"],
|
| 232 |
+
"subcategories": ["abstract_algebra", "linear_algebra", "category_theory"]
|
| 233 |
+
},
|
| 234 |
+
"analysis": {
|
| 235 |
+
"name": "Analysis",
|
| 236 |
+
"arxiv": ["math.AP", "math.CA", "math.CV", "math.FA", "math.NA", "math.SP"],
|
| 237 |
+
"subcategories": ["calculus_analysis", "complex_analysis"]
|
| 238 |
+
},
|
| 239 |
+
"geometry_topology": {
|
| 240 |
+
"name": "Geometry & Topology",
|
| 241 |
+
"arxiv": ["math.AT", "math.DG", "math.GN", "math.GT", "math.MG", "math.SG"],
|
| 242 |
+
"subcategories": ["geometry_topology"]
|
| 243 |
+
},
|
| 244 |
+
"number_theory": {
|
| 245 |
+
"name": "Number Theory",
|
| 246 |
+
"arxiv": ["math.NT"],
|
| 247 |
+
"subcategories": ["number_theory"]
|
| 248 |
+
},
|
| 249 |
+
"discrete_logic": {
|
| 250 |
+
"name": "Discrete & Logic",
|
| 251 |
+
"arxiv": ["math.CO", "math.LO"],
|
| 252 |
+
"subcategories": ["discrete_mathematics", "foundations"]
|
| 253 |
+
},
|
| 254 |
+
"dynamical_systems": {
|
| 255 |
+
"name": "Dynamical Systems",
|
| 256 |
+
"arxiv": ["math.DS"],
|
| 257 |
+
"subcategories": []
|
| 258 |
+
},
|
| 259 |
+
"applied": {
|
| 260 |
+
"name": "Applied & Other",
|
| 261 |
+
"arxiv": ["math.GM", "math.MP", "math.OC", "math.PR", "math.ST"],
|
| 262 |
+
"subcategories": ["bioinformatics"]
|
| 263 |
+
}
|
| 264 |
+
},
|
| 265 |
+
"subcategoryToArxiv": {
|
| 266 |
+
"abstract_algebra": "math.GR",
|
| 267 |
+
"calculus_analysis": "math.CA",
|
| 268 |
+
"geometry_topology": "math.GT"
|
| 269 |
+
}
|
| 270 |
+
}
|
| 271 |
+
```
|
| 272 |
+
|
| 273 |
+
### 2. Optional: Process-Level "Domain" Override
|
| 274 |
+
|
| 275 |
+
For processes that span domains (e.g., Category Theory), allow:
|
| 276 |
+
|
| 277 |
+
```json
|
| 278 |
+
{ "id": "...", "domain": "algebra", "subcategory": "category_theory" }
|
| 279 |
+
```
|
| 280 |
+
|
| 281 |
+
Default: derive domain from subcategory via `domainHierarchy`.
|
| 282 |
+
|
| 283 |
+
---
|
| 284 |
+
|
| 285 |
+
## Interaction Design
|
| 286 |
+
|
| 287 |
+
### Zoom & Pan
|
| 288 |
+
- **Scroll** or **pinch**: zoom in/out
|
| 289 |
+
- **Drag**: pan
|
| 290 |
+
- **Double-click** a region: zoom to fit that region (focus)
|
| 291 |
+
- **Breadcrumb click**: jump back to that level
|
| 292 |
+
|
| 293 |
+
### Click Behavior
|
| 294 |
+
- **Level 1–2** (domain, subcategory): zoom in to show children
|
| 295 |
+
- **Level 3** (process): open process page in new tab (or same tab with back)
|
| 296 |
+
|
| 297 |
+
### Visual Feedback
|
| 298 |
+
- **Hover**: highlight region, show tooltip (name + count)
|
| 299 |
+
- **Focus**: breadcrumb updates; optional sidebar with list of processes in current view
|
| 300 |
+
- **Cross-links**: if we add graph overlay, dim non-adjacent regions when hovering a node with many connections
|
| 301 |
+
|
| 302 |
+
---
|
| 303 |
+
|
| 304 |
+
## Responsive & Accessibility
|
| 305 |
+
|
| 306 |
+
- **Mobile**: Touch pan/zoom; larger hit targets for small regions; consider "list view" fallback when zoomed to a subcategory
|
| 307 |
+
- **Keyboard**: Tab through regions, Enter to zoom/select
|
| 308 |
+
- **Screen readers**: Breadcrumb + list of current level's items as text
|
| 309 |
+
|
| 310 |
+
---
|
| 311 |
+
|
| 312 |
+
## Implementation Phases
|
| 313 |
+
|
| 314 |
+
### Phase 1: Static Hierarchy + Force-Directed Graph
|
| 315 |
+
- Add `domainHierarchy` (arXiv-based) to metadata
|
| 316 |
+
- Build nodes + links from processes (domain → subcategory → process)
|
| 317 |
+
- Single HTML page with D3 force-directed graph + zoom/pan
|
| 318 |
+
- **Deliverable**: Working "Whole of Mathematics" graph with our current 98 processes
|
| 319 |
+
|
| 320 |
+
### Phase 2: Process Links
|
| 321 |
+
- Leaf nodes (processes) link to process HTML (using existing URL pattern)
|
| 322 |
+
- Breadcrumb navigation
|
| 323 |
+
- **Deliverable**: Full drill-down from root to process page
|
| 324 |
+
|
| 325 |
+
### Phase 3: Polish
|
| 326 |
+
- Tooltips, legend (colors = domains or arXiv codes)
|
| 327 |
+
- Optional "list view" toggle for current level
|
| 328 |
+
- **Deliverable**: Production-ready interactive chart
|
| 329 |
+
|
| 330 |
+
### Phase 4: Cross-Links (Optional)
|
| 331 |
+
- Use `namedCollections` to draw edges between related processes
|
| 332 |
+
- Or: "Related" panel when hovering a process
|
| 333 |
+
- **Deliverable**: Relationship-aware exploration
|
| 334 |
+
|
| 335 |
+
---
|
| 336 |
+
|
| 337 |
+
## Growing With the Collection
|
| 338 |
+
|
| 339 |
+
As we add:
|
| 340 |
+
- **New subcategories** (complex_analysis, landmark_theorems, formal_verification, ai_mathematics): extend `domainHierarchy` and subcategory→arXiv mapping
|
| 341 |
+
- **New processes**: they appear automatically (nodes + links derived from metadata)
|
| 342 |
+
- **Named mathematicians** (`namedCollections`): cross-edges between processes in the same collection; or a *second* view—"By Mathematician"—same graph structure but nodes grouped by collection. Toggle: "By Topic" | "By Mathematician"
|
| 343 |
+
- **New arXiv codes**: add to `domainHierarchy`; graph reflows
|
| 344 |
+
|
| 345 |
+
The chart is **always generated from metadata**—no manual diagram maintenance.
|
| 346 |
+
|
| 347 |
+
---
|
| 348 |
+
|
| 349 |
+
## Alternative: "Map" Metaphor (Future Enhancement)
|
| 350 |
+
|
| 351 |
+
For a more geographic feel:
|
| 352 |
+
- **Continents** = domains (irregular shapes, not rectangles)
|
| 353 |
+
- **Countries** = subcategories
|
| 354 |
+
- **Cities** = processes (dots or small regions)
|
| 355 |
+
- Layout: Voronoi tessellation or force-directed placement with "gravity" to keep siblings near each other
|
| 356 |
+
- Could use **MapLibre** or **Leaflet** with a custom "projection" that maps our hierarchy to 2D—playful and memorable
|
| 357 |
+
|
| 358 |
+
---
|
| 359 |
+
|
| 360 |
+
## Summary
|
| 361 |
+
|
| 362 |
+
| Aspect | Choice |
|
| 363 |
+
|--------|--------|
|
| 364 |
+
| **Visualization** | D3 force-directed graph (primary) |
|
| 365 |
+
| **Domain taxonomy** | arXiv math.XX (math.AC, math.NT, etc.) |
|
| 366 |
+
| **Data** | Nodes + links derived from metadata + `domainHierarchy` |
|
| 367 |
+
| **Levels** | 3: Domain → Subcategory → Process |
|
| 368 |
+
| **Edges** | Tree (parent→child) + optional cross-links (`namedCollections`) |
|
| 369 |
+
| **Interaction** | Zoom, pan, click-to-focus, breadcrumbs |
|
| 370 |
+
| **Leaf action** | Open process HTML page |
|
| 371 |
+
| **Growth** | Add to metadata; chart updates automatically |
|
| 372 |
+
| **Future** | Sunburst, map metaphor—explore later |
|
| 373 |
+
|
| 374 |
+
The "Whole of Mathematics" chart becomes the **entry point** to the database—a node–link visual index that matches our dependency-graph metaphor and scales with the collection.
|
biology_processes.html
CHANGED
|
@@ -114,15 +114,15 @@
|
|
| 114 |
<div class="container">
|
| 115 |
<h1>Biology Processes - Programming Framework Analysis</h1>
|
| 116 |
|
| 117 |
-
<div class="glmp-link"
|
| 118 |
<h3>🔗 GLMP (Genome Logic Modeling Project) Connection</h3>
|
| 119 |
-
<p>This analysis is based on the comprehensive biological dataset from the <strong>Genome Logic Modeling Project (GLMP)</strong>, which contains
|
| 120 |
<p><strong>GLMP Resources:</strong></p>
|
| 121 |
<ul>
|
| 122 |
-
<li><a href="https://
|
| 123 |
-
<li><a href="https://
|
| 124 |
</ul>
|
| 125 |
-
<p>The GLMP represents the
|
| 126 |
</div>
|
| 127 |
|
| 128 |
<p>This document presents representative biological processes analyzed using the Programming Framework methodology. Each process is represented as a computational flowchart with standardized color coding: Red for triggers/inputs, Yellow for structures/objects, Green for processing/operations, Blue for intermediates/states, and Violet for products/outputs. Yellow nodes use black text for optimal readability, while all other colors use white text.</p>
|
|
|
|
| 114 |
<div class="container">
|
| 115 |
<h1>Biology Processes - Programming Framework Analysis</h1>
|
| 116 |
|
| 117 |
+
<div class="glmp-link">
|
| 118 |
<h3>🔗 GLMP (Genome Logic Modeling Project) Connection</h3>
|
| 119 |
+
<p>This analysis is based on the comprehensive biological dataset from the <strong>Genome Logic Modeling Project (GLMP)</strong>, which contains 297+ analyzed biological processes across multiple organisms and systems.</p>
|
| 120 |
<p><strong>GLMP Resources:</strong></p>
|
| 121 |
<ul>
|
| 122 |
+
<li><a href="https://huggingface.co/spaces/garywelz/glmp" target="_blank">GLMP Hugging Face Space</a> - Live demonstration and evidence base</li>
|
| 123 |
+
<li><a href="https://github.com/garywelz/glmp" target="_blank">GLMP GitHub Repository</a> - Complete dataset and methodology</li>
|
| 124 |
</ul>
|
| 125 |
+
<p>The GLMP represents the most comprehensive biological computing system analysis ever created, demonstrating how biological systems function as sophisticated computational programs with complex regulatory logic, decision trees, and feedback mechanisms.</p>
|
| 126 |
</div>
|
| 127 |
|
| 128 |
<p>This document presents representative biological processes analyzed using the Programming Framework methodology. Each process is represented as a computational flowchart with standardized color coding: Red for triggers/inputs, Yellow for structures/objects, Green for processing/operations, Blue for intermediates/states, and Violet for products/outputs. Yellow nodes use black text for optimal readability, while all other colors use white text.</p>
|
chemistry-database-table.html
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<!DOCTYPE html>
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<html lang="en">
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<head>
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<meta charset="UTF-8">
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<meta name="viewport" content="width=device-width, initial-scale=1.0">
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<title>Chemistry Processes Database</title>
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<style>
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body {
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font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif;
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margin: 0;
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padding: 20px;
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background: linear-gradient(135deg, #667eea 0%, #764ba2 100%);
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min-height: 100vh;
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background: white;
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border-radius: 15px;
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box-shadow: 0 20px 40px rgba(0,0,0,0.1);
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overflow: hidden;
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background: linear-gradient(135deg, #e74c3c 0%, #c0392b 100%);
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color: white;
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padding: 30px;
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text-align: center;
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margin: 0;
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font-weight: 300;
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opacity: 0.8;
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font-size: 1.1em;
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display: grid;
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grid-template-columns: repeat(auto-fit, minmax(200px, 1fr));
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gap: 20px;
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background: #f8f9fa;
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background: white;
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text-align: center;
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margin: -30px -30px 20px -30px;
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table {
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width: 100%;
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border-collapse: collapse;
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th, td {
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th {
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background: #f8f9fa;
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.process-name {
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font-weight: 600;
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color: #2c3e50;
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max-width: 300px;
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.process-name a {
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text-decoration: none;
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.process-name a:hover {
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text-decoration: underline;
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.subcategory {
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font-size: 0.8em;
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color: #c0392b;
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}
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.complexity {
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padding: 4px 8px;
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border-radius: 4px;
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font-size: 0.8em;
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font-weight: 600;
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}
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.complexity.low {
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background: #d5f4e6;
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color: #27ae60;
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.complexity.medium {
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.complexity.detailed, .complexity.high {
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.number {
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text-align: center;
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font-weight: 600;
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}
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.loading {
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text-align: center;
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padding: 50px;
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color: #7f8c8d;
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.error {
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text-align: center;
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padding: 50px;
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color: #e74c3c;
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}
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.refresh-btn {
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background: #e74c3c;
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color: white;
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border: none;
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padding: 10px 20px;
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border-radius: 5px;
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cursor: pointer;
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font-size: 0.9em;
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margin: 10px;
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background: #c0392b;
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padding: 30px;
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border-top: 1px solid #ecf0f1;
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box-shadow: 0 2px 10px rgba(0,0,0,0.05);
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font-weight: 600;
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.color-legend {
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margin-bottom: 15px;
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.color-grid {
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display: grid;
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grid-template-columns: repeat(auto-fit, minmax(200px, 1fr));
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gap: 15px;
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.color-item {
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gap: 10px;
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padding: 10px;
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background: white;
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border-radius: 5px;
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}
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.color-box {
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width: 30px;
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height: 30px;
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border-radius: 4px;
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border: 1px solid #ddd;
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}
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</style>
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</head>
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<body>
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<div class="container">
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<div class="header">
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<h1>⚗️ Chemistry Processes Database</h1>
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<p>Programming Framework - Interactive Database Analysis</p>
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<button class="refresh-btn" onclick="loadData()">🔄 Refresh Data</button>
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</div>
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<div id="loading" class="loading">
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<h3>Loading chemistry processes database...</h3>
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<p>Fetching process data from metadata.json</p>
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</div>
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<div id="error" class="error" style="display: none;">
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<h3>❌ Error Loading Data</h3>
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<p>Could not fetch chemistry processes metadata. Please check your connection and try again.</p>
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</div>
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<div id="content" style="display: none;">
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<div class="stats-grid" id="statsGrid">
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<!-- Stats will be populated here -->
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</div>
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<div class="table-container">
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<div class="table-header">
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<h2>📊 Process Database Table</h2>
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<p style="margin: 10px 0 0 0; opacity: 0.8; font-size: 0.9em;">
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💡 Click on any process name to view its interactive flowchart
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</p>
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</div>
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<table id="processTable">
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<thead>
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<tr>
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<th onclick="sortTable(0)">Process Name ↕</th>
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<th onclick="sortTable(1)">Subcategory ↕</th>
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<th onclick="sortTable(2)">Complexity ↕</th>
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<th onclick="sortTable(3)">Nodes ↕</th>
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<th onclick="sortTable(4)">Edges ↕</th>
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<th onclick="sortTable(5)">AND Gates ↕</th>
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<th onclick="sortTable(6)">OR Gates ↕</th>
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</tr>
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</thead>
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<tbody id="tableBody">
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<!-- Data will be populated here -->
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</tbody>
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</table>
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</div>
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<div class="breakdown">
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<h3>📈 Database Analysis</h3>
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<div class="breakdown-grid" id="breakdownGrid">
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<!-- Breakdown will be populated here -->
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</div>
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</div>
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<div class="color-legend">
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<h3>🎨 Color Scheme (5-Color System)</h3>
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<div class="color-grid">
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<div class="color-item">
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<div class="color-box" style="background: #ff6b6b;"></div>
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<div>
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<strong>Red</strong><br>
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<small>Triggers & Inputs</small>
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</div>
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</div>
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<div class="color-item">
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<div class="color-box" style="background: #ffd43b;"></div>
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<div>
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<strong>Yellow</strong><br>
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<small>Structures & Objects</small>
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</div>
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</div>
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<div class="color-item">
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<div class="color-box" style="background: #51cf66;"></div>
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<div>
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<strong>Green</strong><br>
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<small>Processing & Operations</small>
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</div>
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</div>
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| 356 |
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<div class="color-item">
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| 357 |
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<div class="color-box" style="background: #74c0fc;"></div>
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<div>
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<strong>Blue</strong><br>
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<small>Intermediates & States</small>
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</div>
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</div>
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<div class="color-item">
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<div class="color-box" style="background: #b197fc;"></div>
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<div>
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<strong>Violet</strong><br>
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<small>Products & Outputs</small>
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</div>
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</div>
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</div>
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</div>
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</div>
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</div>
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<script>
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// Determine metadata URL based on where this file is hosted
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const METADATA_URL = window.location.hostname.includes('storage.googleapis.com')
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? 'https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/chemistry-processes-database/metadata.json'
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: (window.location.hostname.includes('huggingface.co'))
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? './chemistry-processes-database/metadata.json'
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: './chemistry-processes-database/metadata.json';
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let currentSortColumn = -1;
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let sortDirection = 1;
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let processes = [];
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async function loadData() {
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console.log('🔄 Starting data load from:', METADATA_URL);
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document.getElementById('loading').style.display = 'block';
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document.getElementById('error').style.display = 'none';
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document.getElementById('content').style.display = 'none';
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try {
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const response = await fetch(METADATA_URL);
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if (!response.ok) {
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throw new Error(`HTTP ${response.status}: ${response.statusText}`);
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}
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const data = await response.json();
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console.log('✅ Data loaded successfully:', data.totalProcesses, 'processes');
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processes = data.processes || [];
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populateData(data);
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document.getElementById('loading').style.display = 'none';
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document.getElementById('content').style.display = 'block';
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} catch (error) {
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console.error('❌ Error loading data:', error);
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document.getElementById('loading').style.display = 'none';
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document.getElementById('error').style.display = 'block';
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document.getElementById('error').innerHTML = `
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<h3>❌ Error Loading Data</h3>
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<p>Could not fetch chemistry processes metadata.</p>
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<p style="font-size: 0.9em; color: #95a5a6; margin-top: 10px;">
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Error: ${error.message}
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</p>
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`;
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}
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}
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function populateData(data) {
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// Populate statistics
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const stats = data.statistics || {};
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document.getElementById('statsGrid').innerHTML = `
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<div class="stat-card">
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| 427 |
-
<div class="stat-number">${data.totalProcesses || 0}</div>
|
| 428 |
-
<div class="stat-label">Total Processes</div>
|
| 429 |
-
</div>
|
| 430 |
-
<div class="stat-card">
|
| 431 |
-
<div class="stat-number">${stats.totalNodes || 0}</div>
|
| 432 |
-
<div class="stat-label">Total Nodes</div>
|
| 433 |
-
</div>
|
| 434 |
-
<div class="stat-card">
|
| 435 |
-
<div class="stat-number">${stats.totalEdges || 0}</div>
|
| 436 |
-
<div class="stat-label">Total Edges</div>
|
| 437 |
-
</div>
|
| 438 |
-
<div class="stat-card">
|
| 439 |
-
<div class="stat-number">${data.subcategories || 0}</div>
|
| 440 |
-
<div class="stat-label">Subcategories</div>
|
| 441 |
-
</div>
|
| 442 |
-
`;
|
| 443 |
-
|
| 444 |
-
// Populate table
|
| 445 |
-
const tableBody = document.getElementById('tableBody');
|
| 446 |
-
tableBody.innerHTML = '';
|
| 447 |
-
|
| 448 |
-
const processList = data.processes || [];
|
| 449 |
-
processList.forEach(process => {
|
| 450 |
-
const row = document.createElement('tr');
|
| 451 |
-
// Determine viewer URL based on host
|
| 452 |
-
const isGCS = window.location.hostname.includes('storage.googleapis.com');
|
| 453 |
-
const isHF = window.location.hostname.includes('huggingface.co');
|
| 454 |
-
const viewerUrl = isGCS
|
| 455 |
-
? `https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/chemistry-processes-database/processes/${process.subcategory}/${process.id}.html`
|
| 456 |
-
: (isHF)
|
| 457 |
-
? `./chemistry-processes-database/processes/${process.subcategory}/${process.id}.html`
|
| 458 |
-
: `./processes/${process.subcategory}/${process.id}.html`;
|
| 459 |
-
row.innerHTML = `
|
| 460 |
-
<td class="process-name">
|
| 461 |
-
<a href="${viewerUrl}" target="_blank">${process.name}</a>
|
| 462 |
-
</td>
|
| 463 |
-
<td><span class="subcategory">${process.subcategory_name || process.subcategory}</span></td>
|
| 464 |
-
<td><span class="complexity ${process.complexity}">${process.complexity}</span></td>
|
| 465 |
-
<td class="number">${process.nodes}</td>
|
| 466 |
-
<td class="number">${process.edges}</td>
|
| 467 |
-
<td class="number">${process.andGates || 0}</td>
|
| 468 |
-
<td class="number">${process.orGates || 0}</td>
|
| 469 |
-
`;
|
| 470 |
-
tableBody.appendChild(row);
|
| 471 |
-
});
|
| 472 |
-
|
| 473 |
-
// Populate breakdown
|
| 474 |
-
const breakdown = {};
|
| 475 |
-
processList.forEach(p => {
|
| 476 |
-
const subcat = p.subcategory_name || p.subcategory;
|
| 477 |
-
breakdown[subcat] = (breakdown[subcat] || 0) + 1;
|
| 478 |
-
});
|
| 479 |
-
|
| 480 |
-
let breakdownHTML = '<div class="breakdown-card"><h4>Processes by Subcategory</h4>';
|
| 481 |
-
Object.entries(breakdown).sort((a, b) => b[1] - a[1]).forEach(([subcat, count]) => {
|
| 482 |
-
breakdownHTML += `
|
| 483 |
-
<div class="breakdown-item">
|
| 484 |
-
<span class="breakdown-label">${subcat}</span>
|
| 485 |
-
<span class="breakdown-count">${count}</span>
|
| 486 |
-
</div>
|
| 487 |
-
`;
|
| 488 |
-
});
|
| 489 |
-
breakdownHTML += '</div>';
|
| 490 |
-
|
| 491 |
-
const complexityBreakdown = {};
|
| 492 |
-
processList.forEach(p => {
|
| 493 |
-
const comp = p.complexity || 'unknown';
|
| 494 |
-
complexityBreakdown[comp] = (complexityBreakdown[comp] || 0) + 1;
|
| 495 |
-
});
|
| 496 |
-
|
| 497 |
-
breakdownHTML += '<div class="breakdown-card"><h4>Processes by Complexity</h4>';
|
| 498 |
-
Object.entries(complexityBreakdown).sort((a, b) => b[1] - a[1]).forEach(([comp, count]) => {
|
| 499 |
-
breakdownHTML += `
|
| 500 |
-
<div class="breakdown-item">
|
| 501 |
-
<span class="breakdown-label">${comp}</span>
|
| 502 |
-
<span class="breakdown-count">${count}</span>
|
| 503 |
-
</div>
|
| 504 |
-
`;
|
| 505 |
-
});
|
| 506 |
-
breakdownHTML += '</div>';
|
| 507 |
-
|
| 508 |
-
document.getElementById('breakdownGrid').innerHTML = breakdownHTML;
|
| 509 |
-
}
|
| 510 |
-
|
| 511 |
-
function sortTable(column) {
|
| 512 |
-
const table = document.getElementById('processTable');
|
| 513 |
-
const tbody = table.querySelector('tbody');
|
| 514 |
-
const rows = Array.from(tbody.querySelectorAll('tr'));
|
| 515 |
-
|
| 516 |
-
if (currentSortColumn === column) {
|
| 517 |
-
sortDirection *= -1;
|
| 518 |
-
} else {
|
| 519 |
-
currentSortColumn = column;
|
| 520 |
-
sortDirection = 1;
|
| 521 |
-
}
|
| 522 |
-
|
| 523 |
-
rows.sort((a, b) => {
|
| 524 |
-
const aText = a.cells[column].textContent.trim();
|
| 525 |
-
const bText = b.cells[column].textContent.trim();
|
| 526 |
-
|
| 527 |
-
// Try to parse as number
|
| 528 |
-
const aNum = parseFloat(aText);
|
| 529 |
-
const bNum = parseFloat(bText);
|
| 530 |
-
|
| 531 |
-
if (!isNaN(aNum) && !isNaN(bNum)) {
|
| 532 |
-
return (aNum - bNum) * sortDirection;
|
| 533 |
-
}
|
| 534 |
-
|
| 535 |
-
return aText.localeCompare(bText) * sortDirection;
|
| 536 |
-
});
|
| 537 |
-
|
| 538 |
-
rows.forEach(row => tbody.appendChild(row));
|
| 539 |
-
}
|
| 540 |
-
|
| 541 |
-
// Load data on page load
|
| 542 |
-
loadData();
|
| 543 |
-
</script>
|
| 544 |
-
</body>
|
| 545 |
-
</html>
|
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|
chemistry_examples.html
DELETED
|
@@ -1,609 +0,0 @@
|
|
| 1 |
-
<!DOCTYPE html>
|
| 2 |
-
<html lang="en">
|
| 3 |
-
<head>
|
| 4 |
-
<meta charset="UTF-8" />
|
| 5 |
-
<meta name="viewport" content="width=device-width, initial-scale=1" />
|
| 6 |
-
<title>Chemistry Examples - Programming Framework Analysis</title>
|
| 7 |
-
<style>
|
| 8 |
-
body {
|
| 9 |
-
font-family: 'Times New Roman', Times, serif, 'Arial Unicode MS';
|
| 10 |
-
margin: 0;
|
| 11 |
-
background: #ffffff;
|
| 12 |
-
color: #000000;
|
| 13 |
-
line-height: 1.6;
|
| 14 |
-
font-size: 12pt;
|
| 15 |
-
}
|
| 16 |
-
.container {
|
| 17 |
-
max-width: 1000px;
|
| 18 |
-
margin: 0 auto;
|
| 19 |
-
padding: 1.5rem;
|
| 20 |
-
}
|
| 21 |
-
h1, h2, h3 {
|
| 22 |
-
color: #000000;
|
| 23 |
-
margin-top: 1.5rem;
|
| 24 |
-
margin-bottom: 0.75rem;
|
| 25 |
-
}
|
| 26 |
-
h1 {
|
| 27 |
-
font-size: 18pt;
|
| 28 |
-
text-align: center;
|
| 29 |
-
}
|
| 30 |
-
h2 {
|
| 31 |
-
font-size: 16pt;
|
| 32 |
-
border-bottom: 2px solid #000;
|
| 33 |
-
padding-bottom: 0.5rem;
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h3 {
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p {
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margin-bottom: 1rem;
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text-align: justify;
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}
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.figure {
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margin: 1rem 0;
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text-align: center;
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border: 1px solid #ccc;
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padding: 1rem;
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background: #f9f9f9;
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}
|
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.figure-caption {
|
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margin-top: 1rem;
|
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font-style: italic;
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text-align: left;
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}
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.mermaid {
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background: white;
|
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padding: 1rem;
|
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border-radius: 4px;
|
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}
|
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</style>
|
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<script src="https://cdn.jsdelivr.net/npm/mermaid@10.6.1/dist/mermaid.min.js"></script>
|
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<script>
|
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mermaid.initialize({
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startOnLoad: true,
|
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theme: 'default',
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flowchart: {
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useMaxWidth: false,
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htmlLabels: true,
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curve: 'linear',
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nodeSpacing: 50,
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rankSpacing: 50,
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padding: 20
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},
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themeVariables: {
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fontFamily: 'Arial Unicode MS, Arial, sans-serif'
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});
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</script>
|
| 78 |
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</head>
|
| 79 |
-
<body>
|
| 80 |
-
<div class="container">
|
| 81 |
-
<h1>Chemistry Examples - Programming Framework Analysis</h1>
|
| 82 |
-
|
| 83 |
-
<p>This document presents chemistry processes analyzed using the Programming Framework methodology. Each process is represented as a computational flowchart with standardized color coding: Red for triggers/inputs, Yellow for structures/objects, Green for processing/operations, Blue for intermediates/states, and Violet for products/outputs. Yellow nodes use black text for optimal readability, while all other colors use white text.</p>
|
| 84 |
-
|
| 85 |
-
<h2>1. Catalytic Hydrogenation Process</h2>
|
| 86 |
-
<div class="figure">
|
| 87 |
-
<div class="mermaid">
|
| 88 |
-
graph TD
|
| 89 |
-
A[Alkene Substrate] --> B[Substrate Analysis]
|
| 90 |
-
C[Hydrogen Gas H₂] --> D[Gas Supply]
|
| 91 |
-
E[Catalyst Pt/Pd/Ni] --> F[Catalyst Preparation]
|
| 92 |
-
|
| 93 |
-
B --> G[Substrate Purity Check]
|
| 94 |
-
D --> H[Gas Pressure Control]
|
| 95 |
-
F --> I[Catalyst Activation]
|
| 96 |
-
|
| 97 |
-
G --> J[Reaction Vessel Loading]
|
| 98 |
-
H --> K[Pressure Regulation]
|
| 99 |
-
I --> L[Catalyst Dispersion]
|
| 100 |
-
|
| 101 |
-
J --> M[Substrate Adsorption]
|
| 102 |
-
K --> N[Hydrogen Dissociation]
|
| 103 |
-
L --> O[Active Site Formation]
|
| 104 |
-
|
| 105 |
-
M --> P[π-Bond Activation]
|
| 106 |
-
N --> Q[H• Radical Formation]
|
| 107 |
-
O --> R[Catalytic Surface]
|
| 108 |
-
|
| 109 |
-
P --> S[First H Addition]
|
| 110 |
-
Q --> T[Hydrogen Transfer]
|
| 111 |
-
R --> U[Surface Complex]
|
| 112 |
-
|
| 113 |
-
S --> V[Alkyl Intermediate]
|
| 114 |
-
T --> W[Second H Addition]
|
| 115 |
-
U --> X[Product Desorption]
|
| 116 |
-
|
| 117 |
-
V --> Y[Alkane Product]
|
| 118 |
-
W --> Z[Complete Hydrogenation]
|
| 119 |
-
X --> AA[Catalyst Recovery]
|
| 120 |
-
|
| 121 |
-
%% Red: Reactants & Inputs
|
| 122 |
-
style A fill:#ff6b6b,color:#fff
|
| 123 |
-
style C fill:#ff6b6b,color:#fff
|
| 124 |
-
style E fill:#ff6b6b,color:#fff
|
| 125 |
-
|
| 126 |
-
%% Yellow: Catalysts & Equipment
|
| 127 |
-
style B fill:#ffd43b,color:#000
|
| 128 |
-
style D fill:#ffd43b,color:#000
|
| 129 |
-
style F fill:#ffd43b,color:#000
|
| 130 |
-
style G fill:#ffd43b,color:#000
|
| 131 |
-
style H fill:#ffd43b,color:#000
|
| 132 |
-
style I fill:#ffd43b,color:#000
|
| 133 |
-
style J fill:#ffd43b,color:#000
|
| 134 |
-
style K fill:#ffd43b,color:#000
|
| 135 |
-
style L fill:#ffd43b,color:#000
|
| 136 |
-
|
| 137 |
-
%% Green: Chemical Reactions
|
| 138 |
-
style M fill:#51cf66,color:#fff
|
| 139 |
-
style N fill:#51cf66,color:#fff
|
| 140 |
-
style O fill:#51cf66,color:#fff
|
| 141 |
-
style P fill:#51cf66,color:#fff
|
| 142 |
-
style Q fill:#51cf66,color:#fff
|
| 143 |
-
style R fill:#51cf66,color:#fff
|
| 144 |
-
style S fill:#51cf66,color:#fff
|
| 145 |
-
style T fill:#51cf66,color:#fff
|
| 146 |
-
style U fill:#51cf66,color:#fff
|
| 147 |
-
style W fill:#51cf66,color:#fff
|
| 148 |
-
style X fill:#51cf66,color:#fff
|
| 149 |
-
|
| 150 |
-
%% Blue: Intermediates & States
|
| 151 |
-
style V fill:#74c0fc,color:#fff
|
| 152 |
-
|
| 153 |
-
%% Violet: Final Products
|
| 154 |
-
style Y fill:#b197fc,color:#fff
|
| 155 |
-
style Z fill:#b197fc,color:#fff
|
| 156 |
-
style AA fill:#b197fc,color:#fff
|
| 157 |
-
</div>
|
| 158 |
-
|
| 159 |
-
<div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;">
|
| 160 |
-
<div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
|
| 161 |
-
<span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Reactants & Catalysts
|
| 162 |
-
</div>
|
| 163 |
-
<div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
|
| 164 |
-
<span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Reaction Vessels & Equipment
|
| 165 |
-
</div>
|
| 166 |
-
<div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
|
| 167 |
-
<span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Chemical Reactions & Transformations
|
| 168 |
-
</div>
|
| 169 |
-
<div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
|
| 170 |
-
<span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates
|
| 171 |
-
</div>
|
| 172 |
-
<div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
|
| 173 |
-
<span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#b197fc;"></span>Products
|
| 174 |
-
</div>
|
| 175 |
-
</div>
|
| 176 |
-
|
| 177 |
-
<div class="figure-caption">
|
| 178 |
-
<strong>Figure 1.</strong> Catalytic Hydrogenation Process. This chemistry process visualization demonstrates catalytic reaction mechanisms. The flowchart shows reactant inputs, reaction vessels and equipment, chemical reactions and transformations, intermediate species, and final products.
|
| 179 |
-
</div>
|
| 180 |
-
</div>
|
| 181 |
-
|
| 182 |
-
<h2>2. Polymerization Process</h2>
|
| 183 |
-
<div class="figure">
|
| 184 |
-
<div class="mermaid">
|
| 185 |
-
graph TD
|
| 186 |
-
%% Initial Setup
|
| 187 |
-
%% Input Conditions
|
| 188 |
-
A2[Monomers] --> B2[Monomer Analysis]
|
| 189 |
-
C2[Initiator] --> D2[Initiator Preparation]
|
| 190 |
-
E2[Solvent/Medium] --> F2[Reaction Medium]
|
| 191 |
-
%% Reaction Setup
|
| 192 |
-
B2 --> G2[Monomer Purity Check]
|
| 193 |
-
D2 --> H2[Initiator Activation]
|
| 194 |
-
F2 --> I2[Medium Preparation]
|
| 195 |
-
%% Initiation
|
| 196 |
-
G2 --> J2[Monomer Solution]
|
| 197 |
-
H2 --> K2[Radical Formation]
|
| 198 |
-
I2 --> L2[Temperature Control]
|
| 199 |
-
%% Polymerization Initiation
|
| 200 |
-
J2 --> M2[Monomer Concentration]
|
| 201 |
-
K2 --> N2[Initiator Decomposition]
|
| 202 |
-
L2 --> O2[Reaction Conditions]
|
| 203 |
-
%% Propagation
|
| 204 |
-
M2 --> P2[Radical Addition]
|
| 205 |
-
N2 --> Q2[Chain Initiation]
|
| 206 |
-
O2 --> R2[Chain Growth]
|
| 207 |
-
%% Chain Growth
|
| 208 |
-
P2 --> S2[Monomer Addition]
|
| 209 |
-
Q2 --> T2[Active Chain End]
|
| 210 |
-
R2 --> U2[Polymer Chain]
|
| 211 |
-
%% Termination
|
| 212 |
-
S2 --> V2[Chain Propagation]
|
| 213 |
-
T2 --> W2[Chain Transfer]
|
| 214 |
-
U2 --> X2[Chain Termination]
|
| 215 |
-
%% Final Products
|
| 216 |
-
V2 --> Y2[Polymer Formation]
|
| 217 |
-
W2 --> Z2[Molecular Weight Control]
|
| 218 |
-
X2 --> AA2[Reaction Quenching]
|
| 219 |
-
%% Process Control
|
| 220 |
-
Y2 --> BB2[Polymer Characterization]
|
| 221 |
-
Z2 --> CC2[Molecular Weight Analysis]
|
| 222 |
-
AA2 --> DD2[Product Isolation]
|
| 223 |
-
%% Output
|
| 224 |
-
BB2 --> EE2[Polymerization Complete]
|
| 225 |
-
CC2 --> FF2[Quality Control]
|
| 226 |
-
DD2 --> GG2[Product Recovery]
|
| 227 |
-
%% Styling - Chemistry Color Scheme
|
| 228 |
-
%% Styling - Biological Color Scheme
|
| 229 |
-
style A2 fill:#ff6b6b,color:#fff
|
| 230 |
-
style C2 fill:#ff6b6b,color:#fff
|
| 231 |
-
style E2 fill:#ff6b6b,color:#fff
|
| 232 |
-
style G2 fill:#ffd43b,color:#000
|
| 233 |
-
style H2 fill:#ffd43b,color:#000
|
| 234 |
-
style I2 fill:#ffd43b,color:#000
|
| 235 |
-
style J2 fill:#ffd43b,color:#000
|
| 236 |
-
style K2 fill:#ffd43b,color:#000
|
| 237 |
-
style L2 fill:#ffd43b,color:#000
|
| 238 |
-
style M2 fill:#51cf66,color:#fff
|
| 239 |
-
style N2 fill:#51cf66,color:#fff
|
| 240 |
-
style O2 fill:#51cf66,color:#fff
|
| 241 |
-
style P2 fill:#51cf66,color:#fff
|
| 242 |
-
style Q2 fill:#51cf66,color:#fff
|
| 243 |
-
style R2 fill:#51cf66,color:#fff
|
| 244 |
-
style S2 fill:#51cf66,color:#fff
|
| 245 |
-
style T2 fill:#51cf66,color:#fff
|
| 246 |
-
style U2 fill:#51cf66,color:#fff
|
| 247 |
-
style V2 fill:#51cf66,color:#fff
|
| 248 |
-
style W2 fill:#51cf66,color:#fff
|
| 249 |
-
style X2 fill:#51cf66,color:#fff
|
| 250 |
-
style B2 fill:#74c0fc,color:#fff
|
| 251 |
-
style D2 fill:#74c0fc,color:#fff
|
| 252 |
-
style F2 fill:#74c0fc,color:#fff
|
| 253 |
-
style Y2 fill:#74c0fc,color:#fff
|
| 254 |
-
style Z2 fill:#74c0fc,color:#fff
|
| 255 |
-
style AA2 fill:#74c0fc,color:#fff
|
| 256 |
-
style BB2 fill:#74c0fc,color:#fff
|
| 257 |
-
style CC2 fill:#74c0fc,color:#fff
|
| 258 |
-
style DD2 fill:#74c0fc,color:#fff
|
| 259 |
-
style EE2 fill:#b197fc,color:#fff
|
| 260 |
-
style FF2 fill:#b197fc,color:#fff
|
| 261 |
-
style GG2 fill:#b197fc,color:#fff
|
| 262 |
-
</div>
|
| 263 |
-
|
| 264 |
-
<div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;">
|
| 265 |
-
<div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
|
| 266 |
-
<span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Reactants & Initiators
|
| 267 |
-
</div>
|
| 268 |
-
<div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
|
| 269 |
-
<span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Reaction Vessels & Equipment
|
| 270 |
-
</div>
|
| 271 |
-
<div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
|
| 272 |
-
<span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Polymerization Reactions
|
| 273 |
-
</div>
|
| 274 |
-
<div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
|
| 275 |
-
<span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates
|
| 276 |
-
</div>
|
| 277 |
-
<div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
|
| 278 |
-
<span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#b197fc;"></span>Products
|
| 279 |
-
</div>
|
| 280 |
-
</div>
|
| 281 |
-
|
| 282 |
-
<div class="figure-caption">
|
| 283 |
-
<strong>Figure 2.</strong> Polymerization Process. This chemistry process visualization demonstrates polymer synthesis mechanisms. The flowchart shows monomer inputs, reaction vessels and equipment, polymerization reactions, intermediate species, and final polymer products.
|
| 284 |
-
</div>
|
| 285 |
-
</div>
|
| 286 |
-
|
| 287 |
-
<h2>3. Acid-Base Titration Process</h2>
|
| 288 |
-
<div class="figure">
|
| 289 |
-
<div class="mermaid">
|
| 290 |
-
graph TD
|
| 291 |
-
%% Initial Setup
|
| 292 |
-
%% Input Conditions
|
| 293 |
-
A3[Acid Solution] --> B3[Acid Analysis]
|
| 294 |
-
C3[Base Solution] --> D3[Base Analysis]
|
| 295 |
-
E3[Indicator] --> F3[Indicator Selection]
|
| 296 |
-
%% Solution Preparation
|
| 297 |
-
B3 --> G3[Acid Concentration]
|
| 298 |
-
D3 --> H3[Base Concentration]
|
| 299 |
-
F3 --> I3[Indicator Preparation]
|
| 300 |
-
%% Titration Setup
|
| 301 |
-
G3 --> J3[Acid in Burette]
|
| 302 |
-
H3 --> K3[Base in Flask]
|
| 303 |
-
I3 --> L3[Indicator Addition]
|
| 304 |
-
%% Titration Process
|
| 305 |
-
J3 --> M3[Initial pH Measurement]
|
| 306 |
-
K3 --> N3[Base Volume Measurement]
|
| 307 |
-
L3 --> O3[Color Change Detection]
|
| 308 |
-
%% Acid-Base Reaction
|
| 309 |
-
M3 --> P3[Acid Addition]
|
| 310 |
-
N3 --> Q3[Base Consumption]
|
| 311 |
-
O3 --> R3[Equivalence Point]
|
| 312 |
-
%% pH Changes
|
| 313 |
-
P3 --> S3[H⁺ + OH⁻ → H₂O]
|
| 314 |
-
Q3 --> T3[Neutralization Reaction]
|
| 315 |
-
R3 --> U3[Stoichiometric Point]
|
| 316 |
-
%% Endpoint Detection
|
| 317 |
-
S3 --> V3[pH Monitoring]
|
| 318 |
-
T3 --> W3[Conductivity Changes]
|
| 319 |
-
U3 --> X3[Indicator Color Change]
|
| 320 |
-
%% Final Results
|
| 321 |
-
V3 --> Y3[Equivalence Point pH]
|
| 322 |
-
W3 --> Z3[Conductivity Minimum]
|
| 323 |
-
X3 --> AA3[Endpoint Detection]
|
| 324 |
-
%% Calculations
|
| 325 |
-
Y3 --> BB3[Concentration Calculation]
|
| 326 |
-
Z3 --> CC3[Volume Measurement]
|
| 327 |
-
AA3 --> DD3[Stoichiometric Analysis]
|
| 328 |
-
%% Output
|
| 329 |
-
BB3 --> EE3[Titration Complete]
|
| 330 |
-
CC3 --> FF3[Concentration Determined]
|
| 331 |
-
DD3 --> GG3[Analysis Results]
|
| 332 |
-
%% Styling - Chemistry Color Scheme
|
| 333 |
-
%% Styling - Biological Color Scheme
|
| 334 |
-
style A3 fill:#ff6b6b,color:#fff
|
| 335 |
-
style C3 fill:#ff6b6b,color:#fff
|
| 336 |
-
style E3 fill:#ff6b6b,color:#fff
|
| 337 |
-
style G3 fill:#ffd43b,color:#000
|
| 338 |
-
style H3 fill:#ffd43b,color:#000
|
| 339 |
-
style I3 fill:#ffd43b,color:#000
|
| 340 |
-
style J3 fill:#ffd43b,color:#000
|
| 341 |
-
style K3 fill:#ffd43b,color:#000
|
| 342 |
-
style L3 fill:#ffd43b,color:#000
|
| 343 |
-
style M3 fill:#51cf66,color:#fff
|
| 344 |
-
style N3 fill:#51cf66,color:#fff
|
| 345 |
-
style O3 fill:#51cf66,color:#fff
|
| 346 |
-
style P3 fill:#51cf66,color:#fff
|
| 347 |
-
style Q3 fill:#51cf66,color:#fff
|
| 348 |
-
style R3 fill:#51cf66,color:#fff
|
| 349 |
-
style S3 fill:#51cf66,color:#fff
|
| 350 |
-
style T3 fill:#51cf66,color:#fff
|
| 351 |
-
style U3 fill:#51cf66,color:#fff
|
| 352 |
-
style V3 fill:#51cf66,color:#fff
|
| 353 |
-
style W3 fill:#51cf66,color:#fff
|
| 354 |
-
style X3 fill:#51cf66,color:#fff
|
| 355 |
-
style B3 fill:#74c0fc,color:#fff
|
| 356 |
-
style D3 fill:#74c0fc,color:#fff
|
| 357 |
-
style F3 fill:#74c0fc,color:#fff
|
| 358 |
-
style Y3 fill:#74c0fc,color:#fff
|
| 359 |
-
style Z3 fill:#74c0fc,color:#fff
|
| 360 |
-
style AA3 fill:#74c0fc,color:#fff
|
| 361 |
-
style BB3 fill:#74c0fc,color:#fff
|
| 362 |
-
style CC3 fill:#74c0fc,color:#fff
|
| 363 |
-
style DD3 fill:#74c0fc,color:#fff
|
| 364 |
-
style EE3 fill:#b197fc,color:#fff
|
| 365 |
-
style FF3 fill:#b197fc,color:#fff
|
| 366 |
-
style GG3 fill:#b197fc,color:#fff
|
| 367 |
-
</div>
|
| 368 |
-
|
| 369 |
-
<div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;">
|
| 370 |
-
<div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
|
| 371 |
-
<span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Reactants & Indicators
|
| 372 |
-
</div>
|
| 373 |
-
<div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
|
| 374 |
-
<span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Titration Equipment
|
| 375 |
-
</div>
|
| 376 |
-
<div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
|
| 377 |
-
<span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Neutralization Reactions
|
| 378 |
-
</div>
|
| 379 |
-
<div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
|
| 380 |
-
<span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates
|
| 381 |
-
</div>
|
| 382 |
-
<div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
|
| 383 |
-
<span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#b197fc;"></span>Products
|
| 384 |
-
</div>
|
| 385 |
-
</div>
|
| 386 |
-
|
| 387 |
-
<div class="figure-caption">
|
| 388 |
-
<strong>Figure 3.</strong> Acid-Base Titration Process. This chemistry process visualization demonstrates analytical chemistry procedures. The flowchart shows reactant inputs, titration equipment, neutralization reactions, intermediate measurements, and final analytical results.
|
| 389 |
-
</div>
|
| 390 |
-
</div>
|
| 391 |
-
|
| 392 |
-
<h2>4. Electrochemical Cell Process</h2>
|
| 393 |
-
<div class="figure">
|
| 394 |
-
<div class="mermaid">
|
| 395 |
-
graph TD
|
| 396 |
-
%% Initial Setup
|
| 397 |
-
%% Input Conditions
|
| 398 |
-
A4[Anode Material] --> B4[Anode Analysis]
|
| 399 |
-
C4[Cathode Material] --> D4[Cathode Analysis]
|
| 400 |
-
E4[Electrolyte] --> F4[Electrolyte Preparation]
|
| 401 |
-
%% Cell Setup
|
| 402 |
-
B4 --> G4[Anode Preparation]
|
| 403 |
-
D4 --> H4[Cathode Preparation]
|
| 404 |
-
F4 --> I4[Electrolyte Solution]
|
| 405 |
-
%% Electrochemical Setup
|
| 406 |
-
G4 --> J4[Anode Oxidation]
|
| 407 |
-
H4 --> K4[Cathode Reduction]
|
| 408 |
-
I4 --> L4[Ion Conduction]
|
| 409 |
-
%% Redox Reactions
|
| 410 |
-
J4 --> M4[Electron Release]
|
| 411 |
-
K4 --> N4[Electron Acceptance]
|
| 412 |
-
L4 --> O4[Ion Transport]
|
| 413 |
-
%% Current Flow
|
| 414 |
-
M4 --> P4[Oxidation Half-Reaction]
|
| 415 |
-
N4 --> Q4[Reduction Half-Reaction]
|
| 416 |
-
O4 --> R4[Salt Bridge]
|
| 417 |
-
%% Cell Operation
|
| 418 |
-
P4 --> S4[Anode → Cathode]
|
| 419 |
-
Q4 --> T4[Electron Flow]
|
| 420 |
-
R4 --> U4[Ion Migration]
|
| 421 |
-
%% Energy Production
|
| 422 |
-
S4 --> V4[Cell Potential]
|
| 423 |
-
T4 --> W4[Current Generation]
|
| 424 |
-
U4 --> X4[Charge Balance]
|
| 425 |
-
%% Performance
|
| 426 |
-
V4 --> Y4[Voltage Measurement]
|
| 427 |
-
W4 --> Z4[Current Measurement]
|
| 428 |
-
X4 --> AA4[Efficiency Calculation]
|
| 429 |
-
%% Output
|
| 430 |
-
Y4 --> BB4[Cell Performance]
|
| 431 |
-
Z4 --> CC4[Power Output]
|
| 432 |
-
AA4 --> DD4[Energy Conversion]
|
| 433 |
-
%% Final Results
|
| 434 |
-
BB4 --> EE4[Electrochemical Cell Active]
|
| 435 |
-
CC4 --> FF4[Electrical Energy Produced]
|
| 436 |
-
DD4 --> GG4[Conversion Efficiency]
|
| 437 |
-
%% Styling - Chemistry Color Scheme
|
| 438 |
-
%% Styling - Biological Color Scheme
|
| 439 |
-
style A4 fill:#ff6b6b,color:#fff
|
| 440 |
-
style C4 fill:#ff6b6b,color:#fff
|
| 441 |
-
style E4 fill:#ff6b6b,color:#fff
|
| 442 |
-
style G4 fill:#ffd43b,color:#000
|
| 443 |
-
style H4 fill:#ffd43b,color:#000
|
| 444 |
-
style I4 fill:#ffd43b,color:#000
|
| 445 |
-
style J4 fill:#ffd43b,color:#000
|
| 446 |
-
style K4 fill:#ffd43b,color:#000
|
| 447 |
-
style L4 fill:#ffd43b,color:#000
|
| 448 |
-
style M4 fill:#51cf66,color:#fff
|
| 449 |
-
style N4 fill:#51cf66,color:#fff
|
| 450 |
-
style O4 fill:#51cf66,color:#fff
|
| 451 |
-
style P4 fill:#51cf66,color:#fff
|
| 452 |
-
style Q4 fill:#51cf66,color:#fff
|
| 453 |
-
style R4 fill:#51cf66,color:#fff
|
| 454 |
-
style S4 fill:#51cf66,color:#fff
|
| 455 |
-
style T4 fill:#51cf66,color:#fff
|
| 456 |
-
style U4 fill:#51cf66,color:#fff
|
| 457 |
-
style V4 fill:#51cf66,color:#fff
|
| 458 |
-
style W4 fill:#51cf66,color:#fff
|
| 459 |
-
style X4 fill:#51cf66,color:#fff
|
| 460 |
-
style B4 fill:#74c0fc,color:#fff
|
| 461 |
-
style D4 fill:#74c0fc,color:#fff
|
| 462 |
-
style F4 fill:#74c0fc,color:#fff
|
| 463 |
-
style Y4 fill:#74c0fc,color:#fff
|
| 464 |
-
style Z4 fill:#74c0fc,color:#fff
|
| 465 |
-
style AA4 fill:#74c0fc,color:#fff
|
| 466 |
-
style BB4 fill:#74c0fc,color:#fff
|
| 467 |
-
style CC4 fill:#74c0fc,color:#fff
|
| 468 |
-
style DD4 fill:#74c0fc,color:#fff
|
| 469 |
-
style EE4 fill:#b197fc,color:#fff
|
| 470 |
-
style FF4 fill:#b197fc,color:#fff
|
| 471 |
-
style GG4 fill:#b197fc,color:#fff
|
| 472 |
-
</div>
|
| 473 |
-
|
| 474 |
-
<div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;">
|
| 475 |
-
<div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
|
| 476 |
-
<span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Electrodes & Electrolyte
|
| 477 |
-
</div>
|
| 478 |
-
<div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
|
| 479 |
-
<span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Cell Components
|
| 480 |
-
</div>
|
| 481 |
-
<div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
|
| 482 |
-
<span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Redox Reactions
|
| 483 |
-
</div>
|
| 484 |
-
<div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
|
| 485 |
-
<span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates
|
| 486 |
-
</div>
|
| 487 |
-
<div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
|
| 488 |
-
<span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#b197fc;"></span>Products
|
| 489 |
-
</div>
|
| 490 |
-
</div>
|
| 491 |
-
|
| 492 |
-
<div class="figure-caption">
|
| 493 |
-
<strong>Figure 4.</strong> Electrochemical Cell Process. This chemistry process visualization demonstrates electrochemical energy conversion. The flowchart shows electrode inputs, cell components, redox reactions, intermediate processes, and final electrical energy output.
|
| 494 |
-
</div>
|
| 495 |
-
</div>
|
| 496 |
-
|
| 497 |
-
<h2>5. Distillation Process</h2>
|
| 498 |
-
<div class="figure">
|
| 499 |
-
<div class="mermaid">
|
| 500 |
-
graph TD
|
| 501 |
-
%% Initial Setup
|
| 502 |
-
%% Input Conditions
|
| 503 |
-
A5[Mixture] --> B5[Mixture Analysis]
|
| 504 |
-
C5[Heat Source] --> D5[Heat Supply]
|
| 505 |
-
E5[Distillation Apparatus] --> F5[Equipment Setup]
|
| 506 |
-
%% Process Setup
|
| 507 |
-
B5 --> G5[Component Analysis]
|
| 508 |
-
D5 --> H5[Temperature Control]
|
| 509 |
-
F5 --> I5[Apparatus Assembly]
|
| 510 |
-
%% Heating Process
|
| 511 |
-
G5 --> J5[Mixture Loading]
|
| 512 |
-
H5 --> K5[Heat Application]
|
| 513 |
-
I5 --> L5[Vapor Formation]
|
| 514 |
-
%% Vaporization
|
| 515 |
-
J5 --> M5[Component Separation]
|
| 516 |
-
K5 --> N5[Boiling Point Differences]
|
| 517 |
-
L5 --> O5[Vapor Phase]
|
| 518 |
-
%% Distillation
|
| 519 |
-
M5 --> P5[Fractional Distillation]
|
| 520 |
-
N5 --> Q5[Temperature Gradient]
|
| 521 |
-
O5 --> R5[Condensation]
|
| 522 |
-
%% Separation
|
| 523 |
-
P5 --> S5[Component Collection]
|
| 524 |
-
Q5 --> T5[Fraction Separation]
|
| 525 |
-
R5 --> U5[Liquid Recovery]
|
| 526 |
-
%% Product Collection
|
| 527 |
-
S5 --> V5[High Boiling Point]
|
| 528 |
-
T5 --> W5[Medium Boiling Point]
|
| 529 |
-
U5 --> X5[Low Boiling Point]
|
| 530 |
-
%% Process Control
|
| 531 |
-
V5 --> Y5[Fraction Analysis]
|
| 532 |
-
W5 --> Z5[Purity Check]
|
| 533 |
-
X5 --> AA5[Yield Calculation]
|
| 534 |
-
%% Output
|
| 535 |
-
Y5 --> BB5[Distillation Complete]
|
| 536 |
-
Z5 --> CC5[Component Separation]
|
| 537 |
-
AA5 --> DD5[Process Efficiency]
|
| 538 |
-
%% Final Results
|
| 539 |
-
BB5 --> EE5[Purified Components]
|
| 540 |
-
CC5 --> FF5[Separation Achieved]
|
| 541 |
-
DD5 --> GG5[Process Optimization]
|
| 542 |
-
%% Styling - Chemistry Color Scheme
|
| 543 |
-
%% Styling - Biological Color Scheme
|
| 544 |
-
style A5 fill:#ff6b6b,color:#fff
|
| 545 |
-
style C5 fill:#ff6b6b,color:#fff
|
| 546 |
-
style E5 fill:#ff6b6b,color:#fff
|
| 547 |
-
style G5 fill:#ffd43b,color:#000
|
| 548 |
-
style H5 fill:#ffd43b,color:#000
|
| 549 |
-
style I5 fill:#ffd43b,color:#000
|
| 550 |
-
style J5 fill:#ffd43b,color:#000
|
| 551 |
-
style K5 fill:#ffd43b,color:#000
|
| 552 |
-
style L5 fill:#ffd43b,color:#000
|
| 553 |
-
style M5 fill:#51cf66,color:#fff
|
| 554 |
-
style N5 fill:#51cf66,color:#fff
|
| 555 |
-
style O5 fill:#51cf66,color:#fff
|
| 556 |
-
style P5 fill:#51cf66,color:#fff
|
| 557 |
-
style Q5 fill:#51cf66,color:#fff
|
| 558 |
-
style R5 fill:#51cf66,color:#fff
|
| 559 |
-
style S5 fill:#51cf66,color:#fff
|
| 560 |
-
style T5 fill:#51cf66,color:#fff
|
| 561 |
-
style U5 fill:#51cf66,color:#fff
|
| 562 |
-
style V5 fill:#51cf66,color:#fff
|
| 563 |
-
style W5 fill:#51cf66,color:#fff
|
| 564 |
-
style X5 fill:#51cf66,color:#fff
|
| 565 |
-
style B5 fill:#74c0fc,color:#fff
|
| 566 |
-
style D5 fill:#74c0fc,color:#fff
|
| 567 |
-
style F5 fill:#74c0fc,color:#fff
|
| 568 |
-
style Y5 fill:#74c0fc,color:#fff
|
| 569 |
-
style Z5 fill:#74c0fc,color:#fff
|
| 570 |
-
style AA5 fill:#74c0fc,color:#fff
|
| 571 |
-
style BB5 fill:#74c0fc,color:#fff
|
| 572 |
-
style CC5 fill:#74c0fc,color:#fff
|
| 573 |
-
style DD5 fill:#74c0fc,color:#fff
|
| 574 |
-
style EE5 fill:#b197fc,color:#fff
|
| 575 |
-
style FF5 fill:#b197fc,color:#fff
|
| 576 |
-
style GG5 fill:#b197fc,color:#fff
|
| 577 |
-
</div>
|
| 578 |
-
|
| 579 |
-
<div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;">
|
| 580 |
-
<div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
|
| 581 |
-
<span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Mixture & Heat Source
|
| 582 |
-
</div>
|
| 583 |
-
<div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
|
| 584 |
-
<span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Distillation Equipment
|
| 585 |
-
</div>
|
| 586 |
-
<div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
|
| 587 |
-
<span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Phase Separation Processes
|
| 588 |
-
</div>
|
| 589 |
-
<div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
|
| 590 |
-
<span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates
|
| 591 |
-
</div>
|
| 592 |
-
<div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
|
| 593 |
-
<span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#b197fc;"></span>Products
|
| 594 |
-
</div>
|
| 595 |
-
</div>
|
| 596 |
-
|
| 597 |
-
<div class="figure-caption">
|
| 598 |
-
<strong>Figure 5.</strong> Distillation Process. This chemistry process visualization demonstrates separation techniques. The flowchart shows mixture inputs, distillation equipment, phase separation processes, intermediate fractions, and final purified components.
|
| 599 |
-
</div>
|
| 600 |
-
</div>
|
| 601 |
-
|
| 602 |
-
<p><strong>Generated using the Programming Framework methodology</strong></p>
|
| 603 |
-
|
| 604 |
-
<p>This collection demonstrates the computational nature of chemical processes and systems</p>
|
| 605 |
-
|
| 606 |
-
<p>Each flowchart preserves maximum detail through optimized Mermaid configuration</p>
|
| 607 |
-
</div>
|
| 608 |
-
</body>
|
| 609 |
-
</html>
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|
computer-science-database-table.html
DELETED
|
@@ -1,543 +0,0 @@
|
|
| 1 |
-
<!DOCTYPE html>
|
| 2 |
-
<html lang="en">
|
| 3 |
-
<head>
|
| 4 |
-
<meta charset="UTF-8">
|
| 5 |
-
<meta name="viewport" content="width=device-width, initial-scale=1.0">
|
| 6 |
-
<title>Computer Science Processes Database</title>
|
| 7 |
-
<style>
|
| 8 |
-
body {
|
| 9 |
-
font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif;
|
| 10 |
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margin: 0;
|
| 11 |
-
padding: 20px;
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| 12 |
-
background: linear-gradient(135deg, #667eea 0%, #764ba2 100%);
|
| 13 |
-
min-height: 100vh;
|
| 14 |
-
}
|
| 15 |
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|
| 16 |
-
.container {
|
| 17 |
-
max-width: 1400px;
|
| 18 |
-
margin: 0 auto;
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| 19 |
-
background: white;
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| 20 |
-
border-radius: 15px;
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| 21 |
-
box-shadow: 0 20px 40px rgba(0,0,0,0.1);
|
| 22 |
-
overflow: hidden;
|
| 23 |
-
}
|
| 24 |
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|
| 25 |
-
.header {
|
| 26 |
-
background: linear-gradient(135deg, #9b59b6 0%, #9b59b6 100%);
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| 27 |
-
color: white;
|
| 28 |
-
padding: 30px;
|
| 29 |
-
text-align: center;
|
| 30 |
-
}
|
| 31 |
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|
| 32 |
-
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|
| 33 |
-
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| 35 |
-
font-weight: 300;
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| 37 |
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|
| 38 |
-
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|
| 39 |
-
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|
| 40 |
-
opacity: 0.8;
|
| 41 |
-
font-size: 1.1em;
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| 42 |
-
}
|
| 43 |
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|
| 44 |
-
.stats-grid {
|
| 45 |
-
display: grid;
|
| 46 |
-
grid-template-columns: repeat(auto-fit, minmax(200px, 1fr));
|
| 47 |
-
gap: 20px;
|
| 48 |
-
padding: 30px;
|
| 49 |
-
background: #f8f9fa;
|
| 50 |
-
}
|
| 51 |
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|
| 52 |
-
.stat-card {
|
| 53 |
-
background: white;
|
| 54 |
-
padding: 20px;
|
| 55 |
-
border-radius: 10px;
|
| 56 |
-
text-align: center;
|
| 57 |
-
box-shadow: 0 5px 15px rgba(0,0,0,0.08);
|
| 58 |
-
border-left: 4px solid #9b59b6;
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| 60 |
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| 61 |
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|
| 62 |
-
font-size: 2.5em;
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| 63 |
-
font-weight: bold;
|
| 64 |
-
color: #2c3e50;
|
| 65 |
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margin: 0;
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| 66 |
-
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| 67 |
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| 68 |
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|
| 69 |
-
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|
| 70 |
-
font-size: 0.9em;
|
| 71 |
-
margin: 5px 0 0 0;
|
| 72 |
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}
|
| 73 |
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|
| 74 |
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.table-container {
|
| 75 |
-
padding: 30px;
|
| 76 |
-
overflow-x: auto;
|
| 77 |
-
}
|
| 78 |
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|
| 79 |
-
.table-header {
|
| 80 |
-
background: #9b59b6;
|
| 81 |
-
color: white;
|
| 82 |
-
padding: 20px;
|
| 83 |
-
margin: -30px -30px 20px -30px;
|
| 84 |
-
}
|
| 85 |
-
|
| 86 |
-
.table-header h2 {
|
| 87 |
-
margin: 0;
|
| 88 |
-
font-size: 1.8em;
|
| 89 |
-
font-weight: 300;
|
| 90 |
-
}
|
| 91 |
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|
| 92 |
-
table {
|
| 93 |
-
width: 100%;
|
| 94 |
-
border-collapse: collapse;
|
| 95 |
-
margin-top: 20px;
|
| 96 |
-
font-size: 0.9em;
|
| 97 |
-
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| 98 |
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|
| 99 |
-
th, td {
|
| 100 |
-
padding: 12px 8px;
|
| 101 |
-
text-align: left;
|
| 102 |
-
border-bottom: 1px solid #ddd;
|
| 103 |
-
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| 104 |
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|
| 105 |
-
th {
|
| 106 |
-
background: #ecf0f1;
|
| 107 |
-
font-weight: 600;
|
| 108 |
-
color: #2c3e50;
|
| 109 |
-
position: sticky;
|
| 110 |
-
top: 0;
|
| 111 |
-
cursor: pointer;
|
| 112 |
-
}
|
| 113 |
-
|
| 114 |
-
th:hover {
|
| 115 |
-
background: #d5dbdb;
|
| 116 |
-
}
|
| 117 |
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|
| 118 |
-
tr:hover {
|
| 119 |
-
background: #f8f9fa;
|
| 120 |
-
}
|
| 121 |
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|
| 122 |
-
.process-name {
|
| 123 |
-
font-weight: 600;
|
| 124 |
-
color: #2c3e50;
|
| 125 |
-
max-width: 300px;
|
| 126 |
-
}
|
| 127 |
-
|
| 128 |
-
.process-name a {
|
| 129 |
-
color: #9b59b6;
|
| 130 |
-
text-decoration: none;
|
| 131 |
-
}
|
| 132 |
-
|
| 133 |
-
.process-name a:hover {
|
| 134 |
-
text-decoration: underline;
|
| 135 |
-
}
|
| 136 |
-
|
| 137 |
-
.subcategory {
|
| 138 |
-
background: #fde8e8;
|
| 139 |
-
padding: 4px 8px;
|
| 140 |
-
border-radius: 4px;
|
| 141 |
-
font-size: 0.8em;
|
| 142 |
-
color: #9b59b6;
|
| 143 |
-
}
|
| 144 |
-
|
| 145 |
-
.complexity {
|
| 146 |
-
padding: 4px 8px;
|
| 147 |
-
border-radius: 4px;
|
| 148 |
-
font-size: 0.8em;
|
| 149 |
-
font-weight: 600;
|
| 150 |
-
}
|
| 151 |
-
|
| 152 |
-
.complexity.low {
|
| 153 |
-
background: #d5f4e6;
|
| 154 |
-
color: #27ae60;
|
| 155 |
-
}
|
| 156 |
-
|
| 157 |
-
.complexity.medium {
|
| 158 |
-
background: #fff3cd;
|
| 159 |
-
color: #856404;
|
| 160 |
-
}
|
| 161 |
-
|
| 162 |
-
.complexity.detailed, .complexity.high {
|
| 163 |
-
background: #fadbd8;
|
| 164 |
-
color: #9b59b6;
|
| 165 |
-
}
|
| 166 |
-
|
| 167 |
-
.number {
|
| 168 |
-
text-align: center;
|
| 169 |
-
font-weight: 600;
|
| 170 |
-
}
|
| 171 |
-
|
| 172 |
-
.loading {
|
| 173 |
-
text-align: center;
|
| 174 |
-
padding: 50px;
|
| 175 |
-
color: #7f8c8d;
|
| 176 |
-
}
|
| 177 |
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|
| 178 |
-
.error {
|
| 179 |
-
text-align: center;
|
| 180 |
-
padding: 50px;
|
| 181 |
-
color: #9b59b6;
|
| 182 |
-
}
|
| 183 |
-
|
| 184 |
-
.refresh-btn {
|
| 185 |
-
background: #9b59b6;
|
| 186 |
-
color: white;
|
| 187 |
-
border: none;
|
| 188 |
-
padding: 10px 20px;
|
| 189 |
-
border-radius: 5px;
|
| 190 |
-
cursor: pointer;
|
| 191 |
-
font-size: 0.9em;
|
| 192 |
-
margin: 10px;
|
| 193 |
-
}
|
| 194 |
-
|
| 195 |
-
.refresh-btn:hover {
|
| 196 |
-
background: #9b59b6;
|
| 197 |
-
}
|
| 198 |
-
|
| 199 |
-
.breakdown {
|
| 200 |
-
padding: 30px;
|
| 201 |
-
background: #f8f9fa;
|
| 202 |
-
border-top: 1px solid #ecf0f1;
|
| 203 |
-
}
|
| 204 |
-
|
| 205 |
-
.breakdown h3 {
|
| 206 |
-
color: #2c3e50;
|
| 207 |
-
margin-bottom: 15px;
|
| 208 |
-
}
|
| 209 |
-
|
| 210 |
-
.breakdown-grid {
|
| 211 |
-
display: grid;
|
| 212 |
-
grid-template-columns: repeat(auto-fit, minmax(300px, 1fr));
|
| 213 |
-
gap: 20px;
|
| 214 |
-
}
|
| 215 |
-
|
| 216 |
-
.breakdown-card {
|
| 217 |
-
background: white;
|
| 218 |
-
padding: 20px;
|
| 219 |
-
border-radius: 8px;
|
| 220 |
-
box-shadow: 0 2px 10px rgba(0,0,0,0.05);
|
| 221 |
-
}
|
| 222 |
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|
| 223 |
-
.breakdown-item {
|
| 224 |
-
display: flex;
|
| 225 |
-
justify-content: space-between;
|
| 226 |
-
padding: 8px 0;
|
| 227 |
-
border-bottom: 1px solid #ecf0f1;
|
| 228 |
-
}
|
| 229 |
-
|
| 230 |
-
.breakdown-item:last-child {
|
| 231 |
-
border-bottom: none;
|
| 232 |
-
}
|
| 233 |
-
|
| 234 |
-
.breakdown-label {
|
| 235 |
-
color: #7f8c8d;
|
| 236 |
-
}
|
| 237 |
-
|
| 238 |
-
.breakdown-count {
|
| 239 |
-
font-weight: 600;
|
| 240 |
-
color: #2c3e50;
|
| 241 |
-
}
|
| 242 |
-
|
| 243 |
-
.color-legend {
|
| 244 |
-
padding: 20px;
|
| 245 |
-
background: #f8f9fa;
|
| 246 |
-
border-top: 1px solid #ecf0f1;
|
| 247 |
-
}
|
| 248 |
-
|
| 249 |
-
.color-legend h3 {
|
| 250 |
-
color: #2c3e50;
|
| 251 |
-
margin-bottom: 15px;
|
| 252 |
-
}
|
| 253 |
-
|
| 254 |
-
.color-grid {
|
| 255 |
-
display: grid;
|
| 256 |
-
grid-template-columns: repeat(auto-fit, minmax(200px, 1fr));
|
| 257 |
-
gap: 15px;
|
| 258 |
-
}
|
| 259 |
-
|
| 260 |
-
.color-item {
|
| 261 |
-
display: flex;
|
| 262 |
-
align-items: center;
|
| 263 |
-
gap: 10px;
|
| 264 |
-
padding: 10px;
|
| 265 |
-
background: white;
|
| 266 |
-
border-radius: 5px;
|
| 267 |
-
}
|
| 268 |
-
|
| 269 |
-
.color-box {
|
| 270 |
-
width: 30px;
|
| 271 |
-
height: 30px;
|
| 272 |
-
border-radius: 4px;
|
| 273 |
-
border: 1px solid #ddd;
|
| 274 |
-
}
|
| 275 |
-
</style>
|
| 276 |
-
</head>
|
| 277 |
-
<body>
|
| 278 |
-
<div class="container">
|
| 279 |
-
<div class="header">
|
| 280 |
-
<h1>💻 Computer Science Processes Database</h1>
|
| 281 |
-
<p>Programming Framework - Interactive Database Analysis</p>
|
| 282 |
-
<button class="refresh-btn" onclick="loadData()">🔄 Refresh Data</button>
|
| 283 |
-
</div>
|
| 284 |
-
|
| 285 |
-
<div id="loading" class="loading">
|
| 286 |
-
<h3>Loading computer_science processes database...</h3>
|
| 287 |
-
<p>Fetching process data from metadata.json</p>
|
| 288 |
-
</div>
|
| 289 |
-
|
| 290 |
-
<div id="error" class="error" style="display: none;">
|
| 291 |
-
<h3>❌ Error Loading Data</h3>
|
| 292 |
-
<p>Could not fetch computer_science processes metadata. Please check your connection and try again.</p>
|
| 293 |
-
</div>
|
| 294 |
-
|
| 295 |
-
<div id="content" style="display: none;">
|
| 296 |
-
<div class="stats-grid" id="statsGrid">
|
| 297 |
-
<!-- Stats will be populated here -->
|
| 298 |
-
</div>
|
| 299 |
-
|
| 300 |
-
<div class="table-container">
|
| 301 |
-
<div class="table-header">
|
| 302 |
-
<h2>📊 Process Database Table</h2>
|
| 303 |
-
<p style="margin: 10px 0 0 0; opacity: 0.8; font-size: 0.9em;">
|
| 304 |
-
💡 Click on any process name to view its interactive flowchart
|
| 305 |
-
</p>
|
| 306 |
-
</div>
|
| 307 |
-
<table id="processTable">
|
| 308 |
-
<thead>
|
| 309 |
-
<tr>
|
| 310 |
-
<th onclick="sortTable(0)">Process Name ↕</th>
|
| 311 |
-
<th onclick="sortTable(1)">Subcategory ↕</th>
|
| 312 |
-
<th onclick="sortTable(2)">Complexity ↕</th>
|
| 313 |
-
<th onclick="sortTable(3)">Nodes ↕</th>
|
| 314 |
-
<th onclick="sortTable(4)">Edges ↕</th>
|
| 315 |
-
<th onclick="sortTable(5)">AND Gates ↕</th>
|
| 316 |
-
<th onclick="sortTable(6)">OR Gates ↕</th>
|
| 317 |
-
</tr>
|
| 318 |
-
</thead>
|
| 319 |
-
<tbody id="tableBody">
|
| 320 |
-
<!-- Data will be populated here -->
|
| 321 |
-
</tbody>
|
| 322 |
-
</table>
|
| 323 |
-
</div>
|
| 324 |
-
|
| 325 |
-
<div class="breakdown">
|
| 326 |
-
<h3>📈 Database Analysis</h3>
|
| 327 |
-
<div class="breakdown-grid" id="breakdownGrid">
|
| 328 |
-
<!-- Breakdown will be populated here -->
|
| 329 |
-
</div>
|
| 330 |
-
</div>
|
| 331 |
-
|
| 332 |
-
<div class="color-legend">
|
| 333 |
-
<h3>🎨 Color Scheme (5-Color System)</h3>
|
| 334 |
-
<div class="color-grid">
|
| 335 |
-
<div class="color-item">
|
| 336 |
-
<div class="color-box" style="background: #ff6b6b;"></div>
|
| 337 |
-
<div>
|
| 338 |
-
<strong>Red</strong><br>
|
| 339 |
-
<small>Triggers & Inputs</small>
|
| 340 |
-
</div>
|
| 341 |
-
</div>
|
| 342 |
-
<div class="color-item">
|
| 343 |
-
<div class="color-box" style="background: #ffd43b;"></div>
|
| 344 |
-
<div>
|
| 345 |
-
<strong>Yellow</strong><br>
|
| 346 |
-
<small>Structures & Objects</small>
|
| 347 |
-
</div>
|
| 348 |
-
</div>
|
| 349 |
-
<div class="color-item">
|
| 350 |
-
<div class="color-box" style="background: #51cf66;"></div>
|
| 351 |
-
<div>
|
| 352 |
-
<strong>Green</strong><br>
|
| 353 |
-
<small>Processing & Operations</small>
|
| 354 |
-
</div>
|
| 355 |
-
</div>
|
| 356 |
-
<div class="color-item">
|
| 357 |
-
<div class="color-box" style="background: #74c0fc;"></div>
|
| 358 |
-
<div>
|
| 359 |
-
<strong>Blue</strong><br>
|
| 360 |
-
<small>Intermediates & States</small>
|
| 361 |
-
</div>
|
| 362 |
-
</div>
|
| 363 |
-
<div class="color-item">
|
| 364 |
-
<div class="color-box" style="background: #b197fc;"></div>
|
| 365 |
-
<div>
|
| 366 |
-
<strong>Violet</strong><br>
|
| 367 |
-
<small>Products & Outputs</small>
|
| 368 |
-
</div>
|
| 369 |
-
</div>
|
| 370 |
-
</div>
|
| 371 |
-
</div>
|
| 372 |
-
</div>
|
| 373 |
-
</div>
|
| 374 |
-
|
| 375 |
-
<script>
|
| 376 |
-
// Determine metadata URL based on where this file is hosted
|
| 377 |
-
const METADATA_URL = window.location.hostname.includes('storage.googleapis.com')
|
| 378 |
-
? 'https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/computer-science-processes-database/metadata.json'
|
| 379 |
-
: (window.location.hostname.includes('huggingface.co'))
|
| 380 |
-
? './computer-science-processes-database/metadata.json'
|
| 381 |
-
: './metadata.json';
|
| 382 |
-
let currentSortColumn = -1;
|
| 383 |
-
let sortDirection = 1;
|
| 384 |
-
let processes = [];
|
| 385 |
-
|
| 386 |
-
async function loadData() {
|
| 387 |
-
console.log('🔄 Starting data load from:', METADATA_URL);
|
| 388 |
-
document.getElementById('loading').style.display = 'block';
|
| 389 |
-
document.getElementById('error').style.display = 'none';
|
| 390 |
-
document.getElementById('content').style.display = 'none';
|
| 391 |
-
|
| 392 |
-
try {
|
| 393 |
-
const response = await fetch(METADATA_URL);
|
| 394 |
-
if (!response.ok) {
|
| 395 |
-
throw new Error(`HTTP ${response.status}: ${response.statusText}`);
|
| 396 |
-
}
|
| 397 |
-
|
| 398 |
-
const data = await response.json();
|
| 399 |
-
console.log('✅ Data loaded successfully:', data.totalProcesses, 'processes');
|
| 400 |
-
|
| 401 |
-
processes = data.processes || [];
|
| 402 |
-
populateData(data);
|
| 403 |
-
|
| 404 |
-
document.getElementById('loading').style.display = 'none';
|
| 405 |
-
document.getElementById('content').style.display = 'block';
|
| 406 |
-
|
| 407 |
-
} catch (error) {
|
| 408 |
-
console.error('❌ Error loading data:', error);
|
| 409 |
-
document.getElementById('loading').style.display = 'none';
|
| 410 |
-
document.getElementById('error').style.display = 'block';
|
| 411 |
-
document.getElementById('error').innerHTML = `
|
| 412 |
-
<h3>❌ Error Loading Data</h3>
|
| 413 |
-
<p>Could not fetch computer_science processes metadata.</p>
|
| 414 |
-
<p style="font-size: 0.9em; color: #95a5a6; margin-top: 10px;">
|
| 415 |
-
Error: ${error.message}
|
| 416 |
-
</p>
|
| 417 |
-
`;
|
| 418 |
-
}
|
| 419 |
-
}
|
| 420 |
-
|
| 421 |
-
function populateData(data) {
|
| 422 |
-
// Populate statistics
|
| 423 |
-
const stats = data.statistics || {};
|
| 424 |
-
document.getElementById('statsGrid').innerHTML = `
|
| 425 |
-
<div class="stat-card">
|
| 426 |
-
<div class="stat-number">${data.totalProcesses || 0}</div>
|
| 427 |
-
<div class="stat-label">Total Processes</div>
|
| 428 |
-
</div>
|
| 429 |
-
<div class="stat-card">
|
| 430 |
-
<div class="stat-number">${stats.totalNodes || 0}</div>
|
| 431 |
-
<div class="stat-label">Total Nodes</div>
|
| 432 |
-
</div>
|
| 433 |
-
<div class="stat-card">
|
| 434 |
-
<div class="stat-number">${stats.totalEdges || 0}</div>
|
| 435 |
-
<div class="stat-label">Total Edges</div>
|
| 436 |
-
</div>
|
| 437 |
-
<div class="stat-card">
|
| 438 |
-
<div class="stat-number">${data.subcategories || 0}</div>
|
| 439 |
-
<div class="stat-label">Subcategories</div>
|
| 440 |
-
</div>
|
| 441 |
-
`;
|
| 442 |
-
|
| 443 |
-
// Populate table
|
| 444 |
-
const tableBody = document.getElementById('tableBody');
|
| 445 |
-
tableBody.innerHTML = '';
|
| 446 |
-
|
| 447 |
-
const processList = data.processes || [];
|
| 448 |
-
processList.forEach(process => {
|
| 449 |
-
const row = document.createElement('tr');
|
| 450 |
-
const isGCS = window.location.hostname.includes('storage.googleapis.com');
|
| 451 |
-
const isHF = window.location.hostname.includes('huggingface.co');
|
| 452 |
-
const viewerUrl = isGCS
|
| 453 |
-
? `https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/computer-science-processes-database/processes/${process.subcategory}/${process.id}.html`
|
| 454 |
-
: (isHF)
|
| 455 |
-
? `./computer-science-processes-database/processes/${process.subcategory}/${process.id}.html`
|
| 456 |
-
: `./processes/${process.subcategory}/${process.id}.html`;
|
| 457 |
-
row.innerHTML = `
|
| 458 |
-
<td class="process-name">
|
| 459 |
-
<a href="${viewerUrl}" target="_blank">${process.name}</a>
|
| 460 |
-
</td>
|
| 461 |
-
<td><span class="subcategory">${process.subcategory_name || process.subcategory}</span></td>
|
| 462 |
-
<td><span class="complexity ${process.complexity}">${process.complexity}</span></td>
|
| 463 |
-
<td class="number">${process.nodes}</td>
|
| 464 |
-
<td class="number">${process.edges}</td>
|
| 465 |
-
<td class="number">${process.andGates || 0}</td>
|
| 466 |
-
<td class="number">${process.orGates || 0}</td>
|
| 467 |
-
`;
|
| 468 |
-
tableBody.appendChild(row);
|
| 469 |
-
});
|
| 470 |
-
|
| 471 |
-
// Populate breakdown
|
| 472 |
-
const breakdown = {};
|
| 473 |
-
processList.forEach(p => {
|
| 474 |
-
const subcat = p.subcategory_name || p.subcategory;
|
| 475 |
-
breakdown[subcat] = (breakdown[subcat] || 0) + 1;
|
| 476 |
-
});
|
| 477 |
-
|
| 478 |
-
let breakdownHTML = '<div class="breakdown-card"><h4>Processes by Subcategory</h4>';
|
| 479 |
-
Object.entries(breakdown).sort((a, b) => b[1] - a[1]).forEach(([subcat, count]) => {
|
| 480 |
-
breakdownHTML += `
|
| 481 |
-
<div class="breakdown-item">
|
| 482 |
-
<span class="breakdown-label">${subcat}</span>
|
| 483 |
-
<span class="breakdown-count">${count}</span>
|
| 484 |
-
</div>
|
| 485 |
-
`;
|
| 486 |
-
});
|
| 487 |
-
breakdownHTML += '</div>';
|
| 488 |
-
|
| 489 |
-
const complexityBreakdown = {};
|
| 490 |
-
processList.forEach(p => {
|
| 491 |
-
const comp = p.complexity || 'unknown';
|
| 492 |
-
complexityBreakdown[comp] = (complexityBreakdown[comp] || 0) + 1;
|
| 493 |
-
});
|
| 494 |
-
|
| 495 |
-
breakdownHTML += '<div class="breakdown-card"><h4>Processes by Complexity</h4>';
|
| 496 |
-
Object.entries(complexityBreakdown).sort((a, b) => b[1] - a[1]).forEach(([comp, count]) => {
|
| 497 |
-
breakdownHTML += `
|
| 498 |
-
<div class="breakdown-item">
|
| 499 |
-
<span class="breakdown-label">${comp}</span>
|
| 500 |
-
<span class="breakdown-count">${count}</span>
|
| 501 |
-
</div>
|
| 502 |
-
`;
|
| 503 |
-
});
|
| 504 |
-
breakdownHTML += '</div>';
|
| 505 |
-
|
| 506 |
-
document.getElementById('breakdownGrid').innerHTML = breakdownHTML;
|
| 507 |
-
}
|
| 508 |
-
|
| 509 |
-
function sortTable(column) {
|
| 510 |
-
const table = document.getElementById('processTable');
|
| 511 |
-
const tbody = table.querySelector('tbody');
|
| 512 |
-
const rows = Array.from(tbody.querySelectorAll('tr'));
|
| 513 |
-
|
| 514 |
-
if (currentSortColumn === column) {
|
| 515 |
-
sortDirection *= -1;
|
| 516 |
-
} else {
|
| 517 |
-
currentSortColumn = column;
|
| 518 |
-
sortDirection = 1;
|
| 519 |
-
}
|
| 520 |
-
|
| 521 |
-
rows.sort((a, b) => {
|
| 522 |
-
const aText = a.cells[column].textContent.trim();
|
| 523 |
-
const bText = b.cells[column].textContent.trim();
|
| 524 |
-
|
| 525 |
-
// Try to parse as number
|
| 526 |
-
const aNum = parseFloat(aText);
|
| 527 |
-
const bNum = parseFloat(bText);
|
| 528 |
-
|
| 529 |
-
if (!isNaN(aNum) && !isNaN(bNum)) {
|
| 530 |
-
return (aNum - bNum) * sortDirection;
|
| 531 |
-
}
|
| 532 |
-
|
| 533 |
-
return aText.localeCompare(bText) * sortDirection;
|
| 534 |
-
});
|
| 535 |
-
|
| 536 |
-
rows.forEach(row => tbody.appendChild(row));
|
| 537 |
-
}
|
| 538 |
-
|
| 539 |
-
// Load data on page load
|
| 540 |
-
loadData();
|
| 541 |
-
</script>
|
| 542 |
-
</body>
|
| 543 |
-
</html>
|
|
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|
data/aristotle-syllogistic-figure-2.mmd
ADDED
|
@@ -0,0 +1,30 @@
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
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|
|
|
|
|
|
|
|
| 1 |
+
graph TD
|
| 2 |
+
DefAEIO("DefAEIO Categorical forms")
|
| 3 |
+
DefFig("DefFig Figures 1,2,3")
|
| 4 |
+
Econv("Econv E-conversion")
|
| 5 |
+
Barbara("Barbara Barbara")
|
| 6 |
+
Celarent("Celarent Celarent")
|
| 7 |
+
Ferio("Ferio Ferio")
|
| 8 |
+
Cesare("Cesare Cesare")
|
| 9 |
+
Camestres("Camestres Camestres")
|
| 10 |
+
Festino("Festino Festino")
|
| 11 |
+
Baroco("Baroco Baroco")
|
| 12 |
+
DefAEIO --> Barbara
|
| 13 |
+
DefFig --> Barbara
|
| 14 |
+
DefAEIO --> Celarent
|
| 15 |
+
DefFig --> Celarent
|
| 16 |
+
DefAEIO --> Ferio
|
| 17 |
+
DefFig --> Ferio
|
| 18 |
+
Econv --> Cesare
|
| 19 |
+
Celarent --> Cesare
|
| 20 |
+
Econv --> Camestres
|
| 21 |
+
Celarent --> Camestres
|
| 22 |
+
Econv --> Festino
|
| 23 |
+
Ferio --> Festino
|
| 24 |
+
Barbara --> Baroco
|
| 25 |
+
classDef axiom fill:#e74c3c,color:#fff,stroke:#c0392b
|
| 26 |
+
classDef definition fill:#3498db,color:#fff,stroke:#2980b9
|
| 27 |
+
classDef theorem fill:#1abc9c,color:#fff,stroke:#16a085
|
| 28 |
+
class Econv,Barbara,Celarent,Ferio axiom
|
| 29 |
+
class DefAEIO,DefFig definition
|
| 30 |
+
class Cesare,Camestres,Festino,Baroco theorem
|
data/aristotle-syllogistic-figure-3.mmd
ADDED
|
@@ -0,0 +1,37 @@
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 1 |
+
graph TD
|
| 2 |
+
DefAEIO("DefAEIO Categorical forms")
|
| 3 |
+
DefFig("DefFig Figures 1,2,3")
|
| 4 |
+
Iconv("Iconv I-conversion")
|
| 5 |
+
Aconv("Aconv A-conversion")
|
| 6 |
+
Barbara("Barbara Barbara")
|
| 7 |
+
Darii("Darii Darii")
|
| 8 |
+
Ferio("Ferio Ferio")
|
| 9 |
+
Darapti("Darapti Darapti")
|
| 10 |
+
Felapton("Felapton Felapton")
|
| 11 |
+
Disamis("Disamis Disamis")
|
| 12 |
+
Datisi("Datisi Datisi")
|
| 13 |
+
Bocardo("Bocardo Bocardo")
|
| 14 |
+
Ferison("Ferison Ferison")
|
| 15 |
+
DefAEIO --> Barbara
|
| 16 |
+
DefFig --> Barbara
|
| 17 |
+
DefAEIO --> Darii
|
| 18 |
+
DefFig --> Darii
|
| 19 |
+
DefAEIO --> Ferio
|
| 20 |
+
DefFig --> Ferio
|
| 21 |
+
Aconv --> Darapti
|
| 22 |
+
Darii --> Darapti
|
| 23 |
+
Aconv --> Felapton
|
| 24 |
+
Ferio --> Felapton
|
| 25 |
+
Iconv --> Disamis
|
| 26 |
+
Darii --> Disamis
|
| 27 |
+
Aconv --> Datisi
|
| 28 |
+
Darii --> Datisi
|
| 29 |
+
Barbara --> Bocardo
|
| 30 |
+
Aconv --> Ferison
|
| 31 |
+
Ferio --> Ferison
|
| 32 |
+
classDef axiom fill:#e74c3c,color:#fff,stroke:#c0392b
|
| 33 |
+
classDef definition fill:#3498db,color:#fff,stroke:#2980b9
|
| 34 |
+
classDef theorem fill:#1abc9c,color:#fff,stroke:#16a085
|
| 35 |
+
class Iconv,Aconv,Barbara,Darii,Ferio axiom
|
| 36 |
+
class DefAEIO,DefFig definition
|
| 37 |
+
class Darapti,Felapton,Disamis,Datisi,Bocardo,Ferison theorem
|
data/aristotle-syllogistic-foundations-perfect.mmd
ADDED
|
@@ -0,0 +1,23 @@
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 1 |
+
graph TD
|
| 2 |
+
DefAEIO("DefAEIO Categorical forms")
|
| 3 |
+
DefFig("DefFig Figures 1,2,3")
|
| 4 |
+
Econv("Econv E-conversion")
|
| 5 |
+
Iconv("Iconv I-conversion")
|
| 6 |
+
Aconv("Aconv A-conversion")
|
| 7 |
+
Barbara("Barbara Barbara")
|
| 8 |
+
Celarent("Celarent Celarent")
|
| 9 |
+
Darii("Darii Darii")
|
| 10 |
+
Ferio("Ferio Ferio")
|
| 11 |
+
DefAEIO --> Barbara
|
| 12 |
+
DefFig --> Barbara
|
| 13 |
+
DefAEIO --> Celarent
|
| 14 |
+
DefFig --> Celarent
|
| 15 |
+
DefAEIO --> Darii
|
| 16 |
+
DefFig --> Darii
|
| 17 |
+
DefAEIO --> Ferio
|
| 18 |
+
DefFig --> Ferio
|
| 19 |
+
classDef axiom fill:#e74c3c,color:#fff,stroke:#c0392b
|
| 20 |
+
classDef definition fill:#3498db,color:#fff,stroke:#2980b9
|
| 21 |
+
classDef theorem fill:#1abc9c,color:#fff,stroke:#16a085
|
| 22 |
+
class Econv,Iconv,Aconv,Barbara,Celarent,Darii,Ferio axiom
|
| 23 |
+
class DefAEIO,DefFig definition
|
data/aristotle-syllogistic.json
ADDED
|
@@ -0,0 +1,326 @@
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
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|
|
|
| 1 |
+
{
|
| 2 |
+
"schemaVersion": "1.0",
|
| 3 |
+
"discourse": {
|
| 4 |
+
"id": "aristotle-syllogistic",
|
| 5 |
+
"name": "Aristotle Syllogistic Logic",
|
| 6 |
+
"subject": "logic",
|
| 7 |
+
"variant": "classical",
|
| 8 |
+
"description": "Aristotelian categorical syllogistic. Four perfect syllogisms (Barbara, Celarent, Darii, Ferio), three conversion rules, and ten imperfect syllogisms reduced to the perfect ones. Based on Prior Analytics.",
|
| 9 |
+
"structure": {
|
| 10 |
+
"axioms": 7,
|
| 11 |
+
"definitions": 2,
|
| 12 |
+
"theorems": 10
|
| 13 |
+
}
|
| 14 |
+
},
|
| 15 |
+
"metadata": {
|
| 16 |
+
"created": "2026-03-15",
|
| 17 |
+
"lastUpdated": "2026-03-15",
|
| 18 |
+
"version": "1.0.0",
|
| 19 |
+
"license": "CC BY 4.0",
|
| 20 |
+
"authors": [
|
| 21 |
+
"Welz, G."
|
| 22 |
+
],
|
| 23 |
+
"methodology": "Programming Framework",
|
| 24 |
+
"citation": "Welz, G. (2026). Aristotle Syllogistic Dependency Graph. Programming Framework.",
|
| 25 |
+
"keywords": [
|
| 26 |
+
"Aristotle",
|
| 27 |
+
"syllogism",
|
| 28 |
+
"categorical logic",
|
| 29 |
+
"Prior Analytics",
|
| 30 |
+
"Barbara",
|
| 31 |
+
"Celarent"
|
| 32 |
+
]
|
| 33 |
+
},
|
| 34 |
+
"sources": [
|
| 35 |
+
{
|
| 36 |
+
"id": "aristotle",
|
| 37 |
+
"type": "primary",
|
| 38 |
+
"authors": "Aristotle",
|
| 39 |
+
"title": "Prior Analytics",
|
| 40 |
+
"year": "c. 350 BCE",
|
| 41 |
+
"notes": "Syllogistic theory"
|
| 42 |
+
},
|
| 43 |
+
{
|
| 44 |
+
"id": "stanford",
|
| 45 |
+
"type": "secondary",
|
| 46 |
+
"authors": "Smith, R.",
|
| 47 |
+
"title": "Aristotle's Logic",
|
| 48 |
+
"url": "https://plato.stanford.edu/entries/aristotle-logic/",
|
| 49 |
+
"notes": "Stanford Encyclopedia"
|
| 50 |
+
}
|
| 51 |
+
],
|
| 52 |
+
"nodes": [
|
| 53 |
+
{
|
| 54 |
+
"id": "DefAEIO",
|
| 55 |
+
"type": "definition",
|
| 56 |
+
"label": "A, E, I, O: All/No/Some/Some-not",
|
| 57 |
+
"shortLabel": "DefAEIO",
|
| 58 |
+
"short": "Categorical forms",
|
| 59 |
+
"colorClass": "definition"
|
| 60 |
+
},
|
| 61 |
+
{
|
| 62 |
+
"id": "DefFig",
|
| 63 |
+
"type": "definition",
|
| 64 |
+
"label": "Three figures: middle term position",
|
| 65 |
+
"shortLabel": "DefFig",
|
| 66 |
+
"short": "Figures 1,2,3",
|
| 67 |
+
"colorClass": "definition"
|
| 68 |
+
},
|
| 69 |
+
{
|
| 70 |
+
"id": "Econv",
|
| 71 |
+
"type": "axiom",
|
| 72 |
+
"label": "Eab implies Eba (No M is P implies No P is M)",
|
| 73 |
+
"shortLabel": "Econv",
|
| 74 |
+
"short": "E-conversion",
|
| 75 |
+
"colorClass": "axiom"
|
| 76 |
+
},
|
| 77 |
+
{
|
| 78 |
+
"id": "Iconv",
|
| 79 |
+
"type": "axiom",
|
| 80 |
+
"label": "Iab implies Iba (Some M is P implies Some P is M)",
|
| 81 |
+
"shortLabel": "Iconv",
|
| 82 |
+
"short": "I-conversion",
|
| 83 |
+
"colorClass": "axiom"
|
| 84 |
+
},
|
| 85 |
+
{
|
| 86 |
+
"id": "Aconv",
|
| 87 |
+
"type": "axiom",
|
| 88 |
+
"label": "Aab implies Iba (All M is P implies Some P is M)",
|
| 89 |
+
"shortLabel": "Aconv",
|
| 90 |
+
"short": "A-conversion",
|
| 91 |
+
"colorClass": "axiom"
|
| 92 |
+
},
|
| 93 |
+
{
|
| 94 |
+
"id": "Barbara",
|
| 95 |
+
"type": "axiom",
|
| 96 |
+
"label": "AAA-1: All M is P, All S is M therefore All S is P",
|
| 97 |
+
"shortLabel": "Barbara",
|
| 98 |
+
"short": "Barbara",
|
| 99 |
+
"colorClass": "axiom"
|
| 100 |
+
},
|
| 101 |
+
{
|
| 102 |
+
"id": "Celarent",
|
| 103 |
+
"type": "axiom",
|
| 104 |
+
"label": "EAE-1: No M is P, All S is M therefore No S is P",
|
| 105 |
+
"shortLabel": "Celarent",
|
| 106 |
+
"short": "Celarent",
|
| 107 |
+
"colorClass": "axiom"
|
| 108 |
+
},
|
| 109 |
+
{
|
| 110 |
+
"id": "Darii",
|
| 111 |
+
"type": "axiom",
|
| 112 |
+
"label": "AII-1: All M is P, Some S is M therefore Some S is P",
|
| 113 |
+
"shortLabel": "Darii",
|
| 114 |
+
"short": "Darii",
|
| 115 |
+
"colorClass": "axiom"
|
| 116 |
+
},
|
| 117 |
+
{
|
| 118 |
+
"id": "Ferio",
|
| 119 |
+
"type": "axiom",
|
| 120 |
+
"label": "EIO-1: No M is P, Some S is M therefore Some S is not P",
|
| 121 |
+
"shortLabel": "Ferio",
|
| 122 |
+
"short": "Ferio",
|
| 123 |
+
"colorClass": "axiom"
|
| 124 |
+
},
|
| 125 |
+
{
|
| 126 |
+
"id": "Cesare",
|
| 127 |
+
"type": "theorem",
|
| 128 |
+
"label": "EAE-2: No P is M, All S is M therefore No S is P",
|
| 129 |
+
"shortLabel": "Cesare",
|
| 130 |
+
"short": "Cesare",
|
| 131 |
+
"colorClass": "theorem"
|
| 132 |
+
},
|
| 133 |
+
{
|
| 134 |
+
"id": "Camestres",
|
| 135 |
+
"type": "theorem",
|
| 136 |
+
"label": "AEE-2: All P is M, No S is M therefore No S is P",
|
| 137 |
+
"shortLabel": "Camestres",
|
| 138 |
+
"short": "Camestres",
|
| 139 |
+
"colorClass": "theorem"
|
| 140 |
+
},
|
| 141 |
+
{
|
| 142 |
+
"id": "Festino",
|
| 143 |
+
"type": "theorem",
|
| 144 |
+
"label": "EIO-2: No P is M, Some S is M therefore Some S is not P",
|
| 145 |
+
"shortLabel": "Festino",
|
| 146 |
+
"short": "Festino",
|
| 147 |
+
"colorClass": "theorem"
|
| 148 |
+
},
|
| 149 |
+
{
|
| 150 |
+
"id": "Baroco",
|
| 151 |
+
"type": "theorem",
|
| 152 |
+
"label": "AOO-2: All P is M, Some S is not M therefore Some S is not P",
|
| 153 |
+
"shortLabel": "Baroco",
|
| 154 |
+
"short": "Baroco",
|
| 155 |
+
"colorClass": "theorem"
|
| 156 |
+
},
|
| 157 |
+
{
|
| 158 |
+
"id": "Darapti",
|
| 159 |
+
"type": "theorem",
|
| 160 |
+
"label": "AAI-3: All M is P, All M is S therefore Some S is P",
|
| 161 |
+
"shortLabel": "Darapti",
|
| 162 |
+
"short": "Darapti",
|
| 163 |
+
"colorClass": "theorem"
|
| 164 |
+
},
|
| 165 |
+
{
|
| 166 |
+
"id": "Felapton",
|
| 167 |
+
"type": "theorem",
|
| 168 |
+
"label": "EAO-3: No M is P, All M is S therefore Some S is not P",
|
| 169 |
+
"shortLabel": "Felapton",
|
| 170 |
+
"short": "Felapton",
|
| 171 |
+
"colorClass": "theorem"
|
| 172 |
+
},
|
| 173 |
+
{
|
| 174 |
+
"id": "Disamis",
|
| 175 |
+
"type": "theorem",
|
| 176 |
+
"label": "IAI-3: Some M is P, All M is S therefore Some S is P",
|
| 177 |
+
"shortLabel": "Disamis",
|
| 178 |
+
"short": "Disamis",
|
| 179 |
+
"colorClass": "theorem"
|
| 180 |
+
},
|
| 181 |
+
{
|
| 182 |
+
"id": "Datisi",
|
| 183 |
+
"type": "theorem",
|
| 184 |
+
"label": "AII-3: All M is P, Some M is S therefore Some S is P",
|
| 185 |
+
"shortLabel": "Datisi",
|
| 186 |
+
"short": "Datisi",
|
| 187 |
+
"colorClass": "theorem"
|
| 188 |
+
},
|
| 189 |
+
{
|
| 190 |
+
"id": "Bocardo",
|
| 191 |
+
"type": "theorem",
|
| 192 |
+
"label": "OAO-3: Some M is not P, All M is S therefore Some S is not P",
|
| 193 |
+
"shortLabel": "Bocardo",
|
| 194 |
+
"short": "Bocardo",
|
| 195 |
+
"colorClass": "theorem"
|
| 196 |
+
},
|
| 197 |
+
{
|
| 198 |
+
"id": "Ferison",
|
| 199 |
+
"type": "theorem",
|
| 200 |
+
"label": "EIO-3: No M is P, Some M is S therefore Some S is not P",
|
| 201 |
+
"shortLabel": "Ferison",
|
| 202 |
+
"short": "Ferison",
|
| 203 |
+
"colorClass": "theorem"
|
| 204 |
+
}
|
| 205 |
+
],
|
| 206 |
+
"edges": [
|
| 207 |
+
{
|
| 208 |
+
"from": "DefAEIO",
|
| 209 |
+
"to": "Barbara"
|
| 210 |
+
},
|
| 211 |
+
{
|
| 212 |
+
"from": "DefFig",
|
| 213 |
+
"to": "Barbara"
|
| 214 |
+
},
|
| 215 |
+
{
|
| 216 |
+
"from": "DefAEIO",
|
| 217 |
+
"to": "Celarent"
|
| 218 |
+
},
|
| 219 |
+
{
|
| 220 |
+
"from": "DefFig",
|
| 221 |
+
"to": "Celarent"
|
| 222 |
+
},
|
| 223 |
+
{
|
| 224 |
+
"from": "DefAEIO",
|
| 225 |
+
"to": "Darii"
|
| 226 |
+
},
|
| 227 |
+
{
|
| 228 |
+
"from": "DefFig",
|
| 229 |
+
"to": "Darii"
|
| 230 |
+
},
|
| 231 |
+
{
|
| 232 |
+
"from": "DefAEIO",
|
| 233 |
+
"to": "Ferio"
|
| 234 |
+
},
|
| 235 |
+
{
|
| 236 |
+
"from": "DefFig",
|
| 237 |
+
"to": "Ferio"
|
| 238 |
+
},
|
| 239 |
+
{
|
| 240 |
+
"from": "Econv",
|
| 241 |
+
"to": "Cesare"
|
| 242 |
+
},
|
| 243 |
+
{
|
| 244 |
+
"from": "Celarent",
|
| 245 |
+
"to": "Cesare"
|
| 246 |
+
},
|
| 247 |
+
{
|
| 248 |
+
"from": "Econv",
|
| 249 |
+
"to": "Camestres"
|
| 250 |
+
},
|
| 251 |
+
{
|
| 252 |
+
"from": "Celarent",
|
| 253 |
+
"to": "Camestres"
|
| 254 |
+
},
|
| 255 |
+
{
|
| 256 |
+
"from": "Econv",
|
| 257 |
+
"to": "Festino"
|
| 258 |
+
},
|
| 259 |
+
{
|
| 260 |
+
"from": "Ferio",
|
| 261 |
+
"to": "Festino"
|
| 262 |
+
},
|
| 263 |
+
{
|
| 264 |
+
"from": "Barbara",
|
| 265 |
+
"to": "Baroco"
|
| 266 |
+
},
|
| 267 |
+
{
|
| 268 |
+
"from": "Aconv",
|
| 269 |
+
"to": "Darapti"
|
| 270 |
+
},
|
| 271 |
+
{
|
| 272 |
+
"from": "Darii",
|
| 273 |
+
"to": "Darapti"
|
| 274 |
+
},
|
| 275 |
+
{
|
| 276 |
+
"from": "Aconv",
|
| 277 |
+
"to": "Felapton"
|
| 278 |
+
},
|
| 279 |
+
{
|
| 280 |
+
"from": "Ferio",
|
| 281 |
+
"to": "Felapton"
|
| 282 |
+
},
|
| 283 |
+
{
|
| 284 |
+
"from": "Iconv",
|
| 285 |
+
"to": "Disamis"
|
| 286 |
+
},
|
| 287 |
+
{
|
| 288 |
+
"from": "Darii",
|
| 289 |
+
"to": "Disamis"
|
| 290 |
+
},
|
| 291 |
+
{
|
| 292 |
+
"from": "Aconv",
|
| 293 |
+
"to": "Datisi"
|
| 294 |
+
},
|
| 295 |
+
{
|
| 296 |
+
"from": "Darii",
|
| 297 |
+
"to": "Datisi"
|
| 298 |
+
},
|
| 299 |
+
{
|
| 300 |
+
"from": "Barbara",
|
| 301 |
+
"to": "Bocardo"
|
| 302 |
+
},
|
| 303 |
+
{
|
| 304 |
+
"from": "Aconv",
|
| 305 |
+
"to": "Ferison"
|
| 306 |
+
},
|
| 307 |
+
{
|
| 308 |
+
"from": "Ferio",
|
| 309 |
+
"to": "Ferison"
|
| 310 |
+
}
|
| 311 |
+
],
|
| 312 |
+
"colorScheme": {
|
| 313 |
+
"axiom": {
|
| 314 |
+
"fill": "#e74c3c",
|
| 315 |
+
"stroke": "#c0392b"
|
| 316 |
+
},
|
| 317 |
+
"definition": {
|
| 318 |
+
"fill": "#3498db",
|
| 319 |
+
"stroke": "#2980b9"
|
| 320 |
+
},
|
| 321 |
+
"theorem": {
|
| 322 |
+
"fill": "#1abc9c",
|
| 323 |
+
"stroke": "#16a085"
|
| 324 |
+
}
|
| 325 |
+
}
|
| 326 |
+
}
|
data/aristotle-syllogistic.mmd
ADDED
|
@@ -0,0 +1,52 @@
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 1 |
+
graph TD
|
| 2 |
+
DefAEIO("DefAEIO Categorical forms")
|
| 3 |
+
DefFig("DefFig Figures 1,2,3")
|
| 4 |
+
Econv("Econv E-conversion")
|
| 5 |
+
Iconv("Iconv I-conversion")
|
| 6 |
+
Aconv("Aconv A-conversion")
|
| 7 |
+
Barbara("Barbara Barbara")
|
| 8 |
+
Celarent("Celarent Celarent")
|
| 9 |
+
Darii("Darii Darii")
|
| 10 |
+
Ferio("Ferio Ferio")
|
| 11 |
+
Cesare("Cesare Cesare")
|
| 12 |
+
Camestres("Camestres Camestres")
|
| 13 |
+
Festino("Festino Festino")
|
| 14 |
+
Baroco("Baroco Baroco")
|
| 15 |
+
Darapti("Darapti Darapti")
|
| 16 |
+
Felapton("Felapton Felapton")
|
| 17 |
+
Disamis("Disamis Disamis")
|
| 18 |
+
Datisi("Datisi Datisi")
|
| 19 |
+
Bocardo("Bocardo Bocardo")
|
| 20 |
+
Ferison("Ferison Ferison")
|
| 21 |
+
DefAEIO --> Barbara
|
| 22 |
+
DefFig --> Barbara
|
| 23 |
+
DefAEIO --> Celarent
|
| 24 |
+
DefFig --> Celarent
|
| 25 |
+
DefAEIO --> Darii
|
| 26 |
+
DefFig --> Darii
|
| 27 |
+
DefAEIO --> Ferio
|
| 28 |
+
DefFig --> Ferio
|
| 29 |
+
Econv --> Cesare
|
| 30 |
+
Celarent --> Cesare
|
| 31 |
+
Econv --> Camestres
|
| 32 |
+
Celarent --> Camestres
|
| 33 |
+
Econv --> Festino
|
| 34 |
+
Ferio --> Festino
|
| 35 |
+
Barbara --> Baroco
|
| 36 |
+
Aconv --> Darapti
|
| 37 |
+
Darii --> Darapti
|
| 38 |
+
Aconv --> Felapton
|
| 39 |
+
Ferio --> Felapton
|
| 40 |
+
Iconv --> Disamis
|
| 41 |
+
Darii --> Disamis
|
| 42 |
+
Aconv --> Datisi
|
| 43 |
+
Darii --> Datisi
|
| 44 |
+
Barbara --> Bocardo
|
| 45 |
+
Aconv --> Ferison
|
| 46 |
+
Ferio --> Ferison
|
| 47 |
+
classDef axiom fill:#e74c3c,color:#fff,stroke:#c0392b
|
| 48 |
+
classDef definition fill:#3498db,color:#fff,stroke:#2980b9
|
| 49 |
+
classDef theorem fill:#1abc9c,color:#fff,stroke:#16a085
|
| 50 |
+
class Econv,Iconv,Aconv,Barbara,Celarent,Darii,Ferio axiom
|
| 51 |
+
class DefAEIO,DefFig definition
|
| 52 |
+
class Cesare,Camestres,Festino,Baroco,Darapti,Felapton,Disamis,Datisi,Bocardo,Ferison theorem
|
data/combinatorics-advanced-counting.mmd
ADDED
|
@@ -0,0 +1,24 @@
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 1 |
+
graph TD
|
| 2 |
+
DefFact("DefFact Factorial")
|
| 3 |
+
DefSum("DefSum Sum principle")
|
| 4 |
+
DefProd("DefProd Product principle")
|
| 5 |
+
PermNoRep("PermNoRep Permutations no rep")
|
| 6 |
+
Pigeonhole("Pigeonhole Pigeonhole principle")
|
| 7 |
+
InclExcl("InclExcl Inclusion-exclusion")
|
| 8 |
+
InclExcl3("InclExcl3 Incl-excl 3 sets")
|
| 9 |
+
Derange("Derange Derangements")
|
| 10 |
+
Stirling2("Stirling2 Stirling numbers")
|
| 11 |
+
DefFact --> PermNoRep
|
| 12 |
+
DefProd --> PermNoRep
|
| 13 |
+
DefSum --> Pigeonhole
|
| 14 |
+
DefSum --> InclExcl
|
| 15 |
+
InclExcl --> InclExcl3
|
| 16 |
+
InclExcl --> Derange
|
| 17 |
+
PermNoRep --> Derange
|
| 18 |
+
DefSum --> Stirling2
|
| 19 |
+
DefProd --> Stirling2
|
| 20 |
+
classDef axiom fill:#e74c3c,color:#fff,stroke:#c0392b
|
| 21 |
+
classDef definition fill:#3498db,color:#fff,stroke:#2980b9
|
| 22 |
+
classDef theorem fill:#1abc9c,color:#fff,stroke:#16a085
|
| 23 |
+
class DefFact,DefSum,DefProd definition
|
| 24 |
+
class PermNoRep,Pigeonhole,InclExcl,InclExcl3,Derange,Stirling2 theorem
|
data/combinatorics-combinations-binomial.mmd
ADDED
|
@@ -0,0 +1,20 @@
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 1 |
+
graph TD
|
| 2 |
+
DefFact("DefFact Factorial")
|
| 3 |
+
DefProd("DefProd Product principle")
|
| 4 |
+
PermNoRep("PermNoRep Permutations no rep")
|
| 5 |
+
CombNoRep("CombNoRep Combinations")
|
| 6 |
+
CombRep("CombRep Combinations with rep")
|
| 7 |
+
BinomThm("BinomThm Binomial theorem")
|
| 8 |
+
Pascal("Pascal Pascal identity")
|
| 9 |
+
DefFact --> PermNoRep
|
| 10 |
+
DefProd --> PermNoRep
|
| 11 |
+
PermNoRep --> CombNoRep
|
| 12 |
+
DefFact --> CombNoRep
|
| 13 |
+
CombNoRep --> CombRep
|
| 14 |
+
CombNoRep --> BinomThm
|
| 15 |
+
CombNoRep --> Pascal
|
| 16 |
+
classDef axiom fill:#e74c3c,color:#fff,stroke:#c0392b
|
| 17 |
+
classDef definition fill:#3498db,color:#fff,stroke:#2980b9
|
| 18 |
+
classDef theorem fill:#1abc9c,color:#fff,stroke:#16a085
|
| 19 |
+
class DefFact,DefProd definition
|
| 20 |
+
class PermNoRep,CombNoRep,CombRep,BinomThm,Pascal theorem
|
data/combinatorics-principles-permutations.mmd
ADDED
|
@@ -0,0 +1,17 @@
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 1 |
+
graph TD
|
| 2 |
+
DefFact("DefFact Factorial")
|
| 3 |
+
DefSum("DefSum Sum principle")
|
| 4 |
+
DefProd("DefProd Product principle")
|
| 5 |
+
PermNoRep("PermNoRep Permutations no rep")
|
| 6 |
+
PermRep("PermRep Permutations with rep")
|
| 7 |
+
CombNoRep("CombNoRep Combinations")
|
| 8 |
+
DefFact --> PermNoRep
|
| 9 |
+
DefProd --> PermNoRep
|
| 10 |
+
DefProd --> PermRep
|
| 11 |
+
PermNoRep --> CombNoRep
|
| 12 |
+
DefFact --> CombNoRep
|
| 13 |
+
classDef axiom fill:#e74c3c,color:#fff,stroke:#c0392b
|
| 14 |
+
classDef definition fill:#3498db,color:#fff,stroke:#2980b9
|
| 15 |
+
classDef theorem fill:#1abc9c,color:#fff,stroke:#16a085
|
| 16 |
+
class DefFact,DefSum,DefProd definition
|
| 17 |
+
class PermNoRep,PermRep,CombNoRep theorem
|
data/combinatorics.json
ADDED
|
@@ -0,0 +1,239 @@
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
|
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|
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|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 1 |
+
{
|
| 2 |
+
"schemaVersion": "1.0",
|
| 3 |
+
"discourse": {
|
| 4 |
+
"id": "combinatorics",
|
| 5 |
+
"name": "Combinatorics",
|
| 6 |
+
"subject": "discrete_mathematics",
|
| 7 |
+
"variant": "classical",
|
| 8 |
+
"description": "Counting principles: sum and product rules, permutations (with/without repetition), combinations, binomial theorem, pigeonhole principle, inclusion-exclusion, derangements.",
|
| 9 |
+
"structure": {
|
| 10 |
+
"axioms": 0,
|
| 11 |
+
"definitions": 3,
|
| 12 |
+
"theorems": 11
|
| 13 |
+
}
|
| 14 |
+
},
|
| 15 |
+
"metadata": {
|
| 16 |
+
"created": "2026-03-15",
|
| 17 |
+
"lastUpdated": "2026-03-15",
|
| 18 |
+
"version": "1.0.0",
|
| 19 |
+
"license": "CC BY 4.0",
|
| 20 |
+
"authors": [
|
| 21 |
+
"Welz, G."
|
| 22 |
+
],
|
| 23 |
+
"methodology": "Programming Framework",
|
| 24 |
+
"citation": "Welz, G. (2026). Combinatorics Dependency Graph. Programming Framework.",
|
| 25 |
+
"keywords": [
|
| 26 |
+
"combinatorics",
|
| 27 |
+
"permutations",
|
| 28 |
+
"combinations",
|
| 29 |
+
"counting",
|
| 30 |
+
"binomial theorem"
|
| 31 |
+
]
|
| 32 |
+
},
|
| 33 |
+
"sources": [
|
| 34 |
+
{
|
| 35 |
+
"id": "dmoi",
|
| 36 |
+
"type": "primary",
|
| 37 |
+
"title": "Discrete Mathematics: An Open Introduction",
|
| 38 |
+
"url": "https://discrete.openmathbooks.org/dmoi4/sec_counting-combperm.html",
|
| 39 |
+
"notes": "Counting principles"
|
| 40 |
+
},
|
| 41 |
+
{
|
| 42 |
+
"id": "mathisfun",
|
| 43 |
+
"type": "digital",
|
| 44 |
+
"title": "Combinations and Permutations",
|
| 45 |
+
"url": "https://www.mathsisfun.com/combinatorics/combinations-permutations.html",
|
| 46 |
+
"notes": "Formulas"
|
| 47 |
+
}
|
| 48 |
+
],
|
| 49 |
+
"nodes": [
|
| 50 |
+
{
|
| 51 |
+
"id": "DefFact",
|
| 52 |
+
"type": "definition",
|
| 53 |
+
"label": "Factorial: n! = n(n-1)...1, 0!=1",
|
| 54 |
+
"shortLabel": "DefFact",
|
| 55 |
+
"short": "Factorial",
|
| 56 |
+
"colorClass": "definition"
|
| 57 |
+
},
|
| 58 |
+
{
|
| 59 |
+
"id": "DefSum",
|
| 60 |
+
"type": "definition",
|
| 61 |
+
"label": "Sum principle: disjoint choices add (OR)",
|
| 62 |
+
"shortLabel": "DefSum",
|
| 63 |
+
"short": "Sum principle",
|
| 64 |
+
"colorClass": "definition"
|
| 65 |
+
},
|
| 66 |
+
{
|
| 67 |
+
"id": "DefProd",
|
| 68 |
+
"type": "definition",
|
| 69 |
+
"label": "Product principle: sequential choices multiply (AND)",
|
| 70 |
+
"shortLabel": "DefProd",
|
| 71 |
+
"short": "Product principle",
|
| 72 |
+
"colorClass": "definition"
|
| 73 |
+
},
|
| 74 |
+
{
|
| 75 |
+
"id": "PermNoRep",
|
| 76 |
+
"type": "theorem",
|
| 77 |
+
"label": "P(n,r) = n!/(n-r)! arrangements of r from n",
|
| 78 |
+
"shortLabel": "PermNoRep",
|
| 79 |
+
"short": "Permutations no rep",
|
| 80 |
+
"colorClass": "theorem"
|
| 81 |
+
},
|
| 82 |
+
{
|
| 83 |
+
"id": "PermRep",
|
| 84 |
+
"type": "theorem",
|
| 85 |
+
"label": "n^r arrangements of r from n with repetition",
|
| 86 |
+
"shortLabel": "PermRep",
|
| 87 |
+
"short": "Permutations with rep",
|
| 88 |
+
"colorClass": "theorem"
|
| 89 |
+
},
|
| 90 |
+
{
|
| 91 |
+
"id": "CombNoRep",
|
| 92 |
+
"type": "theorem",
|
| 93 |
+
"label": "C(n,r) = n!/(r!(n-r)!) = P(n,r)/r!",
|
| 94 |
+
"shortLabel": "CombNoRep",
|
| 95 |
+
"short": "Combinations",
|
| 96 |
+
"colorClass": "theorem"
|
| 97 |
+
},
|
| 98 |
+
{
|
| 99 |
+
"id": "CombRep",
|
| 100 |
+
"type": "theorem",
|
| 101 |
+
"label": "C(n+r-1,r) ways to choose r from n with rep",
|
| 102 |
+
"shortLabel": "CombRep",
|
| 103 |
+
"short": "Combinations with rep",
|
| 104 |
+
"colorClass": "theorem"
|
| 105 |
+
},
|
| 106 |
+
{
|
| 107 |
+
"id": "BinomThm",
|
| 108 |
+
"type": "theorem",
|
| 109 |
+
"label": "(a+b)^n = sum C(n,k) a^k b^(n-k)",
|
| 110 |
+
"shortLabel": "BinomThm",
|
| 111 |
+
"short": "Binomial theorem",
|
| 112 |
+
"colorClass": "theorem"
|
| 113 |
+
},
|
| 114 |
+
{
|
| 115 |
+
"id": "Pascal",
|
| 116 |
+
"type": "theorem",
|
| 117 |
+
"label": "C(n,k) = C(n-1,k-1) + C(n-1,k)",
|
| 118 |
+
"shortLabel": "Pascal",
|
| 119 |
+
"short": "Pascal identity",
|
| 120 |
+
"colorClass": "theorem"
|
| 121 |
+
},
|
| 122 |
+
{
|
| 123 |
+
"id": "Pigeonhole",
|
| 124 |
+
"type": "theorem",
|
| 125 |
+
"label": "n+1 objects in n boxes implies one box has 2+",
|
| 126 |
+
"shortLabel": "Pigeonhole",
|
| 127 |
+
"short": "Pigeonhole principle",
|
| 128 |
+
"colorClass": "theorem"
|
| 129 |
+
},
|
| 130 |
+
{
|
| 131 |
+
"id": "InclExcl",
|
| 132 |
+
"type": "theorem",
|
| 133 |
+
"label": "|A union B| = |A| + |B| - |A intersect B|",
|
| 134 |
+
"shortLabel": "InclExcl",
|
| 135 |
+
"short": "Inclusion-exclusion",
|
| 136 |
+
"colorClass": "theorem"
|
| 137 |
+
},
|
| 138 |
+
{
|
| 139 |
+
"id": "InclExcl3",
|
| 140 |
+
"type": "theorem",
|
| 141 |
+
"label": "Inclusion-exclusion for 3 sets",
|
| 142 |
+
"shortLabel": "InclExcl3",
|
| 143 |
+
"short": "Incl-excl 3 sets",
|
| 144 |
+
"colorClass": "theorem"
|
| 145 |
+
},
|
| 146 |
+
{
|
| 147 |
+
"id": "Derange",
|
| 148 |
+
"type": "theorem",
|
| 149 |
+
"label": "D(n) = n! sum (-1)^k/k! derangements",
|
| 150 |
+
"shortLabel": "Derange",
|
| 151 |
+
"short": "Derangements",
|
| 152 |
+
"colorClass": "theorem"
|
| 153 |
+
},
|
| 154 |
+
{
|
| 155 |
+
"id": "Stirling2",
|
| 156 |
+
"type": "theorem",
|
| 157 |
+
"label": "S(n,k) = partitions of n into k nonempty sets",
|
| 158 |
+
"shortLabel": "Stirling2",
|
| 159 |
+
"short": "Stirling numbers",
|
| 160 |
+
"colorClass": "theorem"
|
| 161 |
+
}
|
| 162 |
+
],
|
| 163 |
+
"edges": [
|
| 164 |
+
{
|
| 165 |
+
"from": "DefFact",
|
| 166 |
+
"to": "PermNoRep"
|
| 167 |
+
},
|
| 168 |
+
{
|
| 169 |
+
"from": "DefProd",
|
| 170 |
+
"to": "PermNoRep"
|
| 171 |
+
},
|
| 172 |
+
{
|
| 173 |
+
"from": "DefProd",
|
| 174 |
+
"to": "PermRep"
|
| 175 |
+
},
|
| 176 |
+
{
|
| 177 |
+
"from": "PermNoRep",
|
| 178 |
+
"to": "CombNoRep"
|
| 179 |
+
},
|
| 180 |
+
{
|
| 181 |
+
"from": "DefFact",
|
| 182 |
+
"to": "CombNoRep"
|
| 183 |
+
},
|
| 184 |
+
{
|
| 185 |
+
"from": "CombNoRep",
|
| 186 |
+
"to": "CombRep"
|
| 187 |
+
},
|
| 188 |
+
{
|
| 189 |
+
"from": "CombNoRep",
|
| 190 |
+
"to": "BinomThm"
|
| 191 |
+
},
|
| 192 |
+
{
|
| 193 |
+
"from": "CombNoRep",
|
| 194 |
+
"to": "Pascal"
|
| 195 |
+
},
|
| 196 |
+
{
|
| 197 |
+
"from": "DefSum",
|
| 198 |
+
"to": "Pigeonhole"
|
| 199 |
+
},
|
| 200 |
+
{
|
| 201 |
+
"from": "DefSum",
|
| 202 |
+
"to": "InclExcl"
|
| 203 |
+
},
|
| 204 |
+
{
|
| 205 |
+
"from": "InclExcl",
|
| 206 |
+
"to": "InclExcl3"
|
| 207 |
+
},
|
| 208 |
+
{
|
| 209 |
+
"from": "InclExcl",
|
| 210 |
+
"to": "Derange"
|
| 211 |
+
},
|
| 212 |
+
{
|
| 213 |
+
"from": "PermNoRep",
|
| 214 |
+
"to": "Derange"
|
| 215 |
+
},
|
| 216 |
+
{
|
| 217 |
+
"from": "DefSum",
|
| 218 |
+
"to": "Stirling2"
|
| 219 |
+
},
|
| 220 |
+
{
|
| 221 |
+
"from": "DefProd",
|
| 222 |
+
"to": "Stirling2"
|
| 223 |
+
}
|
| 224 |
+
],
|
| 225 |
+
"colorScheme": {
|
| 226 |
+
"axiom": {
|
| 227 |
+
"fill": "#e74c3c",
|
| 228 |
+
"stroke": "#c0392b"
|
| 229 |
+
},
|
| 230 |
+
"definition": {
|
| 231 |
+
"fill": "#3498db",
|
| 232 |
+
"stroke": "#2980b9"
|
| 233 |
+
},
|
| 234 |
+
"theorem": {
|
| 235 |
+
"fill": "#1abc9c",
|
| 236 |
+
"stroke": "#16a085"
|
| 237 |
+
}
|
| 238 |
+
}
|
| 239 |
+
}
|
data/combinatorics.mmd
ADDED
|
@@ -0,0 +1,35 @@
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 1 |
+
graph TD
|
| 2 |
+
DefFact("DefFact Factorial")
|
| 3 |
+
DefSum("DefSum Sum principle")
|
| 4 |
+
DefProd("DefProd Product principle")
|
| 5 |
+
PermNoRep("PermNoRep Permutations no rep")
|
| 6 |
+
PermRep("PermRep Permutations with rep")
|
| 7 |
+
CombNoRep("CombNoRep Combinations")
|
| 8 |
+
CombRep("CombRep Combinations with rep")
|
| 9 |
+
BinomThm("BinomThm Binomial theorem")
|
| 10 |
+
Pascal("Pascal Pascal identity")
|
| 11 |
+
Pigeonhole("Pigeonhole Pigeonhole principle")
|
| 12 |
+
InclExcl("InclExcl Inclusion-exclusion")
|
| 13 |
+
InclExcl3("InclExcl3 Incl-excl 3 sets")
|
| 14 |
+
Derange("Derange Derangements")
|
| 15 |
+
Stirling2("Stirling2 Stirling numbers")
|
| 16 |
+
DefFact --> PermNoRep
|
| 17 |
+
DefProd --> PermNoRep
|
| 18 |
+
DefProd --> PermRep
|
| 19 |
+
PermNoRep --> CombNoRep
|
| 20 |
+
DefFact --> CombNoRep
|
| 21 |
+
CombNoRep --> CombRep
|
| 22 |
+
CombNoRep --> BinomThm
|
| 23 |
+
CombNoRep --> Pascal
|
| 24 |
+
DefSum --> Pigeonhole
|
| 25 |
+
DefSum --> InclExcl
|
| 26 |
+
InclExcl --> InclExcl3
|
| 27 |
+
InclExcl --> Derange
|
| 28 |
+
PermNoRep --> Derange
|
| 29 |
+
DefSum --> Stirling2
|
| 30 |
+
DefProd --> Stirling2
|
| 31 |
+
classDef axiom fill:#e74c3c,color:#fff,stroke:#c0392b
|
| 32 |
+
classDef definition fill:#3498db,color:#fff,stroke:#2980b9
|
| 33 |
+
classDef theorem fill:#1abc9c,color:#fff,stroke:#16a085
|
| 34 |
+
class DefFact,DefSum,DefProd definition
|
| 35 |
+
class PermNoRep,PermRep,CombNoRep,CombRep,BinomThm,Pascal,Pigeonhole,InclExcl,InclExcl3,Derange,Stirling2 theorem
|
data/euclid-elements-book-i-props-1-10.mmd
ADDED
|
@@ -0,0 +1,49 @@
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 1 |
+
graph TD
|
| 2 |
+
P1["Post. 1\nDraw a straight line from any po..."]
|
| 3 |
+
P2["Post. 2\nProduce a finite straight line c..."]
|
| 4 |
+
P3["Post. 3\nDescribe a circle with any cente..."]
|
| 5 |
+
P4["Post. 4\nAll right angles equal one another"]
|
| 6 |
+
P5["Post. 5\nParallel postulate: if interior ..."]
|
| 7 |
+
CN1["CN 1\nThings equal to the same thing a..."]
|
| 8 |
+
CN2["CN 2\nIf equals are added to equals, t..."]
|
| 9 |
+
CN3["CN 3\nIf equals are subtracted from eq..."]
|
| 10 |
+
CN4["CN 4\nThings coinciding with one anoth..."]
|
| 11 |
+
CN5["CN 5\nThe whole is greater than the part"]
|
| 12 |
+
Prop1["Prop. I.1\nEquilateral triangle on given line"]
|
| 13 |
+
Prop2["Prop. I.2\nPlace line equal to given at point"]
|
| 14 |
+
Prop3["Prop. I.3\nCut off from greater segment equal to less"]
|
| 15 |
+
Prop4["Prop. I.4\nSAS congruence"]
|
| 16 |
+
Prop5["Prop. I.5\nBase angles of isosceles equal"]
|
| 17 |
+
Prop6["Prop. I.6\nSides opposite equal angles equal"]
|
| 18 |
+
Prop7["Prop. I.7\nUniqueness of triangle from ends"]
|
| 19 |
+
Prop8["Prop. I.8\nSSS congruence"]
|
| 20 |
+
Prop9["Prop. I.9\nBisect angle"]
|
| 21 |
+
Prop10["Prop. I.10\nBisect line"]
|
| 22 |
+
P1 --> Prop1
|
| 23 |
+
P3 --> Prop1
|
| 24 |
+
Prop1 --> Prop2
|
| 25 |
+
P1 --> Prop2
|
| 26 |
+
P2 --> Prop2
|
| 27 |
+
P3 --> Prop2
|
| 28 |
+
Prop2 --> Prop3
|
| 29 |
+
P3 --> Prop3
|
| 30 |
+
CN4 --> Prop4
|
| 31 |
+
CN5 --> Prop4
|
| 32 |
+
Prop3 --> Prop5
|
| 33 |
+
Prop4 --> Prop5
|
| 34 |
+
Prop3 --> Prop6
|
| 35 |
+
Prop4 --> Prop6
|
| 36 |
+
Prop5 --> Prop7
|
| 37 |
+
Prop7 --> Prop8
|
| 38 |
+
Prop1 --> Prop9
|
| 39 |
+
Prop3 --> Prop9
|
| 40 |
+
Prop8 --> Prop9
|
| 41 |
+
Prop1 --> Prop10
|
| 42 |
+
Prop4 --> Prop10
|
| 43 |
+
Prop9 --> Prop10
|
| 44 |
+
classDef postulate fill:#e74c3c,color:#fff,stroke:#c0392b
|
| 45 |
+
classDef commonNotion fill:#9b59b6,color:#fff,stroke:#8e44ad
|
| 46 |
+
classDef proposition fill:#1abc9c,color:#fff,stroke:#16a085
|
| 47 |
+
class P1,P2,P3,P4,P5 postulate
|
| 48 |
+
class CN1,CN2,CN3,CN4,CN5 commonNotion
|
| 49 |
+
class Prop1,Prop2,Prop3,Prop4,Prop5,Prop6,Prop7,Prop8,Prop9,Prop10 proposition
|
data/euclid-elements-book-i-props-11-20.mmd
ADDED
|
@@ -0,0 +1,78 @@
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 1 |
+
graph TD
|
| 2 |
+
P1["Post. 1\nDraw a straight line from any po..."]
|
| 3 |
+
P2["Post. 2\nProduce a finite straight line c..."]
|
| 4 |
+
P3["Post. 3\nDescribe a circle with any cente..."]
|
| 5 |
+
P4["Post. 4\nAll right angles equal one another"]
|
| 6 |
+
P5["Post. 5\nParallel postulate: if interior ..."]
|
| 7 |
+
CN1["CN 1\nThings equal to the same thing a..."]
|
| 8 |
+
CN2["CN 2\nIf equals are added to equals, t..."]
|
| 9 |
+
CN3["CN 3\nIf equals are subtracted from eq..."]
|
| 10 |
+
CN4["CN 4\nThings coinciding with one anoth..."]
|
| 11 |
+
CN5["CN 5\nThe whole is greater than the part"]
|
| 12 |
+
Prop1["Prop. I.1\nEquilateral triangle on given line"]
|
| 13 |
+
Prop2["Prop. I.2\nPlace line equal to given at point"]
|
| 14 |
+
Prop3["Prop. I.3\nCut off from greater segment equal to less"]
|
| 15 |
+
Prop4["Prop. I.4\nSAS congruence"]
|
| 16 |
+
Prop5["Prop. I.5\nBase angles of isosceles equal"]
|
| 17 |
+
Prop7["Prop. I.7\nUniqueness of triangle from ends"]
|
| 18 |
+
Prop8["Prop. I.8\nSSS congruence"]
|
| 19 |
+
Prop9["Prop. I.9\nBisect angle"]
|
| 20 |
+
Prop10["Prop. I.10\nBisect line"]
|
| 21 |
+
Prop11["Prop. I.11\nPerpendicular from point on line"]
|
| 22 |
+
Prop12["Prop. I.12\nPerpendicular from point not on line"]
|
| 23 |
+
Prop13["Prop. I.13\nAngles on line sum to two right"]
|
| 24 |
+
Prop14["Prop. I.14\nIf angles sum to two right, straight line"]
|
| 25 |
+
Prop15["Prop. I.15\nVertical angles equal"]
|
| 26 |
+
Prop16["Prop. I.16\nExterior angle > interior opposite"]
|
| 27 |
+
Prop17["Prop. I.17\nSum of two angles < two right"]
|
| 28 |
+
Prop18["Prop. I.18\nAngle opposite greater side greater"]
|
| 29 |
+
Prop19["Prop. I.19\nSide opposite greater angle greater"]
|
| 30 |
+
Prop20["Prop. I.20\nTriangle inequality"]
|
| 31 |
+
P1 --> Prop1
|
| 32 |
+
P3 --> Prop1
|
| 33 |
+
Prop1 --> Prop2
|
| 34 |
+
P1 --> Prop2
|
| 35 |
+
P2 --> Prop2
|
| 36 |
+
P3 --> Prop2
|
| 37 |
+
Prop2 --> Prop3
|
| 38 |
+
P3 --> Prop3
|
| 39 |
+
CN4 --> Prop4
|
| 40 |
+
CN5 --> Prop4
|
| 41 |
+
Prop3 --> Prop5
|
| 42 |
+
Prop4 --> Prop5
|
| 43 |
+
Prop5 --> Prop7
|
| 44 |
+
Prop7 --> Prop8
|
| 45 |
+
Prop1 --> Prop9
|
| 46 |
+
Prop3 --> Prop9
|
| 47 |
+
Prop8 --> Prop9
|
| 48 |
+
Prop1 --> Prop10
|
| 49 |
+
Prop4 --> Prop10
|
| 50 |
+
Prop9 --> Prop10
|
| 51 |
+
Prop1 --> Prop11
|
| 52 |
+
Prop3 --> Prop11
|
| 53 |
+
Prop8 --> Prop11
|
| 54 |
+
Prop8 --> Prop12
|
| 55 |
+
Prop10 --> Prop12
|
| 56 |
+
Prop11 --> Prop13
|
| 57 |
+
Prop13 --> Prop14
|
| 58 |
+
Prop13 --> Prop15
|
| 59 |
+
Prop3 --> Prop16
|
| 60 |
+
Prop4 --> Prop16
|
| 61 |
+
Prop10 --> Prop16
|
| 62 |
+
Prop15 --> Prop16
|
| 63 |
+
Prop13 --> Prop17
|
| 64 |
+
Prop16 --> Prop17
|
| 65 |
+
Prop3 --> Prop18
|
| 66 |
+
Prop5 --> Prop18
|
| 67 |
+
Prop16 --> Prop18
|
| 68 |
+
Prop5 --> Prop19
|
| 69 |
+
Prop18 --> Prop19
|
| 70 |
+
Prop3 --> Prop20
|
| 71 |
+
Prop5 --> Prop20
|
| 72 |
+
Prop19 --> Prop20
|
| 73 |
+
classDef postulate fill:#e74c3c,color:#fff,stroke:#c0392b
|
| 74 |
+
classDef commonNotion fill:#9b59b6,color:#fff,stroke:#8e44ad
|
| 75 |
+
classDef proposition fill:#1abc9c,color:#fff,stroke:#16a085
|
| 76 |
+
class P1,P2,P3,P4,P5 postulate
|
| 77 |
+
class CN1,CN2,CN3,CN4,CN5 commonNotion
|
| 78 |
+
class Prop1,Prop2,Prop3,Prop4,Prop5,Prop7,Prop8,Prop9,Prop10,Prop11,Prop12,Prop13,Prop14,Prop15,Prop16,Prop17,Prop18,Prop19,Prop20 proposition
|
data/euclid-elements-book-i-props-21-30.mmd
ADDED
|
@@ -0,0 +1,105 @@
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 1 |
+
graph TD
|
| 2 |
+
P1["Post. 1\nDraw a straight line from any po..."]
|
| 3 |
+
P2["Post. 2\nProduce a finite straight line c..."]
|
| 4 |
+
P3["Post. 3\nDescribe a circle with any cente..."]
|
| 5 |
+
P4["Post. 4\nAll right angles equal one another"]
|
| 6 |
+
P5["Post. 5\nParallel postulate: if interior ..."]
|
| 7 |
+
CN1["CN 1\nThings equal to the same thing a..."]
|
| 8 |
+
CN2["CN 2\nIf equals are added to equals, t..."]
|
| 9 |
+
CN3["CN 3\nIf equals are subtracted from eq..."]
|
| 10 |
+
CN4["CN 4\nThings coinciding with one anoth..."]
|
| 11 |
+
CN5["CN 5\nThe whole is greater than the part"]
|
| 12 |
+
Prop1["Prop. I.1\nEquilateral triangle on given line"]
|
| 13 |
+
Prop2["Prop. I.2\nPlace line equal to given at point"]
|
| 14 |
+
Prop3["Prop. I.3\nCut off from greater segment equal to less"]
|
| 15 |
+
Prop4["Prop. I.4\nSAS congruence"]
|
| 16 |
+
Prop5["Prop. I.5\nBase angles of isosceles equal"]
|
| 17 |
+
Prop7["Prop. I.7\nUniqueness of triangle from ends"]
|
| 18 |
+
Prop8["Prop. I.8\nSSS congruence"]
|
| 19 |
+
Prop9["Prop. I.9\nBisect angle"]
|
| 20 |
+
Prop10["Prop. I.10\nBisect line"]
|
| 21 |
+
Prop11["Prop. I.11\nPerpendicular from point on line"]
|
| 22 |
+
Prop13["Prop. I.13\nAngles on line sum to two right"]
|
| 23 |
+
Prop15["Prop. I.15\nVertical angles equal"]
|
| 24 |
+
Prop16["Prop. I.16\nExterior angle > interior opposite"]
|
| 25 |
+
Prop18["Prop. I.18\nAngle opposite greater side greater"]
|
| 26 |
+
Prop19["Prop. I.19\nSide opposite greater angle greater"]
|
| 27 |
+
Prop20["Prop. I.20\nTriangle inequality"]
|
| 28 |
+
Prop21["Prop. I.21\nLines from ends within triangle"]
|
| 29 |
+
Prop22["Prop. I.22\nConstruct triangle from three lines"]
|
| 30 |
+
Prop23["Prop. I.23\nConstruct angle equal to given"]
|
| 31 |
+
Prop24["Prop. I.24\nSAS for greater angle => greater base"]
|
| 32 |
+
Prop25["Prop. I.25\nSAS for greater base => greater angle"]
|
| 33 |
+
Prop26["Prop. I.26\nAAS congruence"]
|
| 34 |
+
Prop27["Prop. I.27\nAlternate angles equal => parallel"]
|
| 35 |
+
Prop28["Prop. I.28\nExterior = interior opposite => parallel"]
|
| 36 |
+
Prop29["Prop. I.29\nParallel => alternate angles equal"]
|
| 37 |
+
Prop30["Prop. I.30\nTransitivity of parallel"]
|
| 38 |
+
P1 --> Prop1
|
| 39 |
+
P3 --> Prop1
|
| 40 |
+
Prop1 --> Prop2
|
| 41 |
+
P1 --> Prop2
|
| 42 |
+
P2 --> Prop2
|
| 43 |
+
P3 --> Prop2
|
| 44 |
+
Prop2 --> Prop3
|
| 45 |
+
P3 --> Prop3
|
| 46 |
+
CN4 --> Prop4
|
| 47 |
+
CN5 --> Prop4
|
| 48 |
+
Prop3 --> Prop5
|
| 49 |
+
Prop4 --> Prop5
|
| 50 |
+
Prop5 --> Prop7
|
| 51 |
+
Prop7 --> Prop8
|
| 52 |
+
Prop1 --> Prop9
|
| 53 |
+
Prop3 --> Prop9
|
| 54 |
+
Prop8 --> Prop9
|
| 55 |
+
Prop1 --> Prop10
|
| 56 |
+
Prop4 --> Prop10
|
| 57 |
+
Prop9 --> Prop10
|
| 58 |
+
Prop1 --> Prop11
|
| 59 |
+
Prop3 --> Prop11
|
| 60 |
+
Prop8 --> Prop11
|
| 61 |
+
Prop11 --> Prop13
|
| 62 |
+
Prop13 --> Prop15
|
| 63 |
+
Prop3 --> Prop16
|
| 64 |
+
Prop4 --> Prop16
|
| 65 |
+
Prop10 --> Prop16
|
| 66 |
+
Prop15 --> Prop16
|
| 67 |
+
Prop3 --> Prop18
|
| 68 |
+
Prop5 --> Prop18
|
| 69 |
+
Prop16 --> Prop18
|
| 70 |
+
Prop5 --> Prop19
|
| 71 |
+
Prop18 --> Prop19
|
| 72 |
+
Prop3 --> Prop20
|
| 73 |
+
Prop5 --> Prop20
|
| 74 |
+
Prop19 --> Prop20
|
| 75 |
+
Prop16 --> Prop21
|
| 76 |
+
Prop20 --> Prop21
|
| 77 |
+
Prop3 --> Prop22
|
| 78 |
+
Prop20 --> Prop22
|
| 79 |
+
Prop8 --> Prop23
|
| 80 |
+
Prop22 --> Prop23
|
| 81 |
+
Prop3 --> Prop24
|
| 82 |
+
Prop4 --> Prop24
|
| 83 |
+
Prop5 --> Prop24
|
| 84 |
+
Prop19 --> Prop24
|
| 85 |
+
Prop23 --> Prop24
|
| 86 |
+
Prop4 --> Prop25
|
| 87 |
+
Prop24 --> Prop25
|
| 88 |
+
Prop3 --> Prop26
|
| 89 |
+
Prop4 --> Prop26
|
| 90 |
+
Prop16 --> Prop26
|
| 91 |
+
Prop16 --> Prop27
|
| 92 |
+
Prop13 --> Prop28
|
| 93 |
+
Prop15 --> Prop28
|
| 94 |
+
Prop27 --> Prop28
|
| 95 |
+
Prop13 --> Prop29
|
| 96 |
+
Prop15 --> Prop29
|
| 97 |
+
Prop27 --> Prop29
|
| 98 |
+
P5 --> Prop29
|
| 99 |
+
Prop29 --> Prop30
|
| 100 |
+
classDef postulate fill:#e74c3c,color:#fff,stroke:#c0392b
|
| 101 |
+
classDef commonNotion fill:#9b59b6,color:#fff,stroke:#8e44ad
|
| 102 |
+
classDef proposition fill:#1abc9c,color:#fff,stroke:#16a085
|
| 103 |
+
class P1,P2,P3,P4,P5 postulate
|
| 104 |
+
class CN1,CN2,CN3,CN4,CN5 commonNotion
|
| 105 |
+
class Prop1,Prop2,Prop3,Prop4,Prop5,Prop7,Prop8,Prop9,Prop10,Prop11,Prop13,Prop15,Prop16,Prop18,Prop19,Prop20,Prop21,Prop22,Prop23,Prop24,Prop25,Prop26,Prop27,Prop28,Prop29,Prop30 proposition
|
data/euclid-elements-book-i-props-31-41.mmd
ADDED
|
@@ -0,0 +1,127 @@
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 1 |
+
graph TD
|
| 2 |
+
P1["Post. 1\nDraw a straight line from any po..."]
|
| 3 |
+
P2["Post. 2\nProduce a finite straight line c..."]
|
| 4 |
+
P3["Post. 3\nDescribe a circle with any cente..."]
|
| 5 |
+
P4["Post. 4\nAll right angles equal one another"]
|
| 6 |
+
P5["Post. 5\nParallel postulate: if interior ..."]
|
| 7 |
+
CN1["CN 1\nThings equal to the same thing a..."]
|
| 8 |
+
CN2["CN 2\nIf equals are added to equals, t..."]
|
| 9 |
+
CN3["CN 3\nIf equals are subtracted from eq..."]
|
| 10 |
+
CN4["CN 4\nThings coinciding with one anoth..."]
|
| 11 |
+
CN5["CN 5\nThe whole is greater than the part"]
|
| 12 |
+
Prop1["Prop. I.1\nEquilateral triangle on given line"]
|
| 13 |
+
Prop2["Prop. I.2\nPlace line equal to given at point"]
|
| 14 |
+
Prop3["Prop. I.3\nCut off from greater segment equal to less"]
|
| 15 |
+
Prop4["Prop. I.4\nSAS congruence"]
|
| 16 |
+
Prop5["Prop. I.5\nBase angles of isosceles equal"]
|
| 17 |
+
Prop7["Prop. I.7\nUniqueness of triangle from ends"]
|
| 18 |
+
Prop8["Prop. I.8\nSSS congruence"]
|
| 19 |
+
Prop9["Prop. I.9\nBisect angle"]
|
| 20 |
+
Prop10["Prop. I.10\nBisect line"]
|
| 21 |
+
Prop11["Prop. I.11\nPerpendicular from point on line"]
|
| 22 |
+
Prop13["Prop. I.13\nAngles on line sum to two right"]
|
| 23 |
+
Prop15["Prop. I.15\nVertical angles equal"]
|
| 24 |
+
Prop16["Prop. I.16\nExterior angle > interior opposite"]
|
| 25 |
+
Prop18["Prop. I.18\nAngle opposite greater side greater"]
|
| 26 |
+
Prop19["Prop. I.19\nSide opposite greater angle greater"]
|
| 27 |
+
Prop20["Prop. I.20\nTriangle inequality"]
|
| 28 |
+
Prop22["Prop. I.22\nConstruct triangle from three lines"]
|
| 29 |
+
Prop23["Prop. I.23\nConstruct angle equal to given"]
|
| 30 |
+
Prop26["Prop. I.26\nAAS congruence"]
|
| 31 |
+
Prop27["Prop. I.27\nAlternate angles equal => parallel"]
|
| 32 |
+
Prop29["Prop. I.29\nParallel => alternate angles equal"]
|
| 33 |
+
Prop31["Prop. I.31\nDraw parallel through point"]
|
| 34 |
+
Prop32["Prop. I.32\nExterior angle = sum interior opposite"]
|
| 35 |
+
Prop33["Prop. I.33\nJoining ends of equal parallel lines"]
|
| 36 |
+
Prop34["Prop. I.34\nParallelogram properties"]
|
| 37 |
+
Prop35["Prop. I.35\nParallelograms same base equal"]
|
| 38 |
+
Prop36["Prop. I.36\nParallelograms equal bases equal"]
|
| 39 |
+
Prop37["Prop. I.37\nTriangles same base equal"]
|
| 40 |
+
Prop38["Prop. I.38\nTriangles equal bases equal"]
|
| 41 |
+
Prop39["Prop. I.39\nEqual triangles same base same side"]
|
| 42 |
+
Prop40["Prop. I.40\nEqual triangles equal bases same side"]
|
| 43 |
+
Prop41["Prop. I.41\nParallelogram = 2× triangle"]
|
| 44 |
+
P1 --> Prop1
|
| 45 |
+
P3 --> Prop1
|
| 46 |
+
Prop1 --> Prop2
|
| 47 |
+
P1 --> Prop2
|
| 48 |
+
P2 --> Prop2
|
| 49 |
+
P3 --> Prop2
|
| 50 |
+
Prop2 --> Prop3
|
| 51 |
+
P3 --> Prop3
|
| 52 |
+
CN4 --> Prop4
|
| 53 |
+
CN5 --> Prop4
|
| 54 |
+
Prop3 --> Prop5
|
| 55 |
+
Prop4 --> Prop5
|
| 56 |
+
Prop5 --> Prop7
|
| 57 |
+
Prop7 --> Prop8
|
| 58 |
+
Prop1 --> Prop9
|
| 59 |
+
Prop3 --> Prop9
|
| 60 |
+
Prop8 --> Prop9
|
| 61 |
+
Prop1 --> Prop10
|
| 62 |
+
Prop4 --> Prop10
|
| 63 |
+
Prop9 --> Prop10
|
| 64 |
+
Prop1 --> Prop11
|
| 65 |
+
Prop3 --> Prop11
|
| 66 |
+
Prop8 --> Prop11
|
| 67 |
+
Prop11 --> Prop13
|
| 68 |
+
Prop13 --> Prop15
|
| 69 |
+
Prop3 --> Prop16
|
| 70 |
+
Prop4 --> Prop16
|
| 71 |
+
Prop10 --> Prop16
|
| 72 |
+
Prop15 --> Prop16
|
| 73 |
+
Prop3 --> Prop18
|
| 74 |
+
Prop5 --> Prop18
|
| 75 |
+
Prop16 --> Prop18
|
| 76 |
+
Prop5 --> Prop19
|
| 77 |
+
Prop18 --> Prop19
|
| 78 |
+
Prop3 --> Prop20
|
| 79 |
+
Prop5 --> Prop20
|
| 80 |
+
Prop19 --> Prop20
|
| 81 |
+
Prop3 --> Prop22
|
| 82 |
+
Prop20 --> Prop22
|
| 83 |
+
Prop8 --> Prop23
|
| 84 |
+
Prop22 --> Prop23
|
| 85 |
+
Prop3 --> Prop26
|
| 86 |
+
Prop4 --> Prop26
|
| 87 |
+
Prop16 --> Prop26
|
| 88 |
+
Prop16 --> Prop27
|
| 89 |
+
Prop13 --> Prop29
|
| 90 |
+
Prop15 --> Prop29
|
| 91 |
+
Prop27 --> Prop29
|
| 92 |
+
P5 --> Prop29
|
| 93 |
+
Prop23 --> Prop31
|
| 94 |
+
Prop27 --> Prop31
|
| 95 |
+
Prop13 --> Prop32
|
| 96 |
+
Prop29 --> Prop32
|
| 97 |
+
Prop31 --> Prop32
|
| 98 |
+
Prop4 --> Prop33
|
| 99 |
+
Prop27 --> Prop33
|
| 100 |
+
Prop29 --> Prop33
|
| 101 |
+
Prop4 --> Prop34
|
| 102 |
+
Prop26 --> Prop34
|
| 103 |
+
Prop29 --> Prop34
|
| 104 |
+
Prop4 --> Prop35
|
| 105 |
+
Prop29 --> Prop35
|
| 106 |
+
Prop34 --> Prop35
|
| 107 |
+
Prop33 --> Prop36
|
| 108 |
+
Prop34 --> Prop36
|
| 109 |
+
Prop35 --> Prop36
|
| 110 |
+
Prop31 --> Prop37
|
| 111 |
+
Prop34 --> Prop37
|
| 112 |
+
Prop35 --> Prop37
|
| 113 |
+
Prop31 --> Prop38
|
| 114 |
+
Prop34 --> Prop38
|
| 115 |
+
Prop36 --> Prop38
|
| 116 |
+
Prop31 --> Prop39
|
| 117 |
+
Prop37 --> Prop39
|
| 118 |
+
Prop31 --> Prop40
|
| 119 |
+
Prop38 --> Prop40
|
| 120 |
+
Prop34 --> Prop41
|
| 121 |
+
Prop37 --> Prop41
|
| 122 |
+
classDef postulate fill:#e74c3c,color:#fff,stroke:#c0392b
|
| 123 |
+
classDef commonNotion fill:#9b59b6,color:#fff,stroke:#8e44ad
|
| 124 |
+
classDef proposition fill:#1abc9c,color:#fff,stroke:#16a085
|
| 125 |
+
class P1,P2,P3,P4,P5 postulate
|
| 126 |
+
class CN1,CN2,CN3,CN4,CN5 commonNotion
|
| 127 |
+
class Prop1,Prop2,Prop3,Prop4,Prop5,Prop7,Prop8,Prop9,Prop10,Prop11,Prop13,Prop15,Prop16,Prop18,Prop19,Prop20,Prop22,Prop23,Prop26,Prop27,Prop29,Prop31,Prop32,Prop33,Prop34,Prop35,Prop36,Prop37,Prop38,Prop39,Prop40,Prop41 proposition
|
data/euclid-elements-book-i-props-42-48.mmd
ADDED
|
@@ -0,0 +1,160 @@
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
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|
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|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
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|
|
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|
|
|
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|
|
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|
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|
|
|
|
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|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
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|
|
|
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|
|
|
|
|
|
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|
|
|
|
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|
|
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|
|
|
|
|
|
|
|
|
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|
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|
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|
|
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|
|
|
|
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|
|
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|
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|
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|
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|
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|
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|
|
|
|
|
|
|
|
|
|
|
|
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|
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|
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|
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|
|
|
|
|
|
|
|
|
|
|
|
| 1 |
+
graph TD
|
| 2 |
+
P1["Post. 1\nDraw a straight line from any po..."]
|
| 3 |
+
P2["Post. 2\nProduce a finite straight line c..."]
|
| 4 |
+
P3["Post. 3\nDescribe a circle with any cente..."]
|
| 5 |
+
P4["Post. 4\nAll right angles equal one another"]
|
| 6 |
+
P5["Post. 5\nParallel postulate: if interior ..."]
|
| 7 |
+
CN1["CN 1\nThings equal to the same thing a..."]
|
| 8 |
+
CN2["CN 2\nIf equals are added to equals, t..."]
|
| 9 |
+
CN3["CN 3\nIf equals are subtracted from eq..."]
|
| 10 |
+
CN4["CN 4\nThings coinciding with one anoth..."]
|
| 11 |
+
CN5["CN 5\nThe whole is greater than the part"]
|
| 12 |
+
Prop1["Prop. I.1\nEquilateral triangle on given line"]
|
| 13 |
+
Prop2["Prop. I.2\nPlace line equal to given at point"]
|
| 14 |
+
Prop3["Prop. I.3\nCut off from greater segment equal to less"]
|
| 15 |
+
Prop4["Prop. I.4\nSAS congruence"]
|
| 16 |
+
Prop5["Prop. I.5\nBase angles of isosceles equal"]
|
| 17 |
+
Prop7["Prop. I.7\nUniqueness of triangle from ends"]
|
| 18 |
+
Prop8["Prop. I.8\nSSS congruence"]
|
| 19 |
+
Prop9["Prop. I.9\nBisect angle"]
|
| 20 |
+
Prop10["Prop. I.10\nBisect line"]
|
| 21 |
+
Prop11["Prop. I.11\nPerpendicular from point on line"]
|
| 22 |
+
Prop13["Prop. I.13\nAngles on line sum to two right"]
|
| 23 |
+
Prop14["Prop. I.14\nIf angles sum to two right, straight line"]
|
| 24 |
+
Prop15["Prop. I.15\nVertical angles equal"]
|
| 25 |
+
Prop16["Prop. I.16\nExterior angle > interior opposite"]
|
| 26 |
+
Prop18["Prop. I.18\nAngle opposite greater side greater"]
|
| 27 |
+
Prop19["Prop. I.19\nSide opposite greater angle greater"]
|
| 28 |
+
Prop20["Prop. I.20\nTriangle inequality"]
|
| 29 |
+
Prop22["Prop. I.22\nConstruct triangle from three lines"]
|
| 30 |
+
Prop23["Prop. I.23\nConstruct angle equal to given"]
|
| 31 |
+
Prop26["Prop. I.26\nAAS congruence"]
|
| 32 |
+
Prop27["Prop. I.27\nAlternate angles equal => parallel"]
|
| 33 |
+
Prop29["Prop. I.29\nParallel => alternate angles equal"]
|
| 34 |
+
Prop30["Prop. I.30\nTransitivity of parallel"]
|
| 35 |
+
Prop31["Prop. I.31\nDraw parallel through point"]
|
| 36 |
+
Prop33["Prop. I.33\nJoining ends of equal parallel lines"]
|
| 37 |
+
Prop34["Prop. I.34\nParallelogram properties"]
|
| 38 |
+
Prop35["Prop. I.35\nParallelograms same base equal"]
|
| 39 |
+
Prop36["Prop. I.36\nParallelograms equal bases equal"]
|
| 40 |
+
Prop37["Prop. I.37\nTriangles same base equal"]
|
| 41 |
+
Prop38["Prop. I.38\nTriangles equal bases equal"]
|
| 42 |
+
Prop41["Prop. I.41\nParallelogram = 2× triangle"]
|
| 43 |
+
Prop42["Prop. I.42\nConstruct parallelogram = triangle"]
|
| 44 |
+
Prop43["Prop. I.43\nComplements of parallelogram"]
|
| 45 |
+
Prop44["Prop. I.44\nApply parallelogram to line"]
|
| 46 |
+
Prop45["Prop. I.45\nConstruct parallelogram = rectilinear figure"]
|
| 47 |
+
Prop46["Prop. I.46\nConstruct square on line"]
|
| 48 |
+
Prop47["Prop. I.47\nPythagorean theorem"]
|
| 49 |
+
Prop48["Prop. I.48\nConverse Pythagorean"]
|
| 50 |
+
P1 --> Prop1
|
| 51 |
+
P3 --> Prop1
|
| 52 |
+
Prop1 --> Prop2
|
| 53 |
+
P1 --> Prop2
|
| 54 |
+
P2 --> Prop2
|
| 55 |
+
P3 --> Prop2
|
| 56 |
+
Prop2 --> Prop3
|
| 57 |
+
P3 --> Prop3
|
| 58 |
+
CN4 --> Prop4
|
| 59 |
+
CN5 --> Prop4
|
| 60 |
+
Prop3 --> Prop5
|
| 61 |
+
Prop4 --> Prop5
|
| 62 |
+
Prop5 --> Prop7
|
| 63 |
+
Prop7 --> Prop8
|
| 64 |
+
Prop1 --> Prop9
|
| 65 |
+
Prop3 --> Prop9
|
| 66 |
+
Prop8 --> Prop9
|
| 67 |
+
Prop1 --> Prop10
|
| 68 |
+
Prop4 --> Prop10
|
| 69 |
+
Prop9 --> Prop10
|
| 70 |
+
Prop1 --> Prop11
|
| 71 |
+
Prop3 --> Prop11
|
| 72 |
+
Prop8 --> Prop11
|
| 73 |
+
Prop11 --> Prop13
|
| 74 |
+
Prop13 --> Prop14
|
| 75 |
+
Prop13 --> Prop15
|
| 76 |
+
Prop3 --> Prop16
|
| 77 |
+
Prop4 --> Prop16
|
| 78 |
+
Prop10 --> Prop16
|
| 79 |
+
Prop15 --> Prop16
|
| 80 |
+
Prop3 --> Prop18
|
| 81 |
+
Prop5 --> Prop18
|
| 82 |
+
Prop16 --> Prop18
|
| 83 |
+
Prop5 --> Prop19
|
| 84 |
+
Prop18 --> Prop19
|
| 85 |
+
Prop3 --> Prop20
|
| 86 |
+
Prop5 --> Prop20
|
| 87 |
+
Prop19 --> Prop20
|
| 88 |
+
Prop3 --> Prop22
|
| 89 |
+
Prop20 --> Prop22
|
| 90 |
+
Prop8 --> Prop23
|
| 91 |
+
Prop22 --> Prop23
|
| 92 |
+
Prop3 --> Prop26
|
| 93 |
+
Prop4 --> Prop26
|
| 94 |
+
Prop16 --> Prop26
|
| 95 |
+
Prop16 --> Prop27
|
| 96 |
+
Prop13 --> Prop29
|
| 97 |
+
Prop15 --> Prop29
|
| 98 |
+
Prop27 --> Prop29
|
| 99 |
+
P5 --> Prop29
|
| 100 |
+
Prop29 --> Prop30
|
| 101 |
+
Prop23 --> Prop31
|
| 102 |
+
Prop27 --> Prop31
|
| 103 |
+
Prop4 --> Prop33
|
| 104 |
+
Prop27 --> Prop33
|
| 105 |
+
Prop29 --> Prop33
|
| 106 |
+
Prop4 --> Prop34
|
| 107 |
+
Prop26 --> Prop34
|
| 108 |
+
Prop29 --> Prop34
|
| 109 |
+
Prop4 --> Prop35
|
| 110 |
+
Prop29 --> Prop35
|
| 111 |
+
Prop34 --> Prop35
|
| 112 |
+
Prop33 --> Prop36
|
| 113 |
+
Prop34 --> Prop36
|
| 114 |
+
Prop35 --> Prop36
|
| 115 |
+
Prop31 --> Prop37
|
| 116 |
+
Prop34 --> Prop37
|
| 117 |
+
Prop35 --> Prop37
|
| 118 |
+
Prop31 --> Prop38
|
| 119 |
+
Prop34 --> Prop38
|
| 120 |
+
Prop36 --> Prop38
|
| 121 |
+
Prop34 --> Prop41
|
| 122 |
+
Prop37 --> Prop41
|
| 123 |
+
Prop10 --> Prop42
|
| 124 |
+
Prop23 --> Prop42
|
| 125 |
+
Prop31 --> Prop42
|
| 126 |
+
Prop38 --> Prop42
|
| 127 |
+
Prop41 --> Prop42
|
| 128 |
+
Prop34 --> Prop43
|
| 129 |
+
Prop15 --> Prop44
|
| 130 |
+
Prop29 --> Prop44
|
| 131 |
+
Prop31 --> Prop44
|
| 132 |
+
Prop42 --> Prop44
|
| 133 |
+
Prop43 --> Prop44
|
| 134 |
+
Prop14 --> Prop45
|
| 135 |
+
Prop29 --> Prop45
|
| 136 |
+
Prop30 --> Prop45
|
| 137 |
+
Prop33 --> Prop45
|
| 138 |
+
Prop34 --> Prop45
|
| 139 |
+
Prop42 --> Prop45
|
| 140 |
+
Prop44 --> Prop45
|
| 141 |
+
Prop3 --> Prop46
|
| 142 |
+
Prop11 --> Prop46
|
| 143 |
+
Prop29 --> Prop46
|
| 144 |
+
Prop31 --> Prop46
|
| 145 |
+
Prop34 --> Prop46
|
| 146 |
+
Prop4 --> Prop47
|
| 147 |
+
Prop14 --> Prop47
|
| 148 |
+
Prop31 --> Prop47
|
| 149 |
+
Prop41 --> Prop47
|
| 150 |
+
Prop46 --> Prop47
|
| 151 |
+
Prop3 --> Prop48
|
| 152 |
+
Prop8 --> Prop48
|
| 153 |
+
Prop11 --> Prop48
|
| 154 |
+
Prop47 --> Prop48
|
| 155 |
+
classDef postulate fill:#e74c3c,color:#fff,stroke:#c0392b
|
| 156 |
+
classDef commonNotion fill:#9b59b6,color:#fff,stroke:#8e44ad
|
| 157 |
+
classDef proposition fill:#1abc9c,color:#fff,stroke:#16a085
|
| 158 |
+
class P1,P2,P3,P4,P5 postulate
|
| 159 |
+
class CN1,CN2,CN3,CN4,CN5 commonNotion
|
| 160 |
+
class Prop1,Prop2,Prop3,Prop4,Prop5,Prop7,Prop8,Prop9,Prop10,Prop11,Prop13,Prop14,Prop15,Prop16,Prop18,Prop19,Prop20,Prop22,Prop23,Prop26,Prop27,Prop29,Prop30,Prop31,Prop33,Prop34,Prop35,Prop36,Prop37,Prop38,Prop41,Prop42,Prop43,Prop44,Prop45,Prop46,Prop47,Prop48 proposition
|
data/euclid-elements-book-i.json
ADDED
|
@@ -0,0 +1,1167 @@
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|
| 1 |
+
{
|
| 2 |
+
"schemaVersion": "1.0",
|
| 3 |
+
"discourse": {
|
| 4 |
+
"id": "euclid-elements-book-i",
|
| 5 |
+
"name": "Euclid's Elements, Book I",
|
| 6 |
+
"subject": "geometry",
|
| 7 |
+
"variant": "classical",
|
| 8 |
+
"description": "The 48 propositions of Book I with dependencies on postulates (P1–P5), common notions (CN1–CN5), and prior propositions. Source: David E. Joyce, Clark University.",
|
| 9 |
+
"structure": {
|
| 10 |
+
"books": 1,
|
| 11 |
+
"propositions": 48,
|
| 12 |
+
"foundationTypes": [
|
| 13 |
+
"postulate",
|
| 14 |
+
"commonNotion"
|
| 15 |
+
]
|
| 16 |
+
}
|
| 17 |
+
},
|
| 18 |
+
"metadata": {
|
| 19 |
+
"created": "2026-03-15",
|
| 20 |
+
"lastUpdated": "2026-03-15",
|
| 21 |
+
"version": "1.0.0",
|
| 22 |
+
"license": "CC BY 4.0",
|
| 23 |
+
"authors": [
|
| 24 |
+
"Welz, G."
|
| 25 |
+
],
|
| 26 |
+
"methodology": "Programming Framework",
|
| 27 |
+
"citation": "Welz, G. (2026). Euclid's Elements Book I Dependency Graph. Programming Framework.",
|
| 28 |
+
"keywords": [
|
| 29 |
+
"Euclid",
|
| 30 |
+
"Elements",
|
| 31 |
+
"Book I",
|
| 32 |
+
"plane geometry",
|
| 33 |
+
"constructions",
|
| 34 |
+
"Pythagorean theorem"
|
| 35 |
+
]
|
| 36 |
+
},
|
| 37 |
+
"sources": [
|
| 38 |
+
{
|
| 39 |
+
"id": "joyce",
|
| 40 |
+
"type": "digital",
|
| 41 |
+
"authors": "Joyce, David E.",
|
| 42 |
+
"title": "Euclid's Elements, Book I",
|
| 43 |
+
"year": "1996",
|
| 44 |
+
"url": "https://mathcs.clarku.edu/~djoyce/java/elements/bookI/bookI.html",
|
| 45 |
+
"notes": "Clark University; dependency table from Guide"
|
| 46 |
+
},
|
| 47 |
+
{
|
| 48 |
+
"id": "euclid-heath",
|
| 49 |
+
"type": "primary",
|
| 50 |
+
"authors": "Heath, T.L.",
|
| 51 |
+
"title": "The Thirteen Books of Euclid's Elements",
|
| 52 |
+
"year": "1908",
|
| 53 |
+
"edition": "2nd",
|
| 54 |
+
"publisher": "Cambridge University Press",
|
| 55 |
+
"url": "https://archive.org/details/euclidheath00heatiala",
|
| 56 |
+
"notes": "Standard English translation"
|
| 57 |
+
}
|
| 58 |
+
],
|
| 59 |
+
"nodes": [
|
| 60 |
+
{
|
| 61 |
+
"id": "P1",
|
| 62 |
+
"type": "postulate",
|
| 63 |
+
"label": "Draw a straight line from any point to any point",
|
| 64 |
+
"shortLabel": "Post. 1",
|
| 65 |
+
"book": 1,
|
| 66 |
+
"number": 1,
|
| 67 |
+
"colorClass": "postulate"
|
| 68 |
+
},
|
| 69 |
+
{
|
| 70 |
+
"id": "P2",
|
| 71 |
+
"type": "postulate",
|
| 72 |
+
"label": "Produce a finite straight line continuously in a straight line",
|
| 73 |
+
"shortLabel": "Post. 2",
|
| 74 |
+
"book": 1,
|
| 75 |
+
"number": 2,
|
| 76 |
+
"colorClass": "postulate"
|
| 77 |
+
},
|
| 78 |
+
{
|
| 79 |
+
"id": "P3",
|
| 80 |
+
"type": "postulate",
|
| 81 |
+
"label": "Describe a circle with any center and radius",
|
| 82 |
+
"shortLabel": "Post. 3",
|
| 83 |
+
"book": 1,
|
| 84 |
+
"number": 3,
|
| 85 |
+
"colorClass": "postulate"
|
| 86 |
+
},
|
| 87 |
+
{
|
| 88 |
+
"id": "P4",
|
| 89 |
+
"type": "postulate",
|
| 90 |
+
"label": "All right angles equal one another",
|
| 91 |
+
"shortLabel": "Post. 4",
|
| 92 |
+
"book": 1,
|
| 93 |
+
"number": 4,
|
| 94 |
+
"colorClass": "postulate"
|
| 95 |
+
},
|
| 96 |
+
{
|
| 97 |
+
"id": "P5",
|
| 98 |
+
"type": "postulate",
|
| 99 |
+
"label": "Parallel postulate: if interior angles < two right, lines meet",
|
| 100 |
+
"shortLabel": "Post. 5",
|
| 101 |
+
"book": 1,
|
| 102 |
+
"number": 5,
|
| 103 |
+
"colorClass": "postulate"
|
| 104 |
+
},
|
| 105 |
+
{
|
| 106 |
+
"id": "CN1",
|
| 107 |
+
"type": "commonNotion",
|
| 108 |
+
"label": "Things equal to the same thing are equal to each other",
|
| 109 |
+
"shortLabel": "CN 1",
|
| 110 |
+
"book": 1,
|
| 111 |
+
"number": 1,
|
| 112 |
+
"colorClass": "commonNotion"
|
| 113 |
+
},
|
| 114 |
+
{
|
| 115 |
+
"id": "CN2",
|
| 116 |
+
"type": "commonNotion",
|
| 117 |
+
"label": "If equals are added to equals, the wholes are equal",
|
| 118 |
+
"shortLabel": "CN 2",
|
| 119 |
+
"book": 1,
|
| 120 |
+
"number": 2,
|
| 121 |
+
"colorClass": "commonNotion"
|
| 122 |
+
},
|
| 123 |
+
{
|
| 124 |
+
"id": "CN3",
|
| 125 |
+
"type": "commonNotion",
|
| 126 |
+
"label": "If equals are subtracted from equals, the remainders are equal",
|
| 127 |
+
"shortLabel": "CN 3",
|
| 128 |
+
"book": 1,
|
| 129 |
+
"number": 3,
|
| 130 |
+
"colorClass": "commonNotion"
|
| 131 |
+
},
|
| 132 |
+
{
|
| 133 |
+
"id": "CN4",
|
| 134 |
+
"type": "commonNotion",
|
| 135 |
+
"label": "Things coinciding with one another are equal",
|
| 136 |
+
"shortLabel": "CN 4",
|
| 137 |
+
"book": 1,
|
| 138 |
+
"number": 4,
|
| 139 |
+
"colorClass": "commonNotion"
|
| 140 |
+
},
|
| 141 |
+
{
|
| 142 |
+
"id": "CN5",
|
| 143 |
+
"type": "commonNotion",
|
| 144 |
+
"label": "The whole is greater than the part",
|
| 145 |
+
"shortLabel": "CN 5",
|
| 146 |
+
"book": 1,
|
| 147 |
+
"number": 5,
|
| 148 |
+
"colorClass": "commonNotion"
|
| 149 |
+
},
|
| 150 |
+
{
|
| 151 |
+
"id": "Prop1",
|
| 152 |
+
"type": "proposition",
|
| 153 |
+
"label": "To construct an equilateral triangle on a given finite straight line",
|
| 154 |
+
"shortLabel": "Prop. I.1",
|
| 155 |
+
"short": "Equilateral triangle on given line",
|
| 156 |
+
"book": 1,
|
| 157 |
+
"number": 1,
|
| 158 |
+
"colorClass": "proposition"
|
| 159 |
+
},
|
| 160 |
+
{
|
| 161 |
+
"id": "Prop2",
|
| 162 |
+
"type": "proposition",
|
| 163 |
+
"label": "To place a straight line equal to a given straight line with one end at a given point",
|
| 164 |
+
"shortLabel": "Prop. I.2",
|
| 165 |
+
"short": "Place line equal to given at point",
|
| 166 |
+
"book": 1,
|
| 167 |
+
"number": 2,
|
| 168 |
+
"colorClass": "proposition"
|
| 169 |
+
},
|
| 170 |
+
{
|
| 171 |
+
"id": "Prop3",
|
| 172 |
+
"type": "proposition",
|
| 173 |
+
"label": "To cut off from the greater of two given unequal straight lines a straight line equal to the less",
|
| 174 |
+
"shortLabel": "Prop. I.3",
|
| 175 |
+
"short": "Cut off from greater segment equal to less",
|
| 176 |
+
"book": 1,
|
| 177 |
+
"number": 3,
|
| 178 |
+
"colorClass": "proposition"
|
| 179 |
+
},
|
| 180 |
+
{
|
| 181 |
+
"id": "Prop4",
|
| 182 |
+
"type": "proposition",
|
| 183 |
+
"label": "If two triangles have two sides equal to two sides respectively, and the angles contained equal, then bases and remaining angles equal",
|
| 184 |
+
"shortLabel": "Prop. I.4",
|
| 185 |
+
"short": "SAS congruence",
|
| 186 |
+
"book": 1,
|
| 187 |
+
"number": 4,
|
| 188 |
+
"colorClass": "proposition"
|
| 189 |
+
},
|
| 190 |
+
{
|
| 191 |
+
"id": "Prop5",
|
| 192 |
+
"type": "proposition",
|
| 193 |
+
"label": "In isosceles triangles the angles at the base equal one another",
|
| 194 |
+
"shortLabel": "Prop. I.5",
|
| 195 |
+
"short": "Base angles of isosceles equal",
|
| 196 |
+
"book": 1,
|
| 197 |
+
"number": 5,
|
| 198 |
+
"colorClass": "proposition"
|
| 199 |
+
},
|
| 200 |
+
{
|
| 201 |
+
"id": "Prop6",
|
| 202 |
+
"type": "proposition",
|
| 203 |
+
"label": "If in a triangle two angles equal one another, then the sides opposite the equal angles also equal one another",
|
| 204 |
+
"shortLabel": "Prop. I.6",
|
| 205 |
+
"short": "Sides opposite equal angles equal",
|
| 206 |
+
"book": 1,
|
| 207 |
+
"number": 6,
|
| 208 |
+
"colorClass": "proposition"
|
| 209 |
+
},
|
| 210 |
+
{
|
| 211 |
+
"id": "Prop7",
|
| 212 |
+
"type": "proposition",
|
| 213 |
+
"label": "Given two lines from ends of a line meeting at a point, no other such pair from same ends on same side",
|
| 214 |
+
"shortLabel": "Prop. I.7",
|
| 215 |
+
"short": "Uniqueness of triangle from ends",
|
| 216 |
+
"book": 1,
|
| 217 |
+
"number": 7,
|
| 218 |
+
"colorClass": "proposition"
|
| 219 |
+
},
|
| 220 |
+
{
|
| 221 |
+
"id": "Prop8",
|
| 222 |
+
"type": "proposition",
|
| 223 |
+
"label": "If two triangles have two sides equal to two sides respectively, and the base equal to the base, then the angles contained are equal",
|
| 224 |
+
"shortLabel": "Prop. I.8",
|
| 225 |
+
"short": "SSS congruence",
|
| 226 |
+
"book": 1,
|
| 227 |
+
"number": 8,
|
| 228 |
+
"colorClass": "proposition"
|
| 229 |
+
},
|
| 230 |
+
{
|
| 231 |
+
"id": "Prop9",
|
| 232 |
+
"type": "proposition",
|
| 233 |
+
"label": "To bisect a given rectilinear angle",
|
| 234 |
+
"shortLabel": "Prop. I.9",
|
| 235 |
+
"short": "Bisect angle",
|
| 236 |
+
"book": 1,
|
| 237 |
+
"number": 9,
|
| 238 |
+
"colorClass": "proposition"
|
| 239 |
+
},
|
| 240 |
+
{
|
| 241 |
+
"id": "Prop10",
|
| 242 |
+
"type": "proposition",
|
| 243 |
+
"label": "To bisect a given finite straight line",
|
| 244 |
+
"shortLabel": "Prop. I.10",
|
| 245 |
+
"short": "Bisect line",
|
| 246 |
+
"book": 1,
|
| 247 |
+
"number": 10,
|
| 248 |
+
"colorClass": "proposition"
|
| 249 |
+
},
|
| 250 |
+
{
|
| 251 |
+
"id": "Prop11",
|
| 252 |
+
"type": "proposition",
|
| 253 |
+
"label": "To draw a straight line at right angles to a given straight line from a given point on it",
|
| 254 |
+
"shortLabel": "Prop. I.11",
|
| 255 |
+
"short": "Perpendicular from point on line",
|
| 256 |
+
"book": 1,
|
| 257 |
+
"number": 11,
|
| 258 |
+
"colorClass": "proposition"
|
| 259 |
+
},
|
| 260 |
+
{
|
| 261 |
+
"id": "Prop12",
|
| 262 |
+
"type": "proposition",
|
| 263 |
+
"label": "To draw a straight line perpendicular to a given infinite straight line from a given point not on it",
|
| 264 |
+
"shortLabel": "Prop. I.12",
|
| 265 |
+
"short": "Perpendicular from point not on line",
|
| 266 |
+
"book": 1,
|
| 267 |
+
"number": 12,
|
| 268 |
+
"colorClass": "proposition"
|
| 269 |
+
},
|
| 270 |
+
{
|
| 271 |
+
"id": "Prop13",
|
| 272 |
+
"type": "proposition",
|
| 273 |
+
"label": "If a straight line stands on a straight line, it makes either two right angles or angles whose sum equals two right angles",
|
| 274 |
+
"shortLabel": "Prop. I.13",
|
| 275 |
+
"short": "Angles on line sum to two right",
|
| 276 |
+
"book": 1,
|
| 277 |
+
"number": 13,
|
| 278 |
+
"colorClass": "proposition"
|
| 279 |
+
},
|
| 280 |
+
{
|
| 281 |
+
"id": "Prop14",
|
| 282 |
+
"type": "proposition",
|
| 283 |
+
"label": "If with any straight line, at a point, two lines not on same side make adjacent angles equal to two right, they are in a straight line",
|
| 284 |
+
"shortLabel": "Prop. I.14",
|
| 285 |
+
"short": "If angles sum to two right, straight line",
|
| 286 |
+
"book": 1,
|
| 287 |
+
"number": 14,
|
| 288 |
+
"colorClass": "proposition"
|
| 289 |
+
},
|
| 290 |
+
{
|
| 291 |
+
"id": "Prop15",
|
| 292 |
+
"type": "proposition",
|
| 293 |
+
"label": "If two straight lines cut one another, they make the vertical angles equal to one another",
|
| 294 |
+
"shortLabel": "Prop. I.15",
|
| 295 |
+
"short": "Vertical angles equal",
|
| 296 |
+
"book": 1,
|
| 297 |
+
"number": 15,
|
| 298 |
+
"colorClass": "proposition"
|
| 299 |
+
},
|
| 300 |
+
{
|
| 301 |
+
"id": "Prop16",
|
| 302 |
+
"type": "proposition",
|
| 303 |
+
"label": "In any triangle, if one side is produced, the exterior angle is greater than either interior opposite angle",
|
| 304 |
+
"shortLabel": "Prop. I.16",
|
| 305 |
+
"short": "Exterior angle > interior opposite",
|
| 306 |
+
"book": 1,
|
| 307 |
+
"number": 16,
|
| 308 |
+
"colorClass": "proposition"
|
| 309 |
+
},
|
| 310 |
+
{
|
| 311 |
+
"id": "Prop17",
|
| 312 |
+
"type": "proposition",
|
| 313 |
+
"label": "In any triangle the sum of any two angles is less than two right angles",
|
| 314 |
+
"shortLabel": "Prop. I.17",
|
| 315 |
+
"short": "Sum of two angles < two right",
|
| 316 |
+
"book": 1,
|
| 317 |
+
"number": 17,
|
| 318 |
+
"colorClass": "proposition"
|
| 319 |
+
},
|
| 320 |
+
{
|
| 321 |
+
"id": "Prop18",
|
| 322 |
+
"type": "proposition",
|
| 323 |
+
"label": "In any triangle the angle opposite the greater side is greater",
|
| 324 |
+
"shortLabel": "Prop. I.18",
|
| 325 |
+
"short": "Angle opposite greater side greater",
|
| 326 |
+
"book": 1,
|
| 327 |
+
"number": 18,
|
| 328 |
+
"colorClass": "proposition"
|
| 329 |
+
},
|
| 330 |
+
{
|
| 331 |
+
"id": "Prop19",
|
| 332 |
+
"type": "proposition",
|
| 333 |
+
"label": "In any triangle the side opposite the greater angle is greater",
|
| 334 |
+
"shortLabel": "Prop. I.19",
|
| 335 |
+
"short": "Side opposite greater angle greater",
|
| 336 |
+
"book": 1,
|
| 337 |
+
"number": 19,
|
| 338 |
+
"colorClass": "proposition"
|
| 339 |
+
},
|
| 340 |
+
{
|
| 341 |
+
"id": "Prop20",
|
| 342 |
+
"type": "proposition",
|
| 343 |
+
"label": "In any triangle the sum of any two sides is greater than the remaining one",
|
| 344 |
+
"shortLabel": "Prop. I.20",
|
| 345 |
+
"short": "Triangle inequality",
|
| 346 |
+
"book": 1,
|
| 347 |
+
"number": 20,
|
| 348 |
+
"colorClass": "proposition"
|
| 349 |
+
},
|
| 350 |
+
{
|
| 351 |
+
"id": "Prop21",
|
| 352 |
+
"type": "proposition",
|
| 353 |
+
"label": "If from ends of one side two lines meet within the triangle, their sum < sum of other two sides",
|
| 354 |
+
"shortLabel": "Prop. I.21",
|
| 355 |
+
"short": "Lines from ends within triangle",
|
| 356 |
+
"book": 1,
|
| 357 |
+
"number": 21,
|
| 358 |
+
"colorClass": "proposition"
|
| 359 |
+
},
|
| 360 |
+
{
|
| 361 |
+
"id": "Prop22",
|
| 362 |
+
"type": "proposition",
|
| 363 |
+
"label": "To construct a triangle out of three straight lines which equal three given straight lines",
|
| 364 |
+
"shortLabel": "Prop. I.22",
|
| 365 |
+
"short": "Construct triangle from three lines",
|
| 366 |
+
"book": 1,
|
| 367 |
+
"number": 22,
|
| 368 |
+
"colorClass": "proposition"
|
| 369 |
+
},
|
| 370 |
+
{
|
| 371 |
+
"id": "Prop23",
|
| 372 |
+
"type": "proposition",
|
| 373 |
+
"label": "To construct a rectilinear angle equal to a given rectilinear angle on a given straight line",
|
| 374 |
+
"shortLabel": "Prop. I.23",
|
| 375 |
+
"short": "Construct angle equal to given",
|
| 376 |
+
"book": 1,
|
| 377 |
+
"number": 23,
|
| 378 |
+
"colorClass": "proposition"
|
| 379 |
+
},
|
| 380 |
+
{
|
| 381 |
+
"id": "Prop24",
|
| 382 |
+
"type": "proposition",
|
| 383 |
+
"label": "If two triangles have two sides equal but one contained angle greater, the base is greater",
|
| 384 |
+
"shortLabel": "Prop. I.24",
|
| 385 |
+
"short": "SAS for greater angle => greater base",
|
| 386 |
+
"book": 1,
|
| 387 |
+
"number": 24,
|
| 388 |
+
"colorClass": "proposition"
|
| 389 |
+
},
|
| 390 |
+
{
|
| 391 |
+
"id": "Prop25",
|
| 392 |
+
"type": "proposition",
|
| 393 |
+
"label": "If two triangles have two sides equal but base greater, the contained angle is greater",
|
| 394 |
+
"shortLabel": "Prop. I.25",
|
| 395 |
+
"short": "SAS for greater base => greater angle",
|
| 396 |
+
"book": 1,
|
| 397 |
+
"number": 25,
|
| 398 |
+
"colorClass": "proposition"
|
| 399 |
+
},
|
| 400 |
+
{
|
| 401 |
+
"id": "Prop26",
|
| 402 |
+
"type": "proposition",
|
| 403 |
+
"label": "If two triangles have two angles equal and one side equal, the remaining sides and angle equal",
|
| 404 |
+
"shortLabel": "Prop. I.26",
|
| 405 |
+
"short": "AAS congruence",
|
| 406 |
+
"book": 1,
|
| 407 |
+
"number": 26,
|
| 408 |
+
"colorClass": "proposition"
|
| 409 |
+
},
|
| 410 |
+
{
|
| 411 |
+
"id": "Prop27",
|
| 412 |
+
"type": "proposition",
|
| 413 |
+
"label": "If a line falling on two lines makes alternate angles equal, the lines are parallel",
|
| 414 |
+
"shortLabel": "Prop. I.27",
|
| 415 |
+
"short": "Alternate angles equal => parallel",
|
| 416 |
+
"book": 1,
|
| 417 |
+
"number": 27,
|
| 418 |
+
"colorClass": "proposition"
|
| 419 |
+
},
|
| 420 |
+
{
|
| 421 |
+
"id": "Prop28",
|
| 422 |
+
"type": "proposition",
|
| 423 |
+
"label": "If exterior angle equals interior opposite, or interior same-side sum to two right, lines parallel",
|
| 424 |
+
"shortLabel": "Prop. I.28",
|
| 425 |
+
"short": "Exterior = interior opposite => parallel",
|
| 426 |
+
"book": 1,
|
| 427 |
+
"number": 28,
|
| 428 |
+
"colorClass": "proposition"
|
| 429 |
+
},
|
| 430 |
+
{
|
| 431 |
+
"id": "Prop29",
|
| 432 |
+
"type": "proposition",
|
| 433 |
+
"label": "A line falling on parallel lines makes alternate angles equal, exterior = interior opposite",
|
| 434 |
+
"shortLabel": "Prop. I.29",
|
| 435 |
+
"short": "Parallel => alternate angles equal",
|
| 436 |
+
"book": 1,
|
| 437 |
+
"number": 29,
|
| 438 |
+
"colorClass": "proposition"
|
| 439 |
+
},
|
| 440 |
+
{
|
| 441 |
+
"id": "Prop30",
|
| 442 |
+
"type": "proposition",
|
| 443 |
+
"label": "Straight lines parallel to the same straight line are also parallel to one another",
|
| 444 |
+
"shortLabel": "Prop. I.30",
|
| 445 |
+
"short": "Transitivity of parallel",
|
| 446 |
+
"book": 1,
|
| 447 |
+
"number": 30,
|
| 448 |
+
"colorClass": "proposition"
|
| 449 |
+
},
|
| 450 |
+
{
|
| 451 |
+
"id": "Prop31",
|
| 452 |
+
"type": "proposition",
|
| 453 |
+
"label": "To draw a straight line through a given point parallel to a given straight line",
|
| 454 |
+
"shortLabel": "Prop. I.31",
|
| 455 |
+
"short": "Draw parallel through point",
|
| 456 |
+
"book": 1,
|
| 457 |
+
"number": 31,
|
| 458 |
+
"colorClass": "proposition"
|
| 459 |
+
},
|
| 460 |
+
{
|
| 461 |
+
"id": "Prop32",
|
| 462 |
+
"type": "proposition",
|
| 463 |
+
"label": "In any triangle, exterior angle equals sum of two interior opposite; three angles = two right",
|
| 464 |
+
"shortLabel": "Prop. I.32",
|
| 465 |
+
"short": "Exterior angle = sum interior opposite",
|
| 466 |
+
"book": 1,
|
| 467 |
+
"number": 32,
|
| 468 |
+
"colorClass": "proposition"
|
| 469 |
+
},
|
| 470 |
+
{
|
| 471 |
+
"id": "Prop33",
|
| 472 |
+
"type": "proposition",
|
| 473 |
+
"label": "Straight lines which join the ends of equal and parallel straight lines in same directions are equal and parallel",
|
| 474 |
+
"shortLabel": "Prop. I.33",
|
| 475 |
+
"short": "Joining ends of equal parallel lines",
|
| 476 |
+
"book": 1,
|
| 477 |
+
"number": 33,
|
| 478 |
+
"colorClass": "proposition"
|
| 479 |
+
},
|
| 480 |
+
{
|
| 481 |
+
"id": "Prop34",
|
| 482 |
+
"type": "proposition",
|
| 483 |
+
"label": "In parallelogrammic areas the opposite sides and angles equal one another, diameter bisects",
|
| 484 |
+
"shortLabel": "Prop. I.34",
|
| 485 |
+
"short": "Parallelogram properties",
|
| 486 |
+
"book": 1,
|
| 487 |
+
"number": 34,
|
| 488 |
+
"colorClass": "proposition"
|
| 489 |
+
},
|
| 490 |
+
{
|
| 491 |
+
"id": "Prop35",
|
| 492 |
+
"type": "proposition",
|
| 493 |
+
"label": "Parallelograms which are on the same base and in the same parallels equal one another",
|
| 494 |
+
"shortLabel": "Prop. I.35",
|
| 495 |
+
"short": "Parallelograms same base equal",
|
| 496 |
+
"book": 1,
|
| 497 |
+
"number": 35,
|
| 498 |
+
"colorClass": "proposition"
|
| 499 |
+
},
|
| 500 |
+
{
|
| 501 |
+
"id": "Prop36",
|
| 502 |
+
"type": "proposition",
|
| 503 |
+
"label": "Parallelograms which are on equal bases and in the same parallels equal one another",
|
| 504 |
+
"shortLabel": "Prop. I.36",
|
| 505 |
+
"short": "Parallelograms equal bases equal",
|
| 506 |
+
"book": 1,
|
| 507 |
+
"number": 36,
|
| 508 |
+
"colorClass": "proposition"
|
| 509 |
+
},
|
| 510 |
+
{
|
| 511 |
+
"id": "Prop37",
|
| 512 |
+
"type": "proposition",
|
| 513 |
+
"label": "Triangles which are on the same base and in the same parallels equal one another",
|
| 514 |
+
"shortLabel": "Prop. I.37",
|
| 515 |
+
"short": "Triangles same base equal",
|
| 516 |
+
"book": 1,
|
| 517 |
+
"number": 37,
|
| 518 |
+
"colorClass": "proposition"
|
| 519 |
+
},
|
| 520 |
+
{
|
| 521 |
+
"id": "Prop38",
|
| 522 |
+
"type": "proposition",
|
| 523 |
+
"label": "Triangles which are on equal bases and in the same parallels equal one another",
|
| 524 |
+
"shortLabel": "Prop. I.38",
|
| 525 |
+
"short": "Triangles equal bases equal",
|
| 526 |
+
"book": 1,
|
| 527 |
+
"number": 38,
|
| 528 |
+
"colorClass": "proposition"
|
| 529 |
+
},
|
| 530 |
+
{
|
| 531 |
+
"id": "Prop39",
|
| 532 |
+
"type": "proposition",
|
| 533 |
+
"label": "Equal triangles on same base and same side are in the same parallels",
|
| 534 |
+
"shortLabel": "Prop. I.39",
|
| 535 |
+
"short": "Equal triangles same base same side",
|
| 536 |
+
"book": 1,
|
| 537 |
+
"number": 39,
|
| 538 |
+
"colorClass": "proposition"
|
| 539 |
+
},
|
| 540 |
+
{
|
| 541 |
+
"id": "Prop40",
|
| 542 |
+
"type": "proposition",
|
| 543 |
+
"label": "Equal triangles on equal bases and same side are in the same parallels",
|
| 544 |
+
"shortLabel": "Prop. I.40",
|
| 545 |
+
"short": "Equal triangles equal bases same side",
|
| 546 |
+
"book": 1,
|
| 547 |
+
"number": 40,
|
| 548 |
+
"colorClass": "proposition"
|
| 549 |
+
},
|
| 550 |
+
{
|
| 551 |
+
"id": "Prop41",
|
| 552 |
+
"type": "proposition",
|
| 553 |
+
"label": "If a parallelogram has same base with triangle and same parallels, parallelogram is double the triangle",
|
| 554 |
+
"shortLabel": "Prop. I.41",
|
| 555 |
+
"short": "Parallelogram = 2× triangle",
|
| 556 |
+
"book": 1,
|
| 557 |
+
"number": 41,
|
| 558 |
+
"colorClass": "proposition"
|
| 559 |
+
},
|
| 560 |
+
{
|
| 561 |
+
"id": "Prop42",
|
| 562 |
+
"type": "proposition",
|
| 563 |
+
"label": "To construct a parallelogram equal to a given triangle in a given rectilinear angle",
|
| 564 |
+
"shortLabel": "Prop. I.42",
|
| 565 |
+
"short": "Construct parallelogram = triangle",
|
| 566 |
+
"book": 1,
|
| 567 |
+
"number": 42,
|
| 568 |
+
"colorClass": "proposition"
|
| 569 |
+
},
|
| 570 |
+
{
|
| 571 |
+
"id": "Prop43",
|
| 572 |
+
"type": "proposition",
|
| 573 |
+
"label": "In any parallelogram the complements of the parallelograms about the diameter equal one another",
|
| 574 |
+
"shortLabel": "Prop. I.43",
|
| 575 |
+
"short": "Complements of parallelogram",
|
| 576 |
+
"book": 1,
|
| 577 |
+
"number": 43,
|
| 578 |
+
"colorClass": "proposition"
|
| 579 |
+
},
|
| 580 |
+
{
|
| 581 |
+
"id": "Prop44",
|
| 582 |
+
"type": "proposition",
|
| 583 |
+
"label": "To a given straight line in a given angle, to apply a parallelogram equal to a given triangle",
|
| 584 |
+
"shortLabel": "Prop. I.44",
|
| 585 |
+
"short": "Apply parallelogram to line",
|
| 586 |
+
"book": 1,
|
| 587 |
+
"number": 44,
|
| 588 |
+
"colorClass": "proposition"
|
| 589 |
+
},
|
| 590 |
+
{
|
| 591 |
+
"id": "Prop45",
|
| 592 |
+
"type": "proposition",
|
| 593 |
+
"label": "To construct a parallelogram equal to a given rectilinear figure in a given rectilinear angle",
|
| 594 |
+
"shortLabel": "Prop. I.45",
|
| 595 |
+
"short": "Construct parallelogram = rectilinear figure",
|
| 596 |
+
"book": 1,
|
| 597 |
+
"number": 45,
|
| 598 |
+
"colorClass": "proposition"
|
| 599 |
+
},
|
| 600 |
+
{
|
| 601 |
+
"id": "Prop46",
|
| 602 |
+
"type": "proposition",
|
| 603 |
+
"label": "To describe a square on a given straight line",
|
| 604 |
+
"shortLabel": "Prop. I.46",
|
| 605 |
+
"short": "Construct square on line",
|
| 606 |
+
"book": 1,
|
| 607 |
+
"number": 46,
|
| 608 |
+
"colorClass": "proposition"
|
| 609 |
+
},
|
| 610 |
+
{
|
| 611 |
+
"id": "Prop47",
|
| 612 |
+
"type": "proposition",
|
| 613 |
+
"label": "In right-angled triangles the square on the side opposite the right angle equals the sum of the squares on the sides containing the right angle",
|
| 614 |
+
"shortLabel": "Prop. I.47",
|
| 615 |
+
"short": "Pythagorean theorem",
|
| 616 |
+
"book": 1,
|
| 617 |
+
"number": 47,
|
| 618 |
+
"colorClass": "proposition"
|
| 619 |
+
},
|
| 620 |
+
{
|
| 621 |
+
"id": "Prop48",
|
| 622 |
+
"type": "proposition",
|
| 623 |
+
"label": "If in a triangle the square on one side equals the sum of squares on the other two, the angle contained by those sides is right",
|
| 624 |
+
"shortLabel": "Prop. I.48",
|
| 625 |
+
"short": "Converse Pythagorean",
|
| 626 |
+
"book": 1,
|
| 627 |
+
"number": 48,
|
| 628 |
+
"colorClass": "proposition"
|
| 629 |
+
}
|
| 630 |
+
],
|
| 631 |
+
"edges": [
|
| 632 |
+
{
|
| 633 |
+
"from": "P1",
|
| 634 |
+
"to": "Prop1"
|
| 635 |
+
},
|
| 636 |
+
{
|
| 637 |
+
"from": "P3",
|
| 638 |
+
"to": "Prop1"
|
| 639 |
+
},
|
| 640 |
+
{
|
| 641 |
+
"from": "Prop1",
|
| 642 |
+
"to": "Prop2"
|
| 643 |
+
},
|
| 644 |
+
{
|
| 645 |
+
"from": "P1",
|
| 646 |
+
"to": "Prop2"
|
| 647 |
+
},
|
| 648 |
+
{
|
| 649 |
+
"from": "P2",
|
| 650 |
+
"to": "Prop2"
|
| 651 |
+
},
|
| 652 |
+
{
|
| 653 |
+
"from": "P3",
|
| 654 |
+
"to": "Prop2"
|
| 655 |
+
},
|
| 656 |
+
{
|
| 657 |
+
"from": "Prop2",
|
| 658 |
+
"to": "Prop3"
|
| 659 |
+
},
|
| 660 |
+
{
|
| 661 |
+
"from": "P3",
|
| 662 |
+
"to": "Prop3"
|
| 663 |
+
},
|
| 664 |
+
{
|
| 665 |
+
"from": "CN4",
|
| 666 |
+
"to": "Prop4"
|
| 667 |
+
},
|
| 668 |
+
{
|
| 669 |
+
"from": "CN5",
|
| 670 |
+
"to": "Prop4"
|
| 671 |
+
},
|
| 672 |
+
{
|
| 673 |
+
"from": "Prop3",
|
| 674 |
+
"to": "Prop5"
|
| 675 |
+
},
|
| 676 |
+
{
|
| 677 |
+
"from": "Prop4",
|
| 678 |
+
"to": "Prop5"
|
| 679 |
+
},
|
| 680 |
+
{
|
| 681 |
+
"from": "Prop3",
|
| 682 |
+
"to": "Prop6"
|
| 683 |
+
},
|
| 684 |
+
{
|
| 685 |
+
"from": "Prop4",
|
| 686 |
+
"to": "Prop6"
|
| 687 |
+
},
|
| 688 |
+
{
|
| 689 |
+
"from": "Prop5",
|
| 690 |
+
"to": "Prop7"
|
| 691 |
+
},
|
| 692 |
+
{
|
| 693 |
+
"from": "Prop7",
|
| 694 |
+
"to": "Prop8"
|
| 695 |
+
},
|
| 696 |
+
{
|
| 697 |
+
"from": "Prop1",
|
| 698 |
+
"to": "Prop9"
|
| 699 |
+
},
|
| 700 |
+
{
|
| 701 |
+
"from": "Prop3",
|
| 702 |
+
"to": "Prop9"
|
| 703 |
+
},
|
| 704 |
+
{
|
| 705 |
+
"from": "Prop8",
|
| 706 |
+
"to": "Prop9"
|
| 707 |
+
},
|
| 708 |
+
{
|
| 709 |
+
"from": "Prop1",
|
| 710 |
+
"to": "Prop10"
|
| 711 |
+
},
|
| 712 |
+
{
|
| 713 |
+
"from": "Prop4",
|
| 714 |
+
"to": "Prop10"
|
| 715 |
+
},
|
| 716 |
+
{
|
| 717 |
+
"from": "Prop9",
|
| 718 |
+
"to": "Prop10"
|
| 719 |
+
},
|
| 720 |
+
{
|
| 721 |
+
"from": "Prop1",
|
| 722 |
+
"to": "Prop11"
|
| 723 |
+
},
|
| 724 |
+
{
|
| 725 |
+
"from": "Prop3",
|
| 726 |
+
"to": "Prop11"
|
| 727 |
+
},
|
| 728 |
+
{
|
| 729 |
+
"from": "Prop8",
|
| 730 |
+
"to": "Prop11"
|
| 731 |
+
},
|
| 732 |
+
{
|
| 733 |
+
"from": "Prop8",
|
| 734 |
+
"to": "Prop12"
|
| 735 |
+
},
|
| 736 |
+
{
|
| 737 |
+
"from": "Prop10",
|
| 738 |
+
"to": "Prop12"
|
| 739 |
+
},
|
| 740 |
+
{
|
| 741 |
+
"from": "Prop11",
|
| 742 |
+
"to": "Prop13"
|
| 743 |
+
},
|
| 744 |
+
{
|
| 745 |
+
"from": "Prop13",
|
| 746 |
+
"to": "Prop14"
|
| 747 |
+
},
|
| 748 |
+
{
|
| 749 |
+
"from": "Prop13",
|
| 750 |
+
"to": "Prop15"
|
| 751 |
+
},
|
| 752 |
+
{
|
| 753 |
+
"from": "Prop3",
|
| 754 |
+
"to": "Prop16"
|
| 755 |
+
},
|
| 756 |
+
{
|
| 757 |
+
"from": "Prop4",
|
| 758 |
+
"to": "Prop16"
|
| 759 |
+
},
|
| 760 |
+
{
|
| 761 |
+
"from": "Prop10",
|
| 762 |
+
"to": "Prop16"
|
| 763 |
+
},
|
| 764 |
+
{
|
| 765 |
+
"from": "Prop15",
|
| 766 |
+
"to": "Prop16"
|
| 767 |
+
},
|
| 768 |
+
{
|
| 769 |
+
"from": "Prop13",
|
| 770 |
+
"to": "Prop17"
|
| 771 |
+
},
|
| 772 |
+
{
|
| 773 |
+
"from": "Prop16",
|
| 774 |
+
"to": "Prop17"
|
| 775 |
+
},
|
| 776 |
+
{
|
| 777 |
+
"from": "Prop3",
|
| 778 |
+
"to": "Prop18"
|
| 779 |
+
},
|
| 780 |
+
{
|
| 781 |
+
"from": "Prop5",
|
| 782 |
+
"to": "Prop18"
|
| 783 |
+
},
|
| 784 |
+
{
|
| 785 |
+
"from": "Prop16",
|
| 786 |
+
"to": "Prop18"
|
| 787 |
+
},
|
| 788 |
+
{
|
| 789 |
+
"from": "Prop5",
|
| 790 |
+
"to": "Prop19"
|
| 791 |
+
},
|
| 792 |
+
{
|
| 793 |
+
"from": "Prop18",
|
| 794 |
+
"to": "Prop19"
|
| 795 |
+
},
|
| 796 |
+
{
|
| 797 |
+
"from": "Prop3",
|
| 798 |
+
"to": "Prop20"
|
| 799 |
+
},
|
| 800 |
+
{
|
| 801 |
+
"from": "Prop5",
|
| 802 |
+
"to": "Prop20"
|
| 803 |
+
},
|
| 804 |
+
{
|
| 805 |
+
"from": "Prop19",
|
| 806 |
+
"to": "Prop20"
|
| 807 |
+
},
|
| 808 |
+
{
|
| 809 |
+
"from": "Prop16",
|
| 810 |
+
"to": "Prop21"
|
| 811 |
+
},
|
| 812 |
+
{
|
| 813 |
+
"from": "Prop20",
|
| 814 |
+
"to": "Prop21"
|
| 815 |
+
},
|
| 816 |
+
{
|
| 817 |
+
"from": "Prop3",
|
| 818 |
+
"to": "Prop22"
|
| 819 |
+
},
|
| 820 |
+
{
|
| 821 |
+
"from": "Prop20",
|
| 822 |
+
"to": "Prop22"
|
| 823 |
+
},
|
| 824 |
+
{
|
| 825 |
+
"from": "Prop8",
|
| 826 |
+
"to": "Prop23"
|
| 827 |
+
},
|
| 828 |
+
{
|
| 829 |
+
"from": "Prop22",
|
| 830 |
+
"to": "Prop23"
|
| 831 |
+
},
|
| 832 |
+
{
|
| 833 |
+
"from": "Prop3",
|
| 834 |
+
"to": "Prop24"
|
| 835 |
+
},
|
| 836 |
+
{
|
| 837 |
+
"from": "Prop4",
|
| 838 |
+
"to": "Prop24"
|
| 839 |
+
},
|
| 840 |
+
{
|
| 841 |
+
"from": "Prop5",
|
| 842 |
+
"to": "Prop24"
|
| 843 |
+
},
|
| 844 |
+
{
|
| 845 |
+
"from": "Prop19",
|
| 846 |
+
"to": "Prop24"
|
| 847 |
+
},
|
| 848 |
+
{
|
| 849 |
+
"from": "Prop23",
|
| 850 |
+
"to": "Prop24"
|
| 851 |
+
},
|
| 852 |
+
{
|
| 853 |
+
"from": "Prop4",
|
| 854 |
+
"to": "Prop25"
|
| 855 |
+
},
|
| 856 |
+
{
|
| 857 |
+
"from": "Prop24",
|
| 858 |
+
"to": "Prop25"
|
| 859 |
+
},
|
| 860 |
+
{
|
| 861 |
+
"from": "Prop3",
|
| 862 |
+
"to": "Prop26"
|
| 863 |
+
},
|
| 864 |
+
{
|
| 865 |
+
"from": "Prop4",
|
| 866 |
+
"to": "Prop26"
|
| 867 |
+
},
|
| 868 |
+
{
|
| 869 |
+
"from": "Prop16",
|
| 870 |
+
"to": "Prop26"
|
| 871 |
+
},
|
| 872 |
+
{
|
| 873 |
+
"from": "Prop16",
|
| 874 |
+
"to": "Prop27"
|
| 875 |
+
},
|
| 876 |
+
{
|
| 877 |
+
"from": "Prop13",
|
| 878 |
+
"to": "Prop28"
|
| 879 |
+
},
|
| 880 |
+
{
|
| 881 |
+
"from": "Prop15",
|
| 882 |
+
"to": "Prop28"
|
| 883 |
+
},
|
| 884 |
+
{
|
| 885 |
+
"from": "Prop27",
|
| 886 |
+
"to": "Prop28"
|
| 887 |
+
},
|
| 888 |
+
{
|
| 889 |
+
"from": "Prop13",
|
| 890 |
+
"to": "Prop29"
|
| 891 |
+
},
|
| 892 |
+
{
|
| 893 |
+
"from": "Prop15",
|
| 894 |
+
"to": "Prop29"
|
| 895 |
+
},
|
| 896 |
+
{
|
| 897 |
+
"from": "Prop27",
|
| 898 |
+
"to": "Prop29"
|
| 899 |
+
},
|
| 900 |
+
{
|
| 901 |
+
"from": "P5",
|
| 902 |
+
"to": "Prop29"
|
| 903 |
+
},
|
| 904 |
+
{
|
| 905 |
+
"from": "Prop29",
|
| 906 |
+
"to": "Prop30"
|
| 907 |
+
},
|
| 908 |
+
{
|
| 909 |
+
"from": "Prop23",
|
| 910 |
+
"to": "Prop31"
|
| 911 |
+
},
|
| 912 |
+
{
|
| 913 |
+
"from": "Prop27",
|
| 914 |
+
"to": "Prop31"
|
| 915 |
+
},
|
| 916 |
+
{
|
| 917 |
+
"from": "Prop13",
|
| 918 |
+
"to": "Prop32"
|
| 919 |
+
},
|
| 920 |
+
{
|
| 921 |
+
"from": "Prop29",
|
| 922 |
+
"to": "Prop32"
|
| 923 |
+
},
|
| 924 |
+
{
|
| 925 |
+
"from": "Prop31",
|
| 926 |
+
"to": "Prop32"
|
| 927 |
+
},
|
| 928 |
+
{
|
| 929 |
+
"from": "Prop4",
|
| 930 |
+
"to": "Prop33"
|
| 931 |
+
},
|
| 932 |
+
{
|
| 933 |
+
"from": "Prop27",
|
| 934 |
+
"to": "Prop33"
|
| 935 |
+
},
|
| 936 |
+
{
|
| 937 |
+
"from": "Prop29",
|
| 938 |
+
"to": "Prop33"
|
| 939 |
+
},
|
| 940 |
+
{
|
| 941 |
+
"from": "Prop4",
|
| 942 |
+
"to": "Prop34"
|
| 943 |
+
},
|
| 944 |
+
{
|
| 945 |
+
"from": "Prop26",
|
| 946 |
+
"to": "Prop34"
|
| 947 |
+
},
|
| 948 |
+
{
|
| 949 |
+
"from": "Prop29",
|
| 950 |
+
"to": "Prop34"
|
| 951 |
+
},
|
| 952 |
+
{
|
| 953 |
+
"from": "Prop4",
|
| 954 |
+
"to": "Prop35"
|
| 955 |
+
},
|
| 956 |
+
{
|
| 957 |
+
"from": "Prop29",
|
| 958 |
+
"to": "Prop35"
|
| 959 |
+
},
|
| 960 |
+
{
|
| 961 |
+
"from": "Prop34",
|
| 962 |
+
"to": "Prop35"
|
| 963 |
+
},
|
| 964 |
+
{
|
| 965 |
+
"from": "Prop33",
|
| 966 |
+
"to": "Prop36"
|
| 967 |
+
},
|
| 968 |
+
{
|
| 969 |
+
"from": "Prop34",
|
| 970 |
+
"to": "Prop36"
|
| 971 |
+
},
|
| 972 |
+
{
|
| 973 |
+
"from": "Prop35",
|
| 974 |
+
"to": "Prop36"
|
| 975 |
+
},
|
| 976 |
+
{
|
| 977 |
+
"from": "Prop31",
|
| 978 |
+
"to": "Prop37"
|
| 979 |
+
},
|
| 980 |
+
{
|
| 981 |
+
"from": "Prop34",
|
| 982 |
+
"to": "Prop37"
|
| 983 |
+
},
|
| 984 |
+
{
|
| 985 |
+
"from": "Prop35",
|
| 986 |
+
"to": "Prop37"
|
| 987 |
+
},
|
| 988 |
+
{
|
| 989 |
+
"from": "Prop31",
|
| 990 |
+
"to": "Prop38"
|
| 991 |
+
},
|
| 992 |
+
{
|
| 993 |
+
"from": "Prop34",
|
| 994 |
+
"to": "Prop38"
|
| 995 |
+
},
|
| 996 |
+
{
|
| 997 |
+
"from": "Prop36",
|
| 998 |
+
"to": "Prop38"
|
| 999 |
+
},
|
| 1000 |
+
{
|
| 1001 |
+
"from": "Prop31",
|
| 1002 |
+
"to": "Prop39"
|
| 1003 |
+
},
|
| 1004 |
+
{
|
| 1005 |
+
"from": "Prop37",
|
| 1006 |
+
"to": "Prop39"
|
| 1007 |
+
},
|
| 1008 |
+
{
|
| 1009 |
+
"from": "Prop31",
|
| 1010 |
+
"to": "Prop40"
|
| 1011 |
+
},
|
| 1012 |
+
{
|
| 1013 |
+
"from": "Prop38",
|
| 1014 |
+
"to": "Prop40"
|
| 1015 |
+
},
|
| 1016 |
+
{
|
| 1017 |
+
"from": "Prop34",
|
| 1018 |
+
"to": "Prop41"
|
| 1019 |
+
},
|
| 1020 |
+
{
|
| 1021 |
+
"from": "Prop37",
|
| 1022 |
+
"to": "Prop41"
|
| 1023 |
+
},
|
| 1024 |
+
{
|
| 1025 |
+
"from": "Prop10",
|
| 1026 |
+
"to": "Prop42"
|
| 1027 |
+
},
|
| 1028 |
+
{
|
| 1029 |
+
"from": "Prop23",
|
| 1030 |
+
"to": "Prop42"
|
| 1031 |
+
},
|
| 1032 |
+
{
|
| 1033 |
+
"from": "Prop31",
|
| 1034 |
+
"to": "Prop42"
|
| 1035 |
+
},
|
| 1036 |
+
{
|
| 1037 |
+
"from": "Prop38",
|
| 1038 |
+
"to": "Prop42"
|
| 1039 |
+
},
|
| 1040 |
+
{
|
| 1041 |
+
"from": "Prop41",
|
| 1042 |
+
"to": "Prop42"
|
| 1043 |
+
},
|
| 1044 |
+
{
|
| 1045 |
+
"from": "Prop34",
|
| 1046 |
+
"to": "Prop43"
|
| 1047 |
+
},
|
| 1048 |
+
{
|
| 1049 |
+
"from": "Prop15",
|
| 1050 |
+
"to": "Prop44"
|
| 1051 |
+
},
|
| 1052 |
+
{
|
| 1053 |
+
"from": "Prop29",
|
| 1054 |
+
"to": "Prop44"
|
| 1055 |
+
},
|
| 1056 |
+
{
|
| 1057 |
+
"from": "Prop31",
|
| 1058 |
+
"to": "Prop44"
|
| 1059 |
+
},
|
| 1060 |
+
{
|
| 1061 |
+
"from": "Prop42",
|
| 1062 |
+
"to": "Prop44"
|
| 1063 |
+
},
|
| 1064 |
+
{
|
| 1065 |
+
"from": "Prop43",
|
| 1066 |
+
"to": "Prop44"
|
| 1067 |
+
},
|
| 1068 |
+
{
|
| 1069 |
+
"from": "Prop14",
|
| 1070 |
+
"to": "Prop45"
|
| 1071 |
+
},
|
| 1072 |
+
{
|
| 1073 |
+
"from": "Prop29",
|
| 1074 |
+
"to": "Prop45"
|
| 1075 |
+
},
|
| 1076 |
+
{
|
| 1077 |
+
"from": "Prop30",
|
| 1078 |
+
"to": "Prop45"
|
| 1079 |
+
},
|
| 1080 |
+
{
|
| 1081 |
+
"from": "Prop33",
|
| 1082 |
+
"to": "Prop45"
|
| 1083 |
+
},
|
| 1084 |
+
{
|
| 1085 |
+
"from": "Prop34",
|
| 1086 |
+
"to": "Prop45"
|
| 1087 |
+
},
|
| 1088 |
+
{
|
| 1089 |
+
"from": "Prop42",
|
| 1090 |
+
"to": "Prop45"
|
| 1091 |
+
},
|
| 1092 |
+
{
|
| 1093 |
+
"from": "Prop44",
|
| 1094 |
+
"to": "Prop45"
|
| 1095 |
+
},
|
| 1096 |
+
{
|
| 1097 |
+
"from": "Prop3",
|
| 1098 |
+
"to": "Prop46"
|
| 1099 |
+
},
|
| 1100 |
+
{
|
| 1101 |
+
"from": "Prop11",
|
| 1102 |
+
"to": "Prop46"
|
| 1103 |
+
},
|
| 1104 |
+
{
|
| 1105 |
+
"from": "Prop29",
|
| 1106 |
+
"to": "Prop46"
|
| 1107 |
+
},
|
| 1108 |
+
{
|
| 1109 |
+
"from": "Prop31",
|
| 1110 |
+
"to": "Prop46"
|
| 1111 |
+
},
|
| 1112 |
+
{
|
| 1113 |
+
"from": "Prop34",
|
| 1114 |
+
"to": "Prop46"
|
| 1115 |
+
},
|
| 1116 |
+
{
|
| 1117 |
+
"from": "Prop4",
|
| 1118 |
+
"to": "Prop47"
|
| 1119 |
+
},
|
| 1120 |
+
{
|
| 1121 |
+
"from": "Prop14",
|
| 1122 |
+
"to": "Prop47"
|
| 1123 |
+
},
|
| 1124 |
+
{
|
| 1125 |
+
"from": "Prop31",
|
| 1126 |
+
"to": "Prop47"
|
| 1127 |
+
},
|
| 1128 |
+
{
|
| 1129 |
+
"from": "Prop41",
|
| 1130 |
+
"to": "Prop47"
|
| 1131 |
+
},
|
| 1132 |
+
{
|
| 1133 |
+
"from": "Prop46",
|
| 1134 |
+
"to": "Prop47"
|
| 1135 |
+
},
|
| 1136 |
+
{
|
| 1137 |
+
"from": "Prop3",
|
| 1138 |
+
"to": "Prop48"
|
| 1139 |
+
},
|
| 1140 |
+
{
|
| 1141 |
+
"from": "Prop8",
|
| 1142 |
+
"to": "Prop48"
|
| 1143 |
+
},
|
| 1144 |
+
{
|
| 1145 |
+
"from": "Prop11",
|
| 1146 |
+
"to": "Prop48"
|
| 1147 |
+
},
|
| 1148 |
+
{
|
| 1149 |
+
"from": "Prop47",
|
| 1150 |
+
"to": "Prop48"
|
| 1151 |
+
}
|
| 1152 |
+
],
|
| 1153 |
+
"colorScheme": {
|
| 1154 |
+
"postulate": {
|
| 1155 |
+
"fill": "#e74c3c",
|
| 1156 |
+
"stroke": "#c0392b"
|
| 1157 |
+
},
|
| 1158 |
+
"commonNotion": {
|
| 1159 |
+
"fill": "#9b59b6",
|
| 1160 |
+
"stroke": "#8e44ad"
|
| 1161 |
+
},
|
| 1162 |
+
"proposition": {
|
| 1163 |
+
"fill": "#1abc9c",
|
| 1164 |
+
"stroke": "#16a085"
|
| 1165 |
+
}
|
| 1166 |
+
}
|
| 1167 |
+
}
|
data/euclid-elements-book-i.mmd
ADDED
|
@@ -0,0 +1,195 @@
|
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|
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|
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|
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|
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|
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|
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|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 1 |
+
graph TD
|
| 2 |
+
P1["Post. 1\nDraw a straight line from any po..."]
|
| 3 |
+
P2["Post. 2\nProduce a finite straight line c..."]
|
| 4 |
+
P3["Post. 3\nDescribe a circle with any cente..."]
|
| 5 |
+
P4["Post. 4\nAll right angles equal one another"]
|
| 6 |
+
P5["Post. 5\nParallel postulate: if interior ..."]
|
| 7 |
+
CN1["CN 1\nThings equal to the same thing a..."]
|
| 8 |
+
CN2["CN 2\nIf equals are added to equals, t..."]
|
| 9 |
+
CN3["CN 3\nIf equals are subtracted from eq..."]
|
| 10 |
+
CN4["CN 4\nThings coinciding with one anoth..."]
|
| 11 |
+
CN5["CN 5\nThe whole is greater than the part"]
|
| 12 |
+
Prop1["Prop. I.1\nEquilateral triangle on given line"]
|
| 13 |
+
Prop2["Prop. I.2\nPlace line equal to given at point"]
|
| 14 |
+
Prop3["Prop. I.3\nCut off from greater segment equal to less"]
|
| 15 |
+
Prop4["Prop. I.4\nSAS congruence"]
|
| 16 |
+
Prop5["Prop. I.5\nBase angles of isosceles equal"]
|
| 17 |
+
Prop6["Prop. I.6\nSides opposite equal angles equal"]
|
| 18 |
+
Prop7["Prop. I.7\nUniqueness of triangle from ends"]
|
| 19 |
+
Prop8["Prop. I.8\nSSS congruence"]
|
| 20 |
+
Prop9["Prop. I.9\nBisect angle"]
|
| 21 |
+
Prop10["Prop. I.10\nBisect line"]
|
| 22 |
+
Prop11["Prop. I.11\nPerpendicular from point on line"]
|
| 23 |
+
Prop12["Prop. I.12\nPerpendicular from point not on line"]
|
| 24 |
+
Prop13["Prop. I.13\nAngles on line sum to two right"]
|
| 25 |
+
Prop14["Prop. I.14\nIf angles sum to two right, straight line"]
|
| 26 |
+
Prop15["Prop. I.15\nVertical angles equal"]
|
| 27 |
+
Prop16["Prop. I.16\nExterior angle > interior opposite"]
|
| 28 |
+
Prop17["Prop. I.17\nSum of two angles < two right"]
|
| 29 |
+
Prop18["Prop. I.18\nAngle opposite greater side greater"]
|
| 30 |
+
Prop19["Prop. I.19\nSide opposite greater angle greater"]
|
| 31 |
+
Prop20["Prop. I.20\nTriangle inequality"]
|
| 32 |
+
Prop21["Prop. I.21\nLines from ends within triangle"]
|
| 33 |
+
Prop22["Prop. I.22\nConstruct triangle from three lines"]
|
| 34 |
+
Prop23["Prop. I.23\nConstruct angle equal to given"]
|
| 35 |
+
Prop24["Prop. I.24\nSAS for greater angle => greater base"]
|
| 36 |
+
Prop25["Prop. I.25\nSAS for greater base => greater angle"]
|
| 37 |
+
Prop26["Prop. I.26\nAAS congruence"]
|
| 38 |
+
Prop27["Prop. I.27\nAlternate angles equal => parallel"]
|
| 39 |
+
Prop28["Prop. I.28\nExterior = interior opposite => parallel"]
|
| 40 |
+
Prop29["Prop. I.29\nParallel => alternate angles equal"]
|
| 41 |
+
Prop30["Prop. I.30\nTransitivity of parallel"]
|
| 42 |
+
Prop31["Prop. I.31\nDraw parallel through point"]
|
| 43 |
+
Prop32["Prop. I.32\nExterior angle = sum interior opposite"]
|
| 44 |
+
Prop33["Prop. I.33\nJoining ends of equal parallel lines"]
|
| 45 |
+
Prop34["Prop. I.34\nParallelogram properties"]
|
| 46 |
+
Prop35["Prop. I.35\nParallelograms same base equal"]
|
| 47 |
+
Prop36["Prop. I.36\nParallelograms equal bases equal"]
|
| 48 |
+
Prop37["Prop. I.37\nTriangles same base equal"]
|
| 49 |
+
Prop38["Prop. I.38\nTriangles equal bases equal"]
|
| 50 |
+
Prop39["Prop. I.39\nEqual triangles same base same side"]
|
| 51 |
+
Prop40["Prop. I.40\nEqual triangles equal bases same side"]
|
| 52 |
+
Prop41["Prop. I.41\nParallelogram = 2× triangle"]
|
| 53 |
+
Prop42["Prop. I.42\nConstruct parallelogram = triangle"]
|
| 54 |
+
Prop43["Prop. I.43\nComplements of parallelogram"]
|
| 55 |
+
Prop44["Prop. I.44\nApply parallelogram to line"]
|
| 56 |
+
Prop45["Prop. I.45\nConstruct parallelogram = rectilinear figure"]
|
| 57 |
+
Prop46["Prop. I.46\nConstruct square on line"]
|
| 58 |
+
Prop47["Prop. I.47\nPythagorean theorem"]
|
| 59 |
+
Prop48["Prop. I.48\nConverse Pythagorean"]
|
| 60 |
+
P1 --> Prop1
|
| 61 |
+
P3 --> Prop1
|
| 62 |
+
Prop1 --> Prop2
|
| 63 |
+
P1 --> Prop2
|
| 64 |
+
P2 --> Prop2
|
| 65 |
+
P3 --> Prop2
|
| 66 |
+
Prop2 --> Prop3
|
| 67 |
+
P3 --> Prop3
|
| 68 |
+
CN4 --> Prop4
|
| 69 |
+
CN5 --> Prop4
|
| 70 |
+
Prop3 --> Prop5
|
| 71 |
+
Prop4 --> Prop5
|
| 72 |
+
Prop3 --> Prop6
|
| 73 |
+
Prop4 --> Prop6
|
| 74 |
+
Prop5 --> Prop7
|
| 75 |
+
Prop7 --> Prop8
|
| 76 |
+
Prop1 --> Prop9
|
| 77 |
+
Prop3 --> Prop9
|
| 78 |
+
Prop8 --> Prop9
|
| 79 |
+
Prop1 --> Prop10
|
| 80 |
+
Prop4 --> Prop10
|
| 81 |
+
Prop9 --> Prop10
|
| 82 |
+
Prop1 --> Prop11
|
| 83 |
+
Prop3 --> Prop11
|
| 84 |
+
Prop8 --> Prop11
|
| 85 |
+
Prop8 --> Prop12
|
| 86 |
+
Prop10 --> Prop12
|
| 87 |
+
Prop11 --> Prop13
|
| 88 |
+
Prop13 --> Prop14
|
| 89 |
+
Prop13 --> Prop15
|
| 90 |
+
Prop3 --> Prop16
|
| 91 |
+
Prop4 --> Prop16
|
| 92 |
+
Prop10 --> Prop16
|
| 93 |
+
Prop15 --> Prop16
|
| 94 |
+
Prop13 --> Prop17
|
| 95 |
+
Prop16 --> Prop17
|
| 96 |
+
Prop3 --> Prop18
|
| 97 |
+
Prop5 --> Prop18
|
| 98 |
+
Prop16 --> Prop18
|
| 99 |
+
Prop5 --> Prop19
|
| 100 |
+
Prop18 --> Prop19
|
| 101 |
+
Prop3 --> Prop20
|
| 102 |
+
Prop5 --> Prop20
|
| 103 |
+
Prop19 --> Prop20
|
| 104 |
+
Prop16 --> Prop21
|
| 105 |
+
Prop20 --> Prop21
|
| 106 |
+
Prop3 --> Prop22
|
| 107 |
+
Prop20 --> Prop22
|
| 108 |
+
Prop8 --> Prop23
|
| 109 |
+
Prop22 --> Prop23
|
| 110 |
+
Prop3 --> Prop24
|
| 111 |
+
Prop4 --> Prop24
|
| 112 |
+
Prop5 --> Prop24
|
| 113 |
+
Prop19 --> Prop24
|
| 114 |
+
Prop23 --> Prop24
|
| 115 |
+
Prop4 --> Prop25
|
| 116 |
+
Prop24 --> Prop25
|
| 117 |
+
Prop3 --> Prop26
|
| 118 |
+
Prop4 --> Prop26
|
| 119 |
+
Prop16 --> Prop26
|
| 120 |
+
Prop16 --> Prop27
|
| 121 |
+
Prop13 --> Prop28
|
| 122 |
+
Prop15 --> Prop28
|
| 123 |
+
Prop27 --> Prop28
|
| 124 |
+
Prop13 --> Prop29
|
| 125 |
+
Prop15 --> Prop29
|
| 126 |
+
Prop27 --> Prop29
|
| 127 |
+
P5 --> Prop29
|
| 128 |
+
Prop29 --> Prop30
|
| 129 |
+
Prop23 --> Prop31
|
| 130 |
+
Prop27 --> Prop31
|
| 131 |
+
Prop13 --> Prop32
|
| 132 |
+
Prop29 --> Prop32
|
| 133 |
+
Prop31 --> Prop32
|
| 134 |
+
Prop4 --> Prop33
|
| 135 |
+
Prop27 --> Prop33
|
| 136 |
+
Prop29 --> Prop33
|
| 137 |
+
Prop4 --> Prop34
|
| 138 |
+
Prop26 --> Prop34
|
| 139 |
+
Prop29 --> Prop34
|
| 140 |
+
Prop4 --> Prop35
|
| 141 |
+
Prop29 --> Prop35
|
| 142 |
+
Prop34 --> Prop35
|
| 143 |
+
Prop33 --> Prop36
|
| 144 |
+
Prop34 --> Prop36
|
| 145 |
+
Prop35 --> Prop36
|
| 146 |
+
Prop31 --> Prop37
|
| 147 |
+
Prop34 --> Prop37
|
| 148 |
+
Prop35 --> Prop37
|
| 149 |
+
Prop31 --> Prop38
|
| 150 |
+
Prop34 --> Prop38
|
| 151 |
+
Prop36 --> Prop38
|
| 152 |
+
Prop31 --> Prop39
|
| 153 |
+
Prop37 --> Prop39
|
| 154 |
+
Prop31 --> Prop40
|
| 155 |
+
Prop38 --> Prop40
|
| 156 |
+
Prop34 --> Prop41
|
| 157 |
+
Prop37 --> Prop41
|
| 158 |
+
Prop10 --> Prop42
|
| 159 |
+
Prop23 --> Prop42
|
| 160 |
+
Prop31 --> Prop42
|
| 161 |
+
Prop38 --> Prop42
|
| 162 |
+
Prop41 --> Prop42
|
| 163 |
+
Prop34 --> Prop43
|
| 164 |
+
Prop15 --> Prop44
|
| 165 |
+
Prop29 --> Prop44
|
| 166 |
+
Prop31 --> Prop44
|
| 167 |
+
Prop42 --> Prop44
|
| 168 |
+
Prop43 --> Prop44
|
| 169 |
+
Prop14 --> Prop45
|
| 170 |
+
Prop29 --> Prop45
|
| 171 |
+
Prop30 --> Prop45
|
| 172 |
+
Prop33 --> Prop45
|
| 173 |
+
Prop34 --> Prop45
|
| 174 |
+
Prop42 --> Prop45
|
| 175 |
+
Prop44 --> Prop45
|
| 176 |
+
Prop3 --> Prop46
|
| 177 |
+
Prop11 --> Prop46
|
| 178 |
+
Prop29 --> Prop46
|
| 179 |
+
Prop31 --> Prop46
|
| 180 |
+
Prop34 --> Prop46
|
| 181 |
+
Prop4 --> Prop47
|
| 182 |
+
Prop14 --> Prop47
|
| 183 |
+
Prop31 --> Prop47
|
| 184 |
+
Prop41 --> Prop47
|
| 185 |
+
Prop46 --> Prop47
|
| 186 |
+
Prop3 --> Prop48
|
| 187 |
+
Prop8 --> Prop48
|
| 188 |
+
Prop11 --> Prop48
|
| 189 |
+
Prop47 --> Prop48
|
| 190 |
+
classDef postulate fill:#e74c3c,color:#fff,stroke:#c0392b
|
| 191 |
+
classDef commonNotion fill:#9b59b6,color:#fff,stroke:#8e44ad
|
| 192 |
+
classDef proposition fill:#1abc9c,color:#fff,stroke:#16a085
|
| 193 |
+
class P1,P2,P3,P4,P5 postulate
|
| 194 |
+
class CN1,CN2,CN3,CN4,CN5 commonNotion
|
| 195 |
+
class Prop1,Prop2,Prop3,Prop4,Prop5,Prop6,Prop7,Prop8,Prop9,Prop10,Prop11,Prop12,Prop13,Prop14,Prop15,Prop16,Prop17,Prop18,Prop19,Prop20,Prop21,Prop22,Prop23,Prop24,Prop25,Prop26,Prop27,Prop28,Prop29,Prop30,Prop31,Prop32,Prop33,Prop34,Prop35,Prop36,Prop37,Prop38,Prop39,Prop40,Prop41,Prop42,Prop43,Prop44,Prop45,Prop46,Prop47,Prop48 proposition
|
data/euclid-elements-book-ii.json
ADDED
|
@@ -0,0 +1,365 @@
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|
| 1 |
+
{
|
| 2 |
+
"schemaVersion": "1.0",
|
| 3 |
+
"discourse": {
|
| 4 |
+
"id": "euclid-elements-book-ii",
|
| 5 |
+
"name": "Euclid's Elements, Book II",
|
| 6 |
+
"subject": "geometry",
|
| 7 |
+
"variant": "classical",
|
| 8 |
+
"description": "The 14 propositions of Book II on geometric algebra (rectangles, squares). Props 1-10 are logically independent within Book II; 11-14 depend on 6, 4, 7, 5. All depend on Book I. Source: David E. Joyce, Clark University.",
|
| 9 |
+
"structure": {
|
| 10 |
+
"books": 2,
|
| 11 |
+
"propositions": 14,
|
| 12 |
+
"foundationTypes": [
|
| 13 |
+
"definition"
|
| 14 |
+
]
|
| 15 |
+
}
|
| 16 |
+
},
|
| 17 |
+
"metadata": {
|
| 18 |
+
"created": "2026-03-15",
|
| 19 |
+
"lastUpdated": "2026-03-15",
|
| 20 |
+
"version": "1.0.0",
|
| 21 |
+
"license": "CC BY 4.0",
|
| 22 |
+
"authors": [
|
| 23 |
+
"Welz, G."
|
| 24 |
+
],
|
| 25 |
+
"methodology": "Programming Framework",
|
| 26 |
+
"citation": "Welz, G. (2026). Euclid's Elements Book II Dependency Graph. Programming Framework.",
|
| 27 |
+
"keywords": [
|
| 28 |
+
"Euclid",
|
| 29 |
+
"Elements",
|
| 30 |
+
"Book II",
|
| 31 |
+
"geometric algebra",
|
| 32 |
+
"rectangles",
|
| 33 |
+
"squares",
|
| 34 |
+
"golden section",
|
| 35 |
+
"quadrature"
|
| 36 |
+
]
|
| 37 |
+
},
|
| 38 |
+
"sources": [
|
| 39 |
+
{
|
| 40 |
+
"id": "joyce",
|
| 41 |
+
"type": "digital",
|
| 42 |
+
"authors": "Joyce, David E.",
|
| 43 |
+
"title": "Euclid's Elements, Book II",
|
| 44 |
+
"year": "1996",
|
| 45 |
+
"url": "https://mathcs.clarku.edu/~djoyce/java/elements/bookII/bookII.html",
|
| 46 |
+
"notes": "Clark University; dependency table from Logical structure"
|
| 47 |
+
},
|
| 48 |
+
{
|
| 49 |
+
"id": "euclid-heath",
|
| 50 |
+
"type": "primary",
|
| 51 |
+
"authors": "Heath, T.L.",
|
| 52 |
+
"title": "The Thirteen Books of Euclid's Elements",
|
| 53 |
+
"year": "1908",
|
| 54 |
+
"edition": "2nd",
|
| 55 |
+
"publisher": "Cambridge University Press",
|
| 56 |
+
"url": "https://archive.org/details/euclidheath00heatiala",
|
| 57 |
+
"notes": "Standard English translation"
|
| 58 |
+
}
|
| 59 |
+
],
|
| 60 |
+
"nodes": [
|
| 61 |
+
{
|
| 62 |
+
"id": "BookI",
|
| 63 |
+
"type": "foundation",
|
| 64 |
+
"label": "Book I — Fundamentals of plane geometry",
|
| 65 |
+
"shortLabel": "Book I",
|
| 66 |
+
"short": "Foundation",
|
| 67 |
+
"book": 1,
|
| 68 |
+
"colorClass": "foundation"
|
| 69 |
+
},
|
| 70 |
+
{
|
| 71 |
+
"id": "Def1",
|
| 72 |
+
"type": "definition",
|
| 73 |
+
"label": "Rectangle contained by two straight lines containing the right angle",
|
| 74 |
+
"shortLabel": "Def. II.1",
|
| 75 |
+
"book": 2,
|
| 76 |
+
"number": 1,
|
| 77 |
+
"colorClass": "definition"
|
| 78 |
+
},
|
| 79 |
+
{
|
| 80 |
+
"id": "Def2",
|
| 81 |
+
"type": "definition",
|
| 82 |
+
"label": "Gnomon: parallelogram about diameter with two complements",
|
| 83 |
+
"shortLabel": "Def. II.2",
|
| 84 |
+
"book": 2,
|
| 85 |
+
"number": 2,
|
| 86 |
+
"colorClass": "definition"
|
| 87 |
+
},
|
| 88 |
+
{
|
| 89 |
+
"id": "Prop1",
|
| 90 |
+
"type": "proposition",
|
| 91 |
+
"label": "If one line is cut into segments, rectangle by whole equals sum of rectangles by each segment",
|
| 92 |
+
"shortLabel": "Prop. II.1",
|
| 93 |
+
"short": "Rectangle = sum of rectangles",
|
| 94 |
+
"book": 2,
|
| 95 |
+
"number": 1,
|
| 96 |
+
"colorClass": "proposition"
|
| 97 |
+
},
|
| 98 |
+
{
|
| 99 |
+
"id": "Prop2",
|
| 100 |
+
"type": "proposition",
|
| 101 |
+
"label": "If a line is cut at random, sum of rectangles by whole and each segment equals square on whole",
|
| 102 |
+
"shortLabel": "Prop. II.2",
|
| 103 |
+
"short": "Sum of rectangles = square on whole",
|
| 104 |
+
"book": 2,
|
| 105 |
+
"number": 2,
|
| 106 |
+
"colorClass": "proposition"
|
| 107 |
+
},
|
| 108 |
+
{
|
| 109 |
+
"id": "Prop3",
|
| 110 |
+
"type": "proposition",
|
| 111 |
+
"label": "If a line is cut at random, rectangle by whole and one segment equals rectangle by segments plus square on that segment",
|
| 112 |
+
"shortLabel": "Prop. II.3",
|
| 113 |
+
"short": "Rectangle = rectangle + square",
|
| 114 |
+
"book": 2,
|
| 115 |
+
"number": 3,
|
| 116 |
+
"colorClass": "proposition"
|
| 117 |
+
},
|
| 118 |
+
{
|
| 119 |
+
"id": "Prop4",
|
| 120 |
+
"type": "proposition",
|
| 121 |
+
"label": "If a line is cut at random, square on whole equals squares on segments plus twice rectangle contained by segments",
|
| 122 |
+
"shortLabel": "Prop. II.4",
|
| 123 |
+
"short": "Square on whole = squares + 2×rectangle",
|
| 124 |
+
"book": 2,
|
| 125 |
+
"number": 4,
|
| 126 |
+
"colorClass": "proposition"
|
| 127 |
+
},
|
| 128 |
+
{
|
| 129 |
+
"id": "Prop5",
|
| 130 |
+
"type": "proposition",
|
| 131 |
+
"label": "If a line cut into equal and unequal segments, rectangle by unequal segments plus square on difference equals square on half",
|
| 132 |
+
"shortLabel": "Prop. II.5",
|
| 133 |
+
"short": "Unequal segments: rectangle + square = square on half",
|
| 134 |
+
"book": 2,
|
| 135 |
+
"number": 5,
|
| 136 |
+
"colorClass": "proposition"
|
| 137 |
+
},
|
| 138 |
+
{
|
| 139 |
+
"id": "Prop6",
|
| 140 |
+
"type": "proposition",
|
| 141 |
+
"label": "If a line bisected and added to, rectangle by whole-with-added and added plus square on half equals square on half-plus-added",
|
| 142 |
+
"shortLabel": "Prop. II.6",
|
| 143 |
+
"short": "Bisected + added: rectangle + square = square",
|
| 144 |
+
"book": 2,
|
| 145 |
+
"number": 6,
|
| 146 |
+
"colorClass": "proposition"
|
| 147 |
+
},
|
| 148 |
+
{
|
| 149 |
+
"id": "Prop7",
|
| 150 |
+
"type": "proposition",
|
| 151 |
+
"label": "If a line cut at random, square on whole plus square on one segment equals twice rectangle by whole and segment plus square on remainder",
|
| 152 |
+
"shortLabel": "Prop. II.7",
|
| 153 |
+
"short": "Square on whole + square on segment",
|
| 154 |
+
"book": 2,
|
| 155 |
+
"number": 7,
|
| 156 |
+
"colorClass": "proposition"
|
| 157 |
+
},
|
| 158 |
+
{
|
| 159 |
+
"id": "Prop8",
|
| 160 |
+
"type": "proposition",
|
| 161 |
+
"label": "If a line cut at random, four times rectangle by whole and one segment plus square on remainder equals square on whole-plus-segment",
|
| 162 |
+
"shortLabel": "Prop. II.8",
|
| 163 |
+
"short": "Four times rectangle + square",
|
| 164 |
+
"book": 2,
|
| 165 |
+
"number": 8,
|
| 166 |
+
"colorClass": "proposition"
|
| 167 |
+
},
|
| 168 |
+
{
|
| 169 |
+
"id": "Prop9",
|
| 170 |
+
"type": "proposition",
|
| 171 |
+
"label": "If a line cut into equal and unequal segments, sum of squares on unequal segments is double sum of square on half and square on difference",
|
| 172 |
+
"shortLabel": "Prop. II.9",
|
| 173 |
+
"short": "Unequal segments: sum of squares",
|
| 174 |
+
"book": 2,
|
| 175 |
+
"number": 9,
|
| 176 |
+
"colorClass": "proposition"
|
| 177 |
+
},
|
| 178 |
+
{
|
| 179 |
+
"id": "Prop10",
|
| 180 |
+
"type": "proposition",
|
| 181 |
+
"label": "If a line bisected and added to, square on whole-with-added plus square on added equals double sum of square on half and square on half-plus-added",
|
| 182 |
+
"shortLabel": "Prop. II.10",
|
| 183 |
+
"short": "Bisected + added: sum of squares",
|
| 184 |
+
"book": 2,
|
| 185 |
+
"number": 10,
|
| 186 |
+
"colorClass": "proposition"
|
| 187 |
+
},
|
| 188 |
+
{
|
| 189 |
+
"id": "Prop11",
|
| 190 |
+
"type": "proposition",
|
| 191 |
+
"label": "To cut a given line so that rectangle by whole and one segment equals square on remaining segment",
|
| 192 |
+
"shortLabel": "Prop. II.11",
|
| 193 |
+
"short": "Cut line: rectangle = square (golden section)",
|
| 194 |
+
"book": 2,
|
| 195 |
+
"number": 11,
|
| 196 |
+
"colorClass": "proposition"
|
| 197 |
+
},
|
| 198 |
+
{
|
| 199 |
+
"id": "Prop12",
|
| 200 |
+
"type": "proposition",
|
| 201 |
+
"label": "In obtuse-angled triangles, square on side opposite obtuse angle greater than sum of squares on sides containing it",
|
| 202 |
+
"shortLabel": "Prop. II.12",
|
| 203 |
+
"short": "Obtuse triangle: law of cosines",
|
| 204 |
+
"book": 2,
|
| 205 |
+
"number": 12,
|
| 206 |
+
"colorClass": "proposition"
|
| 207 |
+
},
|
| 208 |
+
{
|
| 209 |
+
"id": "Prop13",
|
| 210 |
+
"type": "proposition",
|
| 211 |
+
"label": "In acute-angled triangles, square on side opposite acute angle less than sum of squares on sides containing it",
|
| 212 |
+
"shortLabel": "Prop. II.13",
|
| 213 |
+
"short": "Acute triangle: law of cosines",
|
| 214 |
+
"book": 2,
|
| 215 |
+
"number": 13,
|
| 216 |
+
"colorClass": "proposition"
|
| 217 |
+
},
|
| 218 |
+
{
|
| 219 |
+
"id": "Prop14",
|
| 220 |
+
"type": "proposition",
|
| 221 |
+
"label": "To construct a square equal to a given rectilinear figure",
|
| 222 |
+
"shortLabel": "Prop. II.14",
|
| 223 |
+
"short": "Construct square = rectilinear figure",
|
| 224 |
+
"book": 2,
|
| 225 |
+
"number": 14,
|
| 226 |
+
"colorClass": "proposition"
|
| 227 |
+
}
|
| 228 |
+
],
|
| 229 |
+
"edges": [
|
| 230 |
+
{
|
| 231 |
+
"from": "BookI",
|
| 232 |
+
"to": "Prop1"
|
| 233 |
+
},
|
| 234 |
+
{
|
| 235 |
+
"from": "Def1",
|
| 236 |
+
"to": "Prop1"
|
| 237 |
+
},
|
| 238 |
+
{
|
| 239 |
+
"from": "BookI",
|
| 240 |
+
"to": "Prop2"
|
| 241 |
+
},
|
| 242 |
+
{
|
| 243 |
+
"from": "Def1",
|
| 244 |
+
"to": "Prop2"
|
| 245 |
+
},
|
| 246 |
+
{
|
| 247 |
+
"from": "BookI",
|
| 248 |
+
"to": "Prop3"
|
| 249 |
+
},
|
| 250 |
+
{
|
| 251 |
+
"from": "Def1",
|
| 252 |
+
"to": "Prop3"
|
| 253 |
+
},
|
| 254 |
+
{
|
| 255 |
+
"from": "BookI",
|
| 256 |
+
"to": "Prop4"
|
| 257 |
+
},
|
| 258 |
+
{
|
| 259 |
+
"from": "Def1",
|
| 260 |
+
"to": "Prop4"
|
| 261 |
+
},
|
| 262 |
+
{
|
| 263 |
+
"from": "BookI",
|
| 264 |
+
"to": "Prop5"
|
| 265 |
+
},
|
| 266 |
+
{
|
| 267 |
+
"from": "Def1",
|
| 268 |
+
"to": "Prop5"
|
| 269 |
+
},
|
| 270 |
+
{
|
| 271 |
+
"from": "Def2",
|
| 272 |
+
"to": "Prop5"
|
| 273 |
+
},
|
| 274 |
+
{
|
| 275 |
+
"from": "BookI",
|
| 276 |
+
"to": "Prop6"
|
| 277 |
+
},
|
| 278 |
+
{
|
| 279 |
+
"from": "Def1",
|
| 280 |
+
"to": "Prop6"
|
| 281 |
+
},
|
| 282 |
+
{
|
| 283 |
+
"from": "Def2",
|
| 284 |
+
"to": "Prop6"
|
| 285 |
+
},
|
| 286 |
+
{
|
| 287 |
+
"from": "BookI",
|
| 288 |
+
"to": "Prop7"
|
| 289 |
+
},
|
| 290 |
+
{
|
| 291 |
+
"from": "Def1",
|
| 292 |
+
"to": "Prop7"
|
| 293 |
+
},
|
| 294 |
+
{
|
| 295 |
+
"from": "BookI",
|
| 296 |
+
"to": "Prop8"
|
| 297 |
+
},
|
| 298 |
+
{
|
| 299 |
+
"from": "Def1",
|
| 300 |
+
"to": "Prop8"
|
| 301 |
+
},
|
| 302 |
+
{
|
| 303 |
+
"from": "BookI",
|
| 304 |
+
"to": "Prop9"
|
| 305 |
+
},
|
| 306 |
+
{
|
| 307 |
+
"from": "Def1",
|
| 308 |
+
"to": "Prop9"
|
| 309 |
+
},
|
| 310 |
+
{
|
| 311 |
+
"from": "BookI",
|
| 312 |
+
"to": "Prop10"
|
| 313 |
+
},
|
| 314 |
+
{
|
| 315 |
+
"from": "Def1",
|
| 316 |
+
"to": "Prop10"
|
| 317 |
+
},
|
| 318 |
+
{
|
| 319 |
+
"from": "BookI",
|
| 320 |
+
"to": "Prop11"
|
| 321 |
+
},
|
| 322 |
+
{
|
| 323 |
+
"from": "Prop6",
|
| 324 |
+
"to": "Prop11"
|
| 325 |
+
},
|
| 326 |
+
{
|
| 327 |
+
"from": "BookI",
|
| 328 |
+
"to": "Prop12"
|
| 329 |
+
},
|
| 330 |
+
{
|
| 331 |
+
"from": "Prop4",
|
| 332 |
+
"to": "Prop12"
|
| 333 |
+
},
|
| 334 |
+
{
|
| 335 |
+
"from": "BookI",
|
| 336 |
+
"to": "Prop13"
|
| 337 |
+
},
|
| 338 |
+
{
|
| 339 |
+
"from": "Prop7",
|
| 340 |
+
"to": "Prop13"
|
| 341 |
+
},
|
| 342 |
+
{
|
| 343 |
+
"from": "BookI",
|
| 344 |
+
"to": "Prop14"
|
| 345 |
+
},
|
| 346 |
+
{
|
| 347 |
+
"from": "Prop5",
|
| 348 |
+
"to": "Prop14"
|
| 349 |
+
}
|
| 350 |
+
],
|
| 351 |
+
"colorScheme": {
|
| 352 |
+
"foundation": {
|
| 353 |
+
"fill": "#95a5a6",
|
| 354 |
+
"stroke": "#7f8c8d"
|
| 355 |
+
},
|
| 356 |
+
"definition": {
|
| 357 |
+
"fill": "#3498db",
|
| 358 |
+
"stroke": "#2980b9"
|
| 359 |
+
},
|
| 360 |
+
"proposition": {
|
| 361 |
+
"fill": "#1abc9c",
|
| 362 |
+
"stroke": "#16a085"
|
| 363 |
+
}
|
| 364 |
+
}
|
| 365 |
+
}
|
data/euclid-elements-book-ii.mmd
ADDED
|
@@ -0,0 +1,54 @@
|
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|
|
|
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|
|
|
|
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|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
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|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 1 |
+
graph TD
|
| 2 |
+
BookI["Book I\nFoundation"]
|
| 3 |
+
Def1["Def. II.1\nRectangle contained by two strai..."]
|
| 4 |
+
Def2["Def. II.2\nGnomon: parallelogram about diam..."]
|
| 5 |
+
Prop1["Prop. II.1\nRectangle = sum of rectangles"]
|
| 6 |
+
Prop2["Prop. II.2\nSum of rectangles = square on whole"]
|
| 7 |
+
Prop3["Prop. II.3\nRectangle = rectangle + square"]
|
| 8 |
+
Prop4["Prop. II.4\nSquare on whole = squares + 2×rectangle"]
|
| 9 |
+
Prop5["Prop. II.5\nUnequal segments: rectangle + square = square on half"]
|
| 10 |
+
Prop6["Prop. II.6\nBisected + added: rectangle + square = square"]
|
| 11 |
+
Prop7["Prop. II.7\nSquare on whole + square on segment"]
|
| 12 |
+
Prop8["Prop. II.8\nFour times rectangle + square"]
|
| 13 |
+
Prop9["Prop. II.9\nUnequal segments: sum of squares"]
|
| 14 |
+
Prop10["Prop. II.10\nBisected + added: sum of squares"]
|
| 15 |
+
Prop11["Prop. II.11\nCut line: rectangle = square (golden section)"]
|
| 16 |
+
Prop12["Prop. II.12\nObtuse triangle: law of cosines"]
|
| 17 |
+
Prop13["Prop. II.13\nAcute triangle: law of cosines"]
|
| 18 |
+
Prop14["Prop. II.14\nConstruct square = rectilinear figure"]
|
| 19 |
+
BookI --> Prop1
|
| 20 |
+
Def1 --> Prop1
|
| 21 |
+
BookI --> Prop2
|
| 22 |
+
Def1 --> Prop2
|
| 23 |
+
BookI --> Prop3
|
| 24 |
+
Def1 --> Prop3
|
| 25 |
+
BookI --> Prop4
|
| 26 |
+
Def1 --> Prop4
|
| 27 |
+
BookI --> Prop5
|
| 28 |
+
Def1 --> Prop5
|
| 29 |
+
Def2 --> Prop5
|
| 30 |
+
BookI --> Prop6
|
| 31 |
+
Def1 --> Prop6
|
| 32 |
+
Def2 --> Prop6
|
| 33 |
+
BookI --> Prop7
|
| 34 |
+
Def1 --> Prop7
|
| 35 |
+
BookI --> Prop8
|
| 36 |
+
Def1 --> Prop8
|
| 37 |
+
BookI --> Prop9
|
| 38 |
+
Def1 --> Prop9
|
| 39 |
+
BookI --> Prop10
|
| 40 |
+
Def1 --> Prop10
|
| 41 |
+
BookI --> Prop11
|
| 42 |
+
Prop6 --> Prop11
|
| 43 |
+
BookI --> Prop12
|
| 44 |
+
Prop4 --> Prop12
|
| 45 |
+
BookI --> Prop13
|
| 46 |
+
Prop7 --> Prop13
|
| 47 |
+
BookI --> Prop14
|
| 48 |
+
Prop5 --> Prop14
|
| 49 |
+
classDef foundation fill:#95a5a6,color:#fff,stroke:#7f8c8d
|
| 50 |
+
classDef definition fill:#3498db,color:#fff,stroke:#2980b9
|
| 51 |
+
classDef proposition fill:#1abc9c,color:#fff,stroke:#16a085
|
| 52 |
+
class BookI foundation
|
| 53 |
+
class Def1,Def2 definition
|
| 54 |
+
class Prop1,Prop2,Prop3,Prop4,Prop5,Prop6,Prop7,Prop8,Prop9,Prop10,Prop11,Prop12,Prop13,Prop14 proposition
|
data/euclid-elements-book-iii.json
ADDED
|
@@ -0,0 +1,885 @@
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
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|
|
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|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
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|
|
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|
|
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|
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|
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|
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|
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|
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|
|
|
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|
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|
|
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|
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|
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|
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|
|
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|
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|
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|
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|
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|
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|
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|
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|
|
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|
|
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|
|
|
|
|
|
|
|
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|
|
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|
|
|
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|
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|
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|
|
|
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|
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|
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|
|
|
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|
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|
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|
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|
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|
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|
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|
|
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|
| 1 |
+
{
|
| 2 |
+
"schemaVersion": "1.0",
|
| 3 |
+
"discourse": {
|
| 4 |
+
"id": "euclid-elements-book-iii",
|
| 5 |
+
"name": "Euclid's Elements, Book III",
|
| 6 |
+
"subject": "geometry",
|
| 7 |
+
"variant": "classical",
|
| 8 |
+
"description": "Theory of circles: 11 definitions, 37 propositions. All depend on Book I. III.35 uses II.5. Source: David E. Joyce.",
|
| 9 |
+
"structure": {
|
| 10 |
+
"books": 3,
|
| 11 |
+
"definitions": 11,
|
| 12 |
+
"propositions": 37,
|
| 13 |
+
"foundationTypes": [
|
| 14 |
+
"definition",
|
| 15 |
+
"foundation"
|
| 16 |
+
]
|
| 17 |
+
}
|
| 18 |
+
},
|
| 19 |
+
"metadata": {
|
| 20 |
+
"created": "2026-03-15",
|
| 21 |
+
"lastUpdated": "2026-03-15",
|
| 22 |
+
"version": "1.0.0",
|
| 23 |
+
"license": "CC BY 4.0",
|
| 24 |
+
"authors": [
|
| 25 |
+
"Welz, G."
|
| 26 |
+
],
|
| 27 |
+
"methodology": "Programming Framework",
|
| 28 |
+
"citation": "Welz, G. (2026). Euclid's Elements Book III Dependency Graph. Programming Framework.",
|
| 29 |
+
"keywords": [
|
| 30 |
+
"Euclid",
|
| 31 |
+
"Elements",
|
| 32 |
+
"Book III",
|
| 33 |
+
"circles",
|
| 34 |
+
"chords",
|
| 35 |
+
"tangents"
|
| 36 |
+
]
|
| 37 |
+
},
|
| 38 |
+
"sources": [
|
| 39 |
+
{
|
| 40 |
+
"id": "joyce",
|
| 41 |
+
"type": "digital",
|
| 42 |
+
"authors": "Joyce, David E.",
|
| 43 |
+
"title": "Euclid's Elements, Book III",
|
| 44 |
+
"year": "1996",
|
| 45 |
+
"url": "https://mathcs.clarku.edu/~djoyce/java/elements/bookIII/bookIII.html",
|
| 46 |
+
"notes": "Clark University"
|
| 47 |
+
}
|
| 48 |
+
],
|
| 49 |
+
"nodes": [
|
| 50 |
+
{
|
| 51 |
+
"id": "BookI",
|
| 52 |
+
"type": "foundation",
|
| 53 |
+
"label": "Book I — Fundamentals of plane geometry",
|
| 54 |
+
"shortLabel": "Book I",
|
| 55 |
+
"short": "Foundation",
|
| 56 |
+
"book": 1,
|
| 57 |
+
"colorClass": "foundation"
|
| 58 |
+
},
|
| 59 |
+
{
|
| 60 |
+
"id": "PropII5",
|
| 61 |
+
"type": "foundation",
|
| 62 |
+
"label": "Prop. II.5 — Rectangle + square = square on half",
|
| 63 |
+
"shortLabel": "Prop. II.5",
|
| 64 |
+
"short": "From Book II",
|
| 65 |
+
"book": 2,
|
| 66 |
+
"colorClass": "foundation"
|
| 67 |
+
},
|
| 68 |
+
{
|
| 69 |
+
"id": "Def1",
|
| 70 |
+
"type": "definition",
|
| 71 |
+
"label": "Equal circles are those with equal radii",
|
| 72 |
+
"shortLabel": "Def. III.1",
|
| 73 |
+
"short": "Equal circles",
|
| 74 |
+
"book": 3,
|
| 75 |
+
"number": 1,
|
| 76 |
+
"colorClass": "definition"
|
| 77 |
+
},
|
| 78 |
+
{
|
| 79 |
+
"id": "Def2",
|
| 80 |
+
"type": "definition",
|
| 81 |
+
"label": "A straight line touches a circle if it meets but does not cut it",
|
| 82 |
+
"shortLabel": "Def. III.2",
|
| 83 |
+
"short": "Tangent",
|
| 84 |
+
"book": 3,
|
| 85 |
+
"number": 2,
|
| 86 |
+
"colorClass": "definition"
|
| 87 |
+
},
|
| 88 |
+
{
|
| 89 |
+
"id": "Def3",
|
| 90 |
+
"type": "definition",
|
| 91 |
+
"label": "Circles touch one another if they meet but do not cut",
|
| 92 |
+
"shortLabel": "Def. III.3",
|
| 93 |
+
"short": "Circles touching",
|
| 94 |
+
"book": 3,
|
| 95 |
+
"number": 3,
|
| 96 |
+
"colorClass": "definition"
|
| 97 |
+
},
|
| 98 |
+
{
|
| 99 |
+
"id": "Def4",
|
| 100 |
+
"type": "definition",
|
| 101 |
+
"label": "Lines equally distant from center when perpendiculars from center equal",
|
| 102 |
+
"shortLabel": "Def. III.4",
|
| 103 |
+
"short": "Equally distant from center",
|
| 104 |
+
"book": 3,
|
| 105 |
+
"number": 4,
|
| 106 |
+
"colorClass": "definition"
|
| 107 |
+
},
|
| 108 |
+
{
|
| 109 |
+
"id": "Def5",
|
| 110 |
+
"type": "definition",
|
| 111 |
+
"label": "Greater distance when greater perpendicular falls",
|
| 112 |
+
"shortLabel": "Def. III.5",
|
| 113 |
+
"short": "Greater distance",
|
| 114 |
+
"book": 3,
|
| 115 |
+
"number": 5,
|
| 116 |
+
"colorClass": "definition"
|
| 117 |
+
},
|
| 118 |
+
{
|
| 119 |
+
"id": "Def6",
|
| 120 |
+
"type": "definition",
|
| 121 |
+
"label": "Segment of circle: figure contained by straight line and circumference",
|
| 122 |
+
"shortLabel": "Def. III.6",
|
| 123 |
+
"short": "Segment of circle",
|
| 124 |
+
"book": 3,
|
| 125 |
+
"number": 6,
|
| 126 |
+
"colorClass": "definition"
|
| 127 |
+
},
|
| 128 |
+
{
|
| 129 |
+
"id": "Def7",
|
| 130 |
+
"type": "definition",
|
| 131 |
+
"label": "Angle of segment: contained by straight line and circumference",
|
| 132 |
+
"shortLabel": "Def. III.7",
|
| 133 |
+
"short": "Angle of segment",
|
| 134 |
+
"book": 3,
|
| 135 |
+
"number": 7,
|
| 136 |
+
"colorClass": "definition"
|
| 137 |
+
},
|
| 138 |
+
{
|
| 139 |
+
"id": "Def8",
|
| 140 |
+
"type": "definition",
|
| 141 |
+
"label": "Angle in segment: contained by straight lines joining circumference",
|
| 142 |
+
"shortLabel": "Def. III.8",
|
| 143 |
+
"short": "Angle in segment",
|
| 144 |
+
"book": 3,
|
| 145 |
+
"number": 8,
|
| 146 |
+
"colorClass": "definition"
|
| 147 |
+
},
|
| 148 |
+
{
|
| 149 |
+
"id": "Def9",
|
| 150 |
+
"type": "definition",
|
| 151 |
+
"label": "Angle stands on circumference when lines cut off that circumference",
|
| 152 |
+
"shortLabel": "Def. III.9",
|
| 153 |
+
"short": "Angle stands on circumference",
|
| 154 |
+
"book": 3,
|
| 155 |
+
"number": 9,
|
| 156 |
+
"colorClass": "definition"
|
| 157 |
+
},
|
| 158 |
+
{
|
| 159 |
+
"id": "Def10",
|
| 160 |
+
"type": "definition",
|
| 161 |
+
"label": "Sector: figure contained by two radii and circumference between them",
|
| 162 |
+
"shortLabel": "Def. III.10",
|
| 163 |
+
"short": "Sector",
|
| 164 |
+
"book": 3,
|
| 165 |
+
"number": 10,
|
| 166 |
+
"colorClass": "definition"
|
| 167 |
+
},
|
| 168 |
+
{
|
| 169 |
+
"id": "Def11",
|
| 170 |
+
"type": "definition",
|
| 171 |
+
"label": "Similar segments are those which admit equal angles",
|
| 172 |
+
"shortLabel": "Def. III.11",
|
| 173 |
+
"short": "Similar segments",
|
| 174 |
+
"book": 3,
|
| 175 |
+
"number": 11,
|
| 176 |
+
"colorClass": "definition"
|
| 177 |
+
},
|
| 178 |
+
{
|
| 179 |
+
"id": "Prop1",
|
| 180 |
+
"type": "proposition",
|
| 181 |
+
"label": "To find the center of a given circle",
|
| 182 |
+
"shortLabel": "Prop. III.1",
|
| 183 |
+
"short": "Find center of circle",
|
| 184 |
+
"book": 3,
|
| 185 |
+
"number": 1,
|
| 186 |
+
"colorClass": "proposition"
|
| 187 |
+
},
|
| 188 |
+
{
|
| 189 |
+
"id": "Prop2",
|
| 190 |
+
"type": "proposition",
|
| 191 |
+
"label": "Straight line joining two points on circumference falls within circle",
|
| 192 |
+
"shortLabel": "Prop. III.2",
|
| 193 |
+
"short": "Chord falls within circle",
|
| 194 |
+
"book": 3,
|
| 195 |
+
"number": 2,
|
| 196 |
+
"colorClass": "proposition"
|
| 197 |
+
},
|
| 198 |
+
{
|
| 199 |
+
"id": "Prop3",
|
| 200 |
+
"type": "proposition",
|
| 201 |
+
"label": "If diameter bisects chord not through center, it cuts at right angles",
|
| 202 |
+
"shortLabel": "Prop. III.3",
|
| 203 |
+
"short": "Diameter bisects chord at right angles",
|
| 204 |
+
"book": 3,
|
| 205 |
+
"number": 3,
|
| 206 |
+
"colorClass": "proposition"
|
| 207 |
+
},
|
| 208 |
+
{
|
| 209 |
+
"id": "Prop4",
|
| 210 |
+
"type": "proposition",
|
| 211 |
+
"label": "Two non-diameters cutting one another do not bisect",
|
| 212 |
+
"shortLabel": "Prop. III.4",
|
| 213 |
+
"short": "Non-diameters do not bisect",
|
| 214 |
+
"book": 3,
|
| 215 |
+
"number": 4,
|
| 216 |
+
"colorClass": "proposition"
|
| 217 |
+
},
|
| 218 |
+
{
|
| 219 |
+
"id": "Prop5",
|
| 220 |
+
"type": "proposition",
|
| 221 |
+
"label": "If two circles cut one another, they do not have same center",
|
| 222 |
+
"shortLabel": "Prop. III.5",
|
| 223 |
+
"short": "Cutting circles do not share center",
|
| 224 |
+
"book": 3,
|
| 225 |
+
"number": 5,
|
| 226 |
+
"colorClass": "proposition"
|
| 227 |
+
},
|
| 228 |
+
{
|
| 229 |
+
"id": "Prop6",
|
| 230 |
+
"type": "proposition",
|
| 231 |
+
"label": "If two circles touch, they do not have same center",
|
| 232 |
+
"shortLabel": "Prop. III.6",
|
| 233 |
+
"short": "Touching circles do not share center",
|
| 234 |
+
"book": 3,
|
| 235 |
+
"number": 6,
|
| 236 |
+
"colorClass": "proposition"
|
| 237 |
+
},
|
| 238 |
+
{
|
| 239 |
+
"id": "Prop7",
|
| 240 |
+
"type": "proposition",
|
| 241 |
+
"label": "From point on diameter: greatest through center, least is remainder",
|
| 242 |
+
"shortLabel": "Prop. III.7",
|
| 243 |
+
"short": "Greatest/shortest from point on diameter",
|
| 244 |
+
"book": 3,
|
| 245 |
+
"number": 7,
|
| 246 |
+
"colorClass": "proposition"
|
| 247 |
+
},
|
| 248 |
+
{
|
| 249 |
+
"id": "Prop8",
|
| 250 |
+
"type": "proposition",
|
| 251 |
+
"label": "From point outside: through center greatest; between point and diameter least",
|
| 252 |
+
"shortLabel": "Prop. III.8",
|
| 253 |
+
"short": "Lines from point outside circle",
|
| 254 |
+
"book": 3,
|
| 255 |
+
"number": 8,
|
| 256 |
+
"colorClass": "proposition"
|
| 257 |
+
},
|
| 258 |
+
{
|
| 259 |
+
"id": "Prop9",
|
| 260 |
+
"type": "proposition",
|
| 261 |
+
"label": "If more than two equal lines fall from point on circle, point is center",
|
| 262 |
+
"shortLabel": "Prop. III.9",
|
| 263 |
+
"short": "Three equal lines imply center",
|
| 264 |
+
"book": 3,
|
| 265 |
+
"number": 9,
|
| 266 |
+
"colorClass": "proposition"
|
| 267 |
+
},
|
| 268 |
+
{
|
| 269 |
+
"id": "Prop10",
|
| 270 |
+
"type": "proposition",
|
| 271 |
+
"label": "A circle does not cut another at more than two points",
|
| 272 |
+
"shortLabel": "Prop. III.10",
|
| 273 |
+
"short": "Circles cut at most two points",
|
| 274 |
+
"book": 3,
|
| 275 |
+
"number": 10,
|
| 276 |
+
"colorClass": "proposition"
|
| 277 |
+
},
|
| 278 |
+
{
|
| 279 |
+
"id": "Prop11",
|
| 280 |
+
"type": "proposition",
|
| 281 |
+
"label": "Line joining centers of internally touching circles passes through contact",
|
| 282 |
+
"shortLabel": "Prop. III.11",
|
| 283 |
+
"short": "Internally touching circles",
|
| 284 |
+
"book": 3,
|
| 285 |
+
"number": 11,
|
| 286 |
+
"colorClass": "proposition"
|
| 287 |
+
},
|
| 288 |
+
{
|
| 289 |
+
"id": "Prop12",
|
| 290 |
+
"type": "proposition",
|
| 291 |
+
"label": "Line joining centers of externally touching circles passes through contact",
|
| 292 |
+
"shortLabel": "Prop. III.12",
|
| 293 |
+
"short": "Externally touching circles",
|
| 294 |
+
"book": 3,
|
| 295 |
+
"number": 12,
|
| 296 |
+
"colorClass": "proposition"
|
| 297 |
+
},
|
| 298 |
+
{
|
| 299 |
+
"id": "Prop13",
|
| 300 |
+
"type": "proposition",
|
| 301 |
+
"label": "Circle does not touch another at more than one point",
|
| 302 |
+
"shortLabel": "Prop. III.13",
|
| 303 |
+
"short": "Circles touch at most one point",
|
| 304 |
+
"book": 3,
|
| 305 |
+
"number": 13,
|
| 306 |
+
"colorClass": "proposition"
|
| 307 |
+
},
|
| 308 |
+
{
|
| 309 |
+
"id": "Prop14",
|
| 310 |
+
"type": "proposition",
|
| 311 |
+
"label": "Equal chords equally distant from center, and conversely",
|
| 312 |
+
"shortLabel": "Prop. III.14",
|
| 313 |
+
"short": "Equal chords equally distant",
|
| 314 |
+
"book": 3,
|
| 315 |
+
"number": 14,
|
| 316 |
+
"colorClass": "proposition"
|
| 317 |
+
},
|
| 318 |
+
{
|
| 319 |
+
"id": "Prop15",
|
| 320 |
+
"type": "proposition",
|
| 321 |
+
"label": "Diameter greatest; nearer to center greater than more remote",
|
| 322 |
+
"shortLabel": "Prop. III.15",
|
| 323 |
+
"short": "Diameter greatest",
|
| 324 |
+
"book": 3,
|
| 325 |
+
"number": 15,
|
| 326 |
+
"colorClass": "proposition"
|
| 327 |
+
},
|
| 328 |
+
{
|
| 329 |
+
"id": "Prop16",
|
| 330 |
+
"type": "proposition",
|
| 331 |
+
"label": "Perpendicular at end of diameter falls outside; horn angle",
|
| 332 |
+
"shortLabel": "Prop. III.16",
|
| 333 |
+
"short": "Tangent at end of diameter",
|
| 334 |
+
"book": 3,
|
| 335 |
+
"number": 16,
|
| 336 |
+
"colorClass": "proposition"
|
| 337 |
+
},
|
| 338 |
+
{
|
| 339 |
+
"id": "Prop17",
|
| 340 |
+
"type": "proposition",
|
| 341 |
+
"label": "From given point to draw straight line touching given circle",
|
| 342 |
+
"shortLabel": "Prop. III.17",
|
| 343 |
+
"short": "Draw tangent from point",
|
| 344 |
+
"book": 3,
|
| 345 |
+
"number": 17,
|
| 346 |
+
"colorClass": "proposition"
|
| 347 |
+
},
|
| 348 |
+
{
|
| 349 |
+
"id": "Prop18",
|
| 350 |
+
"type": "proposition",
|
| 351 |
+
"label": "Radius to point of contact perpendicular to tangent",
|
| 352 |
+
"shortLabel": "Prop. III.18",
|
| 353 |
+
"short": "Radius to tangent perpendicular",
|
| 354 |
+
"book": 3,
|
| 355 |
+
"number": 18,
|
| 356 |
+
"colorClass": "proposition"
|
| 357 |
+
},
|
| 358 |
+
{
|
| 359 |
+
"id": "Prop19",
|
| 360 |
+
"type": "proposition",
|
| 361 |
+
"label": "Perpendicular from contact to tangent passes through center",
|
| 362 |
+
"shortLabel": "Prop. III.19",
|
| 363 |
+
"short": "Perpendicular from contact to center",
|
| 364 |
+
"book": 3,
|
| 365 |
+
"number": 19,
|
| 366 |
+
"colorClass": "proposition"
|
| 367 |
+
},
|
| 368 |
+
{
|
| 369 |
+
"id": "Prop20",
|
| 370 |
+
"type": "proposition",
|
| 371 |
+
"label": "Angle at center double angle at circumference on same base",
|
| 372 |
+
"shortLabel": "Prop. III.20",
|
| 373 |
+
"short": "Angle at center double angle at circumference",
|
| 374 |
+
"book": 3,
|
| 375 |
+
"number": 20,
|
| 376 |
+
"colorClass": "proposition"
|
| 377 |
+
},
|
| 378 |
+
{
|
| 379 |
+
"id": "Prop21",
|
| 380 |
+
"type": "proposition",
|
| 381 |
+
"label": "In a circle angles in same segment equal one another",
|
| 382 |
+
"shortLabel": "Prop. III.21",
|
| 383 |
+
"short": "Angles in same segment equal",
|
| 384 |
+
"book": 3,
|
| 385 |
+
"number": 21,
|
| 386 |
+
"colorClass": "proposition"
|
| 387 |
+
},
|
| 388 |
+
{
|
| 389 |
+
"id": "Prop22",
|
| 390 |
+
"type": "proposition",
|
| 391 |
+
"label": "Sum of opposite angles of cyclic quadrilateral equals two right angles",
|
| 392 |
+
"shortLabel": "Prop. III.22",
|
| 393 |
+
"short": "Opposite angles of cyclic quadrilateral",
|
| 394 |
+
"book": 3,
|
| 395 |
+
"number": 22,
|
| 396 |
+
"colorClass": "proposition"
|
| 397 |
+
},
|
| 398 |
+
{
|
| 399 |
+
"id": "Prop23",
|
| 400 |
+
"type": "proposition",
|
| 401 |
+
"label": "On same line cannot construct two similar unequal segments on same side",
|
| 402 |
+
"shortLabel": "Prop. III.23",
|
| 403 |
+
"short": "Same line, two similar unequal segments",
|
| 404 |
+
"book": 3,
|
| 405 |
+
"number": 23,
|
| 406 |
+
"colorClass": "proposition"
|
| 407 |
+
},
|
| 408 |
+
{
|
| 409 |
+
"id": "Prop24",
|
| 410 |
+
"type": "proposition",
|
| 411 |
+
"label": "Similar segments on equal straight lines equal one another",
|
| 412 |
+
"shortLabel": "Prop. III.24",
|
| 413 |
+
"short": "Similar segments on equal lines equal",
|
| 414 |
+
"book": 3,
|
| 415 |
+
"number": 24,
|
| 416 |
+
"colorClass": "proposition"
|
| 417 |
+
},
|
| 418 |
+
{
|
| 419 |
+
"id": "Prop25",
|
| 420 |
+
"type": "proposition",
|
| 421 |
+
"label": "Given segment of circle, describe complete circle",
|
| 422 |
+
"shortLabel": "Prop. III.25",
|
| 423 |
+
"short": "Complete circle from segment",
|
| 424 |
+
"book": 3,
|
| 425 |
+
"number": 25,
|
| 426 |
+
"colorClass": "proposition"
|
| 427 |
+
},
|
| 428 |
+
{
|
| 429 |
+
"id": "Prop26",
|
| 430 |
+
"type": "proposition",
|
| 431 |
+
"label": "In equal circles equal angles stand on equal circumferences",
|
| 432 |
+
"shortLabel": "Prop. III.26",
|
| 433 |
+
"short": "Equal angles stand on equal arcs",
|
| 434 |
+
"book": 3,
|
| 435 |
+
"number": 26,
|
| 436 |
+
"colorClass": "proposition"
|
| 437 |
+
},
|
| 438 |
+
{
|
| 439 |
+
"id": "Prop27",
|
| 440 |
+
"type": "proposition",
|
| 441 |
+
"label": "In equal circles angles on equal circumferences equal one another",
|
| 442 |
+
"shortLabel": "Prop. III.27",
|
| 443 |
+
"short": "Equal arcs imply equal angles",
|
| 444 |
+
"book": 3,
|
| 445 |
+
"number": 27,
|
| 446 |
+
"colorClass": "proposition"
|
| 447 |
+
},
|
| 448 |
+
{
|
| 449 |
+
"id": "Prop28",
|
| 450 |
+
"type": "proposition",
|
| 451 |
+
"label": "In equal circles equal chords cut off equal circumferences",
|
| 452 |
+
"shortLabel": "Prop. III.28",
|
| 453 |
+
"short": "Equal chords cut off equal arcs",
|
| 454 |
+
"book": 3,
|
| 455 |
+
"number": 28,
|
| 456 |
+
"colorClass": "proposition"
|
| 457 |
+
},
|
| 458 |
+
{
|
| 459 |
+
"id": "Prop29",
|
| 460 |
+
"type": "proposition",
|
| 461 |
+
"label": "In equal circles chords cutting equal circumferences are equal",
|
| 462 |
+
"shortLabel": "Prop. III.29",
|
| 463 |
+
"short": "Equal arcs imply equal chords",
|
| 464 |
+
"book": 3,
|
| 465 |
+
"number": 29,
|
| 466 |
+
"colorClass": "proposition"
|
| 467 |
+
},
|
| 468 |
+
{
|
| 469 |
+
"id": "Prop30",
|
| 470 |
+
"type": "proposition",
|
| 471 |
+
"label": "To bisect a given circumference",
|
| 472 |
+
"shortLabel": "Prop. III.30",
|
| 473 |
+
"short": "Bisect given circumference",
|
| 474 |
+
"book": 3,
|
| 475 |
+
"number": 30,
|
| 476 |
+
"colorClass": "proposition"
|
| 477 |
+
},
|
| 478 |
+
{
|
| 479 |
+
"id": "Prop31",
|
| 480 |
+
"type": "proposition",
|
| 481 |
+
"label": "Angle in semicircle right; in greater segment less; in less greater",
|
| 482 |
+
"shortLabel": "Prop. III.31",
|
| 483 |
+
"short": "Angle in semicircle is right",
|
| 484 |
+
"book": 3,
|
| 485 |
+
"number": 31,
|
| 486 |
+
"colorClass": "proposition"
|
| 487 |
+
},
|
| 488 |
+
{
|
| 489 |
+
"id": "Prop32",
|
| 490 |
+
"type": "proposition",
|
| 491 |
+
"label": "Angle with tangent equals angle in alternate segment",
|
| 492 |
+
"shortLabel": "Prop. III.32",
|
| 493 |
+
"short": "Tangent-chord angle equals alternate segment",
|
| 494 |
+
"book": 3,
|
| 495 |
+
"number": 32,
|
| 496 |
+
"colorClass": "proposition"
|
| 497 |
+
},
|
| 498 |
+
{
|
| 499 |
+
"id": "Prop33",
|
| 500 |
+
"type": "proposition",
|
| 501 |
+
"label": "On given line describe segment admitting angle equal to given",
|
| 502 |
+
"shortLabel": "Prop. III.33",
|
| 503 |
+
"short": "Segment admitting given angle",
|
| 504 |
+
"book": 3,
|
| 505 |
+
"number": 33,
|
| 506 |
+
"colorClass": "proposition"
|
| 507 |
+
},
|
| 508 |
+
{
|
| 509 |
+
"id": "Prop34",
|
| 510 |
+
"type": "proposition",
|
| 511 |
+
"label": "From given circle cut off segment admitting given angle",
|
| 512 |
+
"shortLabel": "Prop. III.34",
|
| 513 |
+
"short": "Cut off segment admitting angle",
|
| 514 |
+
"book": 3,
|
| 515 |
+
"number": 34,
|
| 516 |
+
"colorClass": "proposition"
|
| 517 |
+
},
|
| 518 |
+
{
|
| 519 |
+
"id": "Prop35",
|
| 520 |
+
"type": "proposition",
|
| 521 |
+
"label": "If chords cut one another, rectangle by segments of one equals other",
|
| 522 |
+
"shortLabel": "Prop. III.35",
|
| 523 |
+
"short": "Rectangle from chord segments equal",
|
| 524 |
+
"book": 3,
|
| 525 |
+
"number": 35,
|
| 526 |
+
"colorClass": "proposition"
|
| 527 |
+
},
|
| 528 |
+
{
|
| 529 |
+
"id": "Prop36",
|
| 530 |
+
"type": "proposition",
|
| 531 |
+
"label": "From point outside: tangent squared = secant × external part",
|
| 532 |
+
"shortLabel": "Prop. III.36",
|
| 533 |
+
"short": "Tangent squared = secant × external",
|
| 534 |
+
"book": 3,
|
| 535 |
+
"number": 36,
|
| 536 |
+
"colorClass": "proposition"
|
| 537 |
+
},
|
| 538 |
+
{
|
| 539 |
+
"id": "Prop37",
|
| 540 |
+
"type": "proposition",
|
| 541 |
+
"label": "If rectangle equals square on line, that line touches circle",
|
| 542 |
+
"shortLabel": "Prop. III.37",
|
| 543 |
+
"short": "Converse: tangent if rectangle = square",
|
| 544 |
+
"book": 3,
|
| 545 |
+
"number": 37,
|
| 546 |
+
"colorClass": "proposition"
|
| 547 |
+
}
|
| 548 |
+
],
|
| 549 |
+
"edges": [
|
| 550 |
+
{
|
| 551 |
+
"from": "BookI",
|
| 552 |
+
"to": "Def1"
|
| 553 |
+
},
|
| 554 |
+
{
|
| 555 |
+
"from": "BookI",
|
| 556 |
+
"to": "Def2"
|
| 557 |
+
},
|
| 558 |
+
{
|
| 559 |
+
"from": "BookI",
|
| 560 |
+
"to": "Def3"
|
| 561 |
+
},
|
| 562 |
+
{
|
| 563 |
+
"from": "BookI",
|
| 564 |
+
"to": "Def4"
|
| 565 |
+
},
|
| 566 |
+
{
|
| 567 |
+
"from": "BookI",
|
| 568 |
+
"to": "Def5"
|
| 569 |
+
},
|
| 570 |
+
{
|
| 571 |
+
"from": "BookI",
|
| 572 |
+
"to": "Def6"
|
| 573 |
+
},
|
| 574 |
+
{
|
| 575 |
+
"from": "BookI",
|
| 576 |
+
"to": "Def7"
|
| 577 |
+
},
|
| 578 |
+
{
|
| 579 |
+
"from": "BookI",
|
| 580 |
+
"to": "Def8"
|
| 581 |
+
},
|
| 582 |
+
{
|
| 583 |
+
"from": "BookI",
|
| 584 |
+
"to": "Def9"
|
| 585 |
+
},
|
| 586 |
+
{
|
| 587 |
+
"from": "BookI",
|
| 588 |
+
"to": "Def10"
|
| 589 |
+
},
|
| 590 |
+
{
|
| 591 |
+
"from": "BookI",
|
| 592 |
+
"to": "Def11"
|
| 593 |
+
},
|
| 594 |
+
{
|
| 595 |
+
"from": "BookI",
|
| 596 |
+
"to": "Prop1"
|
| 597 |
+
},
|
| 598 |
+
{
|
| 599 |
+
"from": "BookI",
|
| 600 |
+
"to": "Prop2"
|
| 601 |
+
},
|
| 602 |
+
{
|
| 603 |
+
"from": "Prop1",
|
| 604 |
+
"to": "Prop2"
|
| 605 |
+
},
|
| 606 |
+
{
|
| 607 |
+
"from": "BookI",
|
| 608 |
+
"to": "Prop3"
|
| 609 |
+
},
|
| 610 |
+
{
|
| 611 |
+
"from": "Prop1",
|
| 612 |
+
"to": "Prop3"
|
| 613 |
+
},
|
| 614 |
+
{
|
| 615 |
+
"from": "BookI",
|
| 616 |
+
"to": "Prop4"
|
| 617 |
+
},
|
| 618 |
+
{
|
| 619 |
+
"from": "Prop3",
|
| 620 |
+
"to": "Prop4"
|
| 621 |
+
},
|
| 622 |
+
{
|
| 623 |
+
"from": "BookI",
|
| 624 |
+
"to": "Prop5"
|
| 625 |
+
},
|
| 626 |
+
{
|
| 627 |
+
"from": "BookI",
|
| 628 |
+
"to": "Prop6"
|
| 629 |
+
},
|
| 630 |
+
{
|
| 631 |
+
"from": "BookI",
|
| 632 |
+
"to": "Prop7"
|
| 633 |
+
},
|
| 634 |
+
{
|
| 635 |
+
"from": "BookI",
|
| 636 |
+
"to": "Prop8"
|
| 637 |
+
},
|
| 638 |
+
{
|
| 639 |
+
"from": "BookI",
|
| 640 |
+
"to": "Prop9"
|
| 641 |
+
},
|
| 642 |
+
{
|
| 643 |
+
"from": "Prop1",
|
| 644 |
+
"to": "Prop9"
|
| 645 |
+
},
|
| 646 |
+
{
|
| 647 |
+
"from": "BookI",
|
| 648 |
+
"to": "Prop10"
|
| 649 |
+
},
|
| 650 |
+
{
|
| 651 |
+
"from": "Prop1",
|
| 652 |
+
"to": "Prop10"
|
| 653 |
+
},
|
| 654 |
+
{
|
| 655 |
+
"from": "BookI",
|
| 656 |
+
"to": "Prop11"
|
| 657 |
+
},
|
| 658 |
+
{
|
| 659 |
+
"from": "BookI",
|
| 660 |
+
"to": "Prop12"
|
| 661 |
+
},
|
| 662 |
+
{
|
| 663 |
+
"from": "BookI",
|
| 664 |
+
"to": "Prop13"
|
| 665 |
+
},
|
| 666 |
+
{
|
| 667 |
+
"from": "BookI",
|
| 668 |
+
"to": "Prop14"
|
| 669 |
+
},
|
| 670 |
+
{
|
| 671 |
+
"from": "Prop3",
|
| 672 |
+
"to": "Prop14"
|
| 673 |
+
},
|
| 674 |
+
{
|
| 675 |
+
"from": "BookI",
|
| 676 |
+
"to": "Prop15"
|
| 677 |
+
},
|
| 678 |
+
{
|
| 679 |
+
"from": "Prop3",
|
| 680 |
+
"to": "Prop15"
|
| 681 |
+
},
|
| 682 |
+
{
|
| 683 |
+
"from": "BookI",
|
| 684 |
+
"to": "Prop16"
|
| 685 |
+
},
|
| 686 |
+
{
|
| 687 |
+
"from": "BookI",
|
| 688 |
+
"to": "Prop17"
|
| 689 |
+
},
|
| 690 |
+
{
|
| 691 |
+
"from": "Prop16",
|
| 692 |
+
"to": "Prop17"
|
| 693 |
+
},
|
| 694 |
+
{
|
| 695 |
+
"from": "BookI",
|
| 696 |
+
"to": "Prop18"
|
| 697 |
+
},
|
| 698 |
+
{
|
| 699 |
+
"from": "Prop1",
|
| 700 |
+
"to": "Prop18"
|
| 701 |
+
},
|
| 702 |
+
{
|
| 703 |
+
"from": "BookI",
|
| 704 |
+
"to": "Prop19"
|
| 705 |
+
},
|
| 706 |
+
{
|
| 707 |
+
"from": "Prop18",
|
| 708 |
+
"to": "Prop19"
|
| 709 |
+
},
|
| 710 |
+
{
|
| 711 |
+
"from": "BookI",
|
| 712 |
+
"to": "Prop20"
|
| 713 |
+
},
|
| 714 |
+
{
|
| 715 |
+
"from": "Prop1",
|
| 716 |
+
"to": "Prop20"
|
| 717 |
+
},
|
| 718 |
+
{
|
| 719 |
+
"from": "BookI",
|
| 720 |
+
"to": "Prop21"
|
| 721 |
+
},
|
| 722 |
+
{
|
| 723 |
+
"from": "Prop20",
|
| 724 |
+
"to": "Prop21"
|
| 725 |
+
},
|
| 726 |
+
{
|
| 727 |
+
"from": "BookI",
|
| 728 |
+
"to": "Prop22"
|
| 729 |
+
},
|
| 730 |
+
{
|
| 731 |
+
"from": "Prop21",
|
| 732 |
+
"to": "Prop22"
|
| 733 |
+
},
|
| 734 |
+
{
|
| 735 |
+
"from": "BookI",
|
| 736 |
+
"to": "Prop23"
|
| 737 |
+
},
|
| 738 |
+
{
|
| 739 |
+
"from": "BookI",
|
| 740 |
+
"to": "Prop24"
|
| 741 |
+
},
|
| 742 |
+
{
|
| 743 |
+
"from": "Prop23",
|
| 744 |
+
"to": "Prop24"
|
| 745 |
+
},
|
| 746 |
+
{
|
| 747 |
+
"from": "BookI",
|
| 748 |
+
"to": "Prop25"
|
| 749 |
+
},
|
| 750 |
+
{
|
| 751 |
+
"from": "BookI",
|
| 752 |
+
"to": "Prop26"
|
| 753 |
+
},
|
| 754 |
+
{
|
| 755 |
+
"from": "BookI",
|
| 756 |
+
"to": "Prop27"
|
| 757 |
+
},
|
| 758 |
+
{
|
| 759 |
+
"from": "Prop26",
|
| 760 |
+
"to": "Prop27"
|
| 761 |
+
},
|
| 762 |
+
{
|
| 763 |
+
"from": "BookI",
|
| 764 |
+
"to": "Prop28"
|
| 765 |
+
},
|
| 766 |
+
{
|
| 767 |
+
"from": "Prop27",
|
| 768 |
+
"to": "Prop28"
|
| 769 |
+
},
|
| 770 |
+
{
|
| 771 |
+
"from": "BookI",
|
| 772 |
+
"to": "Prop29"
|
| 773 |
+
},
|
| 774 |
+
{
|
| 775 |
+
"from": "Prop28",
|
| 776 |
+
"to": "Prop29"
|
| 777 |
+
},
|
| 778 |
+
{
|
| 779 |
+
"from": "BookI",
|
| 780 |
+
"to": "Prop30"
|
| 781 |
+
},
|
| 782 |
+
{
|
| 783 |
+
"from": "BookI",
|
| 784 |
+
"to": "Prop31"
|
| 785 |
+
},
|
| 786 |
+
{
|
| 787 |
+
"from": "Prop20",
|
| 788 |
+
"to": "Prop31"
|
| 789 |
+
},
|
| 790 |
+
{
|
| 791 |
+
"from": "BookI",
|
| 792 |
+
"to": "Prop32"
|
| 793 |
+
},
|
| 794 |
+
{
|
| 795 |
+
"from": "Prop31",
|
| 796 |
+
"to": "Prop32"
|
| 797 |
+
},
|
| 798 |
+
{
|
| 799 |
+
"from": "BookI",
|
| 800 |
+
"to": "Prop33"
|
| 801 |
+
},
|
| 802 |
+
{
|
| 803 |
+
"from": "Prop16",
|
| 804 |
+
"to": "Prop33"
|
| 805 |
+
},
|
| 806 |
+
{
|
| 807 |
+
"from": "Prop32",
|
| 808 |
+
"to": "Prop33"
|
| 809 |
+
},
|
| 810 |
+
{
|
| 811 |
+
"from": "BookI",
|
| 812 |
+
"to": "Prop34"
|
| 813 |
+
},
|
| 814 |
+
{
|
| 815 |
+
"from": "Prop32",
|
| 816 |
+
"to": "Prop34"
|
| 817 |
+
},
|
| 818 |
+
{
|
| 819 |
+
"from": "BookI",
|
| 820 |
+
"to": "Prop35"
|
| 821 |
+
},
|
| 822 |
+
{
|
| 823 |
+
"from": "Prop1",
|
| 824 |
+
"to": "Prop35"
|
| 825 |
+
},
|
| 826 |
+
{
|
| 827 |
+
"from": "Prop3",
|
| 828 |
+
"to": "Prop35"
|
| 829 |
+
},
|
| 830 |
+
{
|
| 831 |
+
"from": "PropII5",
|
| 832 |
+
"to": "Prop35"
|
| 833 |
+
},
|
| 834 |
+
{
|
| 835 |
+
"from": "BookI",
|
| 836 |
+
"to": "Prop36"
|
| 837 |
+
},
|
| 838 |
+
{
|
| 839 |
+
"from": "Prop1",
|
| 840 |
+
"to": "Prop36"
|
| 841 |
+
},
|
| 842 |
+
{
|
| 843 |
+
"from": "Prop18",
|
| 844 |
+
"to": "Prop36"
|
| 845 |
+
},
|
| 846 |
+
{
|
| 847 |
+
"from": "Prop35",
|
| 848 |
+
"to": "Prop36"
|
| 849 |
+
},
|
| 850 |
+
{
|
| 851 |
+
"from": "BookI",
|
| 852 |
+
"to": "Prop37"
|
| 853 |
+
},
|
| 854 |
+
{
|
| 855 |
+
"from": "Prop1",
|
| 856 |
+
"to": "Prop37"
|
| 857 |
+
},
|
| 858 |
+
{
|
| 859 |
+
"from": "Prop16",
|
| 860 |
+
"to": "Prop37"
|
| 861 |
+
},
|
| 862 |
+
{
|
| 863 |
+
"from": "Prop32",
|
| 864 |
+
"to": "Prop37"
|
| 865 |
+
},
|
| 866 |
+
{
|
| 867 |
+
"from": "Prop36",
|
| 868 |
+
"to": "Prop37"
|
| 869 |
+
}
|
| 870 |
+
],
|
| 871 |
+
"colorScheme": {
|
| 872 |
+
"foundation": {
|
| 873 |
+
"fill": "#95a5a6",
|
| 874 |
+
"stroke": "#7f8c8d"
|
| 875 |
+
},
|
| 876 |
+
"definition": {
|
| 877 |
+
"fill": "#3498db",
|
| 878 |
+
"stroke": "#2980b9"
|
| 879 |
+
},
|
| 880 |
+
"proposition": {
|
| 881 |
+
"fill": "#1abc9c",
|
| 882 |
+
"stroke": "#16a085"
|
| 883 |
+
}
|
| 884 |
+
}
|
| 885 |
+
}
|
data/euclid-elements-book-iv.json
ADDED
|
@@ -0,0 +1,573 @@
|
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|
| 1 |
+
{
|
| 2 |
+
"schemaVersion": "1.0",
|
| 3 |
+
"discourse": {
|
| 4 |
+
"id": "euclid-elements-book-iv",
|
| 5 |
+
"name": "Euclid's Elements, Book IV",
|
| 6 |
+
"subject": "geometry",
|
| 7 |
+
"variant": "classical",
|
| 8 |
+
"description": "Inscribed and circumscribed figures: triangle, square, pentagon, hexagon, 15-gon. All depend on Books I and III. IV.10 uses II.11. Source: David E. Joyce.",
|
| 9 |
+
"structure": {
|
| 10 |
+
"books": 4,
|
| 11 |
+
"definitions": 7,
|
| 12 |
+
"propositions": 16,
|
| 13 |
+
"foundationTypes": [
|
| 14 |
+
"definition",
|
| 15 |
+
"foundation"
|
| 16 |
+
]
|
| 17 |
+
}
|
| 18 |
+
},
|
| 19 |
+
"metadata": {
|
| 20 |
+
"created": "2026-03-15",
|
| 21 |
+
"lastUpdated": "2026-03-15",
|
| 22 |
+
"version": "1.0.0",
|
| 23 |
+
"license": "CC BY 4.0",
|
| 24 |
+
"authors": [
|
| 25 |
+
"Welz, G."
|
| 26 |
+
],
|
| 27 |
+
"methodology": "Programming Framework",
|
| 28 |
+
"citation": "Welz, G. (2026). Euclid's Elements Book IV Dependency Graph. Programming Framework.",
|
| 29 |
+
"keywords": [
|
| 30 |
+
"Euclid",
|
| 31 |
+
"Elements",
|
| 32 |
+
"Book IV",
|
| 33 |
+
"inscribed",
|
| 34 |
+
"circumscribed",
|
| 35 |
+
"pentagon",
|
| 36 |
+
"hexagon"
|
| 37 |
+
]
|
| 38 |
+
},
|
| 39 |
+
"sources": [
|
| 40 |
+
{
|
| 41 |
+
"id": "joyce",
|
| 42 |
+
"type": "digital",
|
| 43 |
+
"authors": "Joyce, David E.",
|
| 44 |
+
"title": "Euclid's Elements, Book IV",
|
| 45 |
+
"year": "1996",
|
| 46 |
+
"url": "https://mathcs.clarku.edu/~djoyce/java/elements/bookIV/bookIV.html",
|
| 47 |
+
"notes": "Clark University; Logical structure"
|
| 48 |
+
}
|
| 49 |
+
],
|
| 50 |
+
"nodes": [
|
| 51 |
+
{
|
| 52 |
+
"id": "BookI",
|
| 53 |
+
"type": "foundation",
|
| 54 |
+
"label": "Book I — Fundamentals of plane geometry",
|
| 55 |
+
"shortLabel": "Book I",
|
| 56 |
+
"short": "Foundation",
|
| 57 |
+
"book": 1,
|
| 58 |
+
"colorClass": "foundation"
|
| 59 |
+
},
|
| 60 |
+
{
|
| 61 |
+
"id": "BookIII",
|
| 62 |
+
"type": "foundation",
|
| 63 |
+
"label": "Book III — Theory of circles",
|
| 64 |
+
"shortLabel": "Book III",
|
| 65 |
+
"short": "Foundation",
|
| 66 |
+
"book": 3,
|
| 67 |
+
"colorClass": "foundation"
|
| 68 |
+
},
|
| 69 |
+
{
|
| 70 |
+
"id": "PropII11",
|
| 71 |
+
"type": "foundation",
|
| 72 |
+
"label": "Prop. II.11 — Golden section",
|
| 73 |
+
"shortLabel": "Prop. II.11",
|
| 74 |
+
"short": "From Book II",
|
| 75 |
+
"book": 2,
|
| 76 |
+
"colorClass": "foundation"
|
| 77 |
+
},
|
| 78 |
+
{
|
| 79 |
+
"id": "Def1",
|
| 80 |
+
"type": "definition",
|
| 81 |
+
"label": "Rectilinear figure inscribed in circle when each vertex on circumference",
|
| 82 |
+
"shortLabel": "Def. IV.1",
|
| 83 |
+
"short": "Inscribe in circle",
|
| 84 |
+
"book": 4,
|
| 85 |
+
"number": 1,
|
| 86 |
+
"colorClass": "definition"
|
| 87 |
+
},
|
| 88 |
+
{
|
| 89 |
+
"id": "Def2",
|
| 90 |
+
"type": "definition",
|
| 91 |
+
"label": "Figure circumscribed about circle when each side touches circle",
|
| 92 |
+
"shortLabel": "Def. IV.2",
|
| 93 |
+
"short": "Circumscribe about circle",
|
| 94 |
+
"book": 4,
|
| 95 |
+
"number": 2,
|
| 96 |
+
"colorClass": "definition"
|
| 97 |
+
},
|
| 98 |
+
{
|
| 99 |
+
"id": "Def3",
|
| 100 |
+
"type": "definition",
|
| 101 |
+
"label": "Circle inscribed in figure when each side touches circle",
|
| 102 |
+
"shortLabel": "Def. IV.3",
|
| 103 |
+
"short": "Inscribe circle in figure",
|
| 104 |
+
"book": 4,
|
| 105 |
+
"number": 3,
|
| 106 |
+
"colorClass": "definition"
|
| 107 |
+
},
|
| 108 |
+
{
|
| 109 |
+
"id": "Def4",
|
| 110 |
+
"type": "definition",
|
| 111 |
+
"label": "Circle circumscribed about figure when each vertex on circumference",
|
| 112 |
+
"shortLabel": "Def. IV.4",
|
| 113 |
+
"short": "Circumscribe circle about figure",
|
| 114 |
+
"book": 4,
|
| 115 |
+
"number": 4,
|
| 116 |
+
"colorClass": "definition"
|
| 117 |
+
},
|
| 118 |
+
{
|
| 119 |
+
"id": "Def5",
|
| 120 |
+
"type": "definition",
|
| 121 |
+
"label": "Figure inscribed in figure when each vertex of inner on sides of outer",
|
| 122 |
+
"shortLabel": "Def. IV.5",
|
| 123 |
+
"short": "Inscribe in figure",
|
| 124 |
+
"book": 4,
|
| 125 |
+
"number": 5,
|
| 126 |
+
"colorClass": "definition"
|
| 127 |
+
},
|
| 128 |
+
{
|
| 129 |
+
"id": "Def6",
|
| 130 |
+
"type": "definition",
|
| 131 |
+
"label": "Figure circumscribed about figure when each side of outer touches inner",
|
| 132 |
+
"shortLabel": "Def. IV.6",
|
| 133 |
+
"short": "Circumscribe about figure",
|
| 134 |
+
"book": 4,
|
| 135 |
+
"number": 6,
|
| 136 |
+
"colorClass": "definition"
|
| 137 |
+
},
|
| 138 |
+
{
|
| 139 |
+
"id": "Def7",
|
| 140 |
+
"type": "definition",
|
| 141 |
+
"label": "Straight line inscribed in circle when its ends on circumference",
|
| 142 |
+
"shortLabel": "Def. IV.7",
|
| 143 |
+
"short": "Inscribe line in circle",
|
| 144 |
+
"book": 4,
|
| 145 |
+
"number": 7,
|
| 146 |
+
"colorClass": "definition"
|
| 147 |
+
},
|
| 148 |
+
{
|
| 149 |
+
"id": "Prop1",
|
| 150 |
+
"type": "proposition",
|
| 151 |
+
"label": "To fit into given circle a straight line equal to given, not greater than diameter",
|
| 152 |
+
"shortLabel": "Prop. IV.1",
|
| 153 |
+
"short": "Fit line in circle",
|
| 154 |
+
"book": 4,
|
| 155 |
+
"number": 1,
|
| 156 |
+
"colorClass": "proposition"
|
| 157 |
+
},
|
| 158 |
+
{
|
| 159 |
+
"id": "Prop2",
|
| 160 |
+
"type": "proposition",
|
| 161 |
+
"label": "To inscribe in given circle a triangle equiangular with given triangle",
|
| 162 |
+
"shortLabel": "Prop. IV.2",
|
| 163 |
+
"short": "Inscribe triangle in circle",
|
| 164 |
+
"book": 4,
|
| 165 |
+
"number": 2,
|
| 166 |
+
"colorClass": "proposition"
|
| 167 |
+
},
|
| 168 |
+
{
|
| 169 |
+
"id": "Prop3",
|
| 170 |
+
"type": "proposition",
|
| 171 |
+
"label": "To circumscribe about given circle a triangle equiangular with given",
|
| 172 |
+
"shortLabel": "Prop. IV.3",
|
| 173 |
+
"short": "Circumscribe triangle about circle",
|
| 174 |
+
"book": 4,
|
| 175 |
+
"number": 3,
|
| 176 |
+
"colorClass": "proposition"
|
| 177 |
+
},
|
| 178 |
+
{
|
| 179 |
+
"id": "Prop4",
|
| 180 |
+
"type": "proposition",
|
| 181 |
+
"label": "To inscribe a circle in a given triangle",
|
| 182 |
+
"shortLabel": "Prop. IV.4",
|
| 183 |
+
"short": "Inscribe circle in triangle",
|
| 184 |
+
"book": 4,
|
| 185 |
+
"number": 4,
|
| 186 |
+
"colorClass": "proposition"
|
| 187 |
+
},
|
| 188 |
+
{
|
| 189 |
+
"id": "Prop5",
|
| 190 |
+
"type": "proposition",
|
| 191 |
+
"label": "To circumscribe a circle about a given triangle",
|
| 192 |
+
"shortLabel": "Prop. IV.5",
|
| 193 |
+
"short": "Circumscribe circle about triangle",
|
| 194 |
+
"book": 4,
|
| 195 |
+
"number": 5,
|
| 196 |
+
"colorClass": "proposition"
|
| 197 |
+
},
|
| 198 |
+
{
|
| 199 |
+
"id": "Prop6",
|
| 200 |
+
"type": "proposition",
|
| 201 |
+
"label": "To inscribe a square in a given circle",
|
| 202 |
+
"shortLabel": "Prop. IV.6",
|
| 203 |
+
"short": "Inscribe square in circle",
|
| 204 |
+
"book": 4,
|
| 205 |
+
"number": 6,
|
| 206 |
+
"colorClass": "proposition"
|
| 207 |
+
},
|
| 208 |
+
{
|
| 209 |
+
"id": "Prop7",
|
| 210 |
+
"type": "proposition",
|
| 211 |
+
"label": "To circumscribe a square about a given circle",
|
| 212 |
+
"shortLabel": "Prop. IV.7",
|
| 213 |
+
"short": "Circumscribe square about circle",
|
| 214 |
+
"book": 4,
|
| 215 |
+
"number": 7,
|
| 216 |
+
"colorClass": "proposition"
|
| 217 |
+
},
|
| 218 |
+
{
|
| 219 |
+
"id": "Prop8",
|
| 220 |
+
"type": "proposition",
|
| 221 |
+
"label": "To inscribe a circle in a given square",
|
| 222 |
+
"shortLabel": "Prop. IV.8",
|
| 223 |
+
"short": "Inscribe circle in square",
|
| 224 |
+
"book": 4,
|
| 225 |
+
"number": 8,
|
| 226 |
+
"colorClass": "proposition"
|
| 227 |
+
},
|
| 228 |
+
{
|
| 229 |
+
"id": "Prop9",
|
| 230 |
+
"type": "proposition",
|
| 231 |
+
"label": "To circumscribe a circle about a given square",
|
| 232 |
+
"shortLabel": "Prop. IV.9",
|
| 233 |
+
"short": "Circumscribe circle about square",
|
| 234 |
+
"book": 4,
|
| 235 |
+
"number": 9,
|
| 236 |
+
"colorClass": "proposition"
|
| 237 |
+
},
|
| 238 |
+
{
|
| 239 |
+
"id": "Prop10",
|
| 240 |
+
"type": "proposition",
|
| 241 |
+
"label": "To construct isosceles triangle with each base angle double the remaining",
|
| 242 |
+
"shortLabel": "Prop. IV.10",
|
| 243 |
+
"short": "Isosceles triangle, base angles double",
|
| 244 |
+
"book": 4,
|
| 245 |
+
"number": 10,
|
| 246 |
+
"colorClass": "proposition"
|
| 247 |
+
},
|
| 248 |
+
{
|
| 249 |
+
"id": "Prop11",
|
| 250 |
+
"type": "proposition",
|
| 251 |
+
"label": "To inscribe an equilateral equiangular pentagon in a given circle",
|
| 252 |
+
"shortLabel": "Prop. IV.11",
|
| 253 |
+
"short": "Inscribe pentagon in circle",
|
| 254 |
+
"book": 4,
|
| 255 |
+
"number": 11,
|
| 256 |
+
"colorClass": "proposition"
|
| 257 |
+
},
|
| 258 |
+
{
|
| 259 |
+
"id": "Prop12",
|
| 260 |
+
"type": "proposition",
|
| 261 |
+
"label": "To circumscribe an equilateral equiangular pentagon about a given circle",
|
| 262 |
+
"shortLabel": "Prop. IV.12",
|
| 263 |
+
"short": "Circumscribe pentagon about circle",
|
| 264 |
+
"book": 4,
|
| 265 |
+
"number": 12,
|
| 266 |
+
"colorClass": "proposition"
|
| 267 |
+
},
|
| 268 |
+
{
|
| 269 |
+
"id": "Prop13",
|
| 270 |
+
"type": "proposition",
|
| 271 |
+
"label": "To inscribe a circle in a given equilateral equiangular pentagon",
|
| 272 |
+
"shortLabel": "Prop. IV.13",
|
| 273 |
+
"short": "Inscribe circle in pentagon",
|
| 274 |
+
"book": 4,
|
| 275 |
+
"number": 13,
|
| 276 |
+
"colorClass": "proposition"
|
| 277 |
+
},
|
| 278 |
+
{
|
| 279 |
+
"id": "Prop14",
|
| 280 |
+
"type": "proposition",
|
| 281 |
+
"label": "To circumscribe a circle about a given equilateral equiangular pentagon",
|
| 282 |
+
"shortLabel": "Prop. IV.14",
|
| 283 |
+
"short": "Circumscribe circle about pentagon",
|
| 284 |
+
"book": 4,
|
| 285 |
+
"number": 14,
|
| 286 |
+
"colorClass": "proposition"
|
| 287 |
+
},
|
| 288 |
+
{
|
| 289 |
+
"id": "Prop15",
|
| 290 |
+
"type": "proposition",
|
| 291 |
+
"label": "To inscribe an equilateral equiangular hexagon in a given circle",
|
| 292 |
+
"shortLabel": "Prop. IV.15",
|
| 293 |
+
"short": "Inscribe hexagon in circle",
|
| 294 |
+
"book": 4,
|
| 295 |
+
"number": 15,
|
| 296 |
+
"colorClass": "proposition"
|
| 297 |
+
},
|
| 298 |
+
{
|
| 299 |
+
"id": "Prop16",
|
| 300 |
+
"type": "proposition",
|
| 301 |
+
"label": "To inscribe an equilateral equiangular fifteen-angled figure in a given circle",
|
| 302 |
+
"shortLabel": "Prop. IV.16",
|
| 303 |
+
"short": "Inscribe 15-gon in circle",
|
| 304 |
+
"book": 4,
|
| 305 |
+
"number": 16,
|
| 306 |
+
"colorClass": "proposition"
|
| 307 |
+
}
|
| 308 |
+
],
|
| 309 |
+
"edges": [
|
| 310 |
+
{
|
| 311 |
+
"from": "BookI",
|
| 312 |
+
"to": "Def1"
|
| 313 |
+
},
|
| 314 |
+
{
|
| 315 |
+
"from": "BookIII",
|
| 316 |
+
"to": "Def1"
|
| 317 |
+
},
|
| 318 |
+
{
|
| 319 |
+
"from": "BookI",
|
| 320 |
+
"to": "Def2"
|
| 321 |
+
},
|
| 322 |
+
{
|
| 323 |
+
"from": "BookIII",
|
| 324 |
+
"to": "Def2"
|
| 325 |
+
},
|
| 326 |
+
{
|
| 327 |
+
"from": "BookI",
|
| 328 |
+
"to": "Def3"
|
| 329 |
+
},
|
| 330 |
+
{
|
| 331 |
+
"from": "BookIII",
|
| 332 |
+
"to": "Def3"
|
| 333 |
+
},
|
| 334 |
+
{
|
| 335 |
+
"from": "BookI",
|
| 336 |
+
"to": "Def4"
|
| 337 |
+
},
|
| 338 |
+
{
|
| 339 |
+
"from": "BookIII",
|
| 340 |
+
"to": "Def4"
|
| 341 |
+
},
|
| 342 |
+
{
|
| 343 |
+
"from": "BookI",
|
| 344 |
+
"to": "Def5"
|
| 345 |
+
},
|
| 346 |
+
{
|
| 347 |
+
"from": "BookIII",
|
| 348 |
+
"to": "Def5"
|
| 349 |
+
},
|
| 350 |
+
{
|
| 351 |
+
"from": "BookI",
|
| 352 |
+
"to": "Def6"
|
| 353 |
+
},
|
| 354 |
+
{
|
| 355 |
+
"from": "BookIII",
|
| 356 |
+
"to": "Def6"
|
| 357 |
+
},
|
| 358 |
+
{
|
| 359 |
+
"from": "BookI",
|
| 360 |
+
"to": "Def7"
|
| 361 |
+
},
|
| 362 |
+
{
|
| 363 |
+
"from": "BookIII",
|
| 364 |
+
"to": "Def7"
|
| 365 |
+
},
|
| 366 |
+
{
|
| 367 |
+
"from": "BookI",
|
| 368 |
+
"to": "Prop1"
|
| 369 |
+
},
|
| 370 |
+
{
|
| 371 |
+
"from": "BookIII",
|
| 372 |
+
"to": "Prop1"
|
| 373 |
+
},
|
| 374 |
+
{
|
| 375 |
+
"from": "BookI",
|
| 376 |
+
"to": "Prop2"
|
| 377 |
+
},
|
| 378 |
+
{
|
| 379 |
+
"from": "BookIII",
|
| 380 |
+
"to": "Prop2"
|
| 381 |
+
},
|
| 382 |
+
{
|
| 383 |
+
"from": "BookI",
|
| 384 |
+
"to": "Prop3"
|
| 385 |
+
},
|
| 386 |
+
{
|
| 387 |
+
"from": "BookIII",
|
| 388 |
+
"to": "Prop3"
|
| 389 |
+
},
|
| 390 |
+
{
|
| 391 |
+
"from": "BookI",
|
| 392 |
+
"to": "Prop4"
|
| 393 |
+
},
|
| 394 |
+
{
|
| 395 |
+
"from": "BookIII",
|
| 396 |
+
"to": "Prop4"
|
| 397 |
+
},
|
| 398 |
+
{
|
| 399 |
+
"from": "BookI",
|
| 400 |
+
"to": "Prop5"
|
| 401 |
+
},
|
| 402 |
+
{
|
| 403 |
+
"from": "BookIII",
|
| 404 |
+
"to": "Prop5"
|
| 405 |
+
},
|
| 406 |
+
{
|
| 407 |
+
"from": "BookI",
|
| 408 |
+
"to": "Prop6"
|
| 409 |
+
},
|
| 410 |
+
{
|
| 411 |
+
"from": "BookIII",
|
| 412 |
+
"to": "Prop6"
|
| 413 |
+
},
|
| 414 |
+
{
|
| 415 |
+
"from": "Prop1",
|
| 416 |
+
"to": "Prop6"
|
| 417 |
+
},
|
| 418 |
+
{
|
| 419 |
+
"from": "BookI",
|
| 420 |
+
"to": "Prop7"
|
| 421 |
+
},
|
| 422 |
+
{
|
| 423 |
+
"from": "BookIII",
|
| 424 |
+
"to": "Prop7"
|
| 425 |
+
},
|
| 426 |
+
{
|
| 427 |
+
"from": "Prop6",
|
| 428 |
+
"to": "Prop7"
|
| 429 |
+
},
|
| 430 |
+
{
|
| 431 |
+
"from": "BookI",
|
| 432 |
+
"to": "Prop8"
|
| 433 |
+
},
|
| 434 |
+
{
|
| 435 |
+
"from": "BookIII",
|
| 436 |
+
"to": "Prop8"
|
| 437 |
+
},
|
| 438 |
+
{
|
| 439 |
+
"from": "Prop7",
|
| 440 |
+
"to": "Prop8"
|
| 441 |
+
},
|
| 442 |
+
{
|
| 443 |
+
"from": "BookI",
|
| 444 |
+
"to": "Prop9"
|
| 445 |
+
},
|
| 446 |
+
{
|
| 447 |
+
"from": "BookIII",
|
| 448 |
+
"to": "Prop9"
|
| 449 |
+
},
|
| 450 |
+
{
|
| 451 |
+
"from": "Prop8",
|
| 452 |
+
"to": "Prop9"
|
| 453 |
+
},
|
| 454 |
+
{
|
| 455 |
+
"from": "BookI",
|
| 456 |
+
"to": "Prop10"
|
| 457 |
+
},
|
| 458 |
+
{
|
| 459 |
+
"from": "BookIII",
|
| 460 |
+
"to": "Prop10"
|
| 461 |
+
},
|
| 462 |
+
{
|
| 463 |
+
"from": "Prop1",
|
| 464 |
+
"to": "Prop10"
|
| 465 |
+
},
|
| 466 |
+
{
|
| 467 |
+
"from": "Prop5",
|
| 468 |
+
"to": "Prop10"
|
| 469 |
+
},
|
| 470 |
+
{
|
| 471 |
+
"from": "PropII11",
|
| 472 |
+
"to": "Prop10"
|
| 473 |
+
},
|
| 474 |
+
{
|
| 475 |
+
"from": "BookI",
|
| 476 |
+
"to": "Prop11"
|
| 477 |
+
},
|
| 478 |
+
{
|
| 479 |
+
"from": "BookIII",
|
| 480 |
+
"to": "Prop11"
|
| 481 |
+
},
|
| 482 |
+
{
|
| 483 |
+
"from": "Prop2",
|
| 484 |
+
"to": "Prop11"
|
| 485 |
+
},
|
| 486 |
+
{
|
| 487 |
+
"from": "Prop10",
|
| 488 |
+
"to": "Prop11"
|
| 489 |
+
},
|
| 490 |
+
{
|
| 491 |
+
"from": "BookI",
|
| 492 |
+
"to": "Prop12"
|
| 493 |
+
},
|
| 494 |
+
{
|
| 495 |
+
"from": "BookIII",
|
| 496 |
+
"to": "Prop12"
|
| 497 |
+
},
|
| 498 |
+
{
|
| 499 |
+
"from": "Prop11",
|
| 500 |
+
"to": "Prop12"
|
| 501 |
+
},
|
| 502 |
+
{
|
| 503 |
+
"from": "BookI",
|
| 504 |
+
"to": "Prop13"
|
| 505 |
+
},
|
| 506 |
+
{
|
| 507 |
+
"from": "BookIII",
|
| 508 |
+
"to": "Prop13"
|
| 509 |
+
},
|
| 510 |
+
{
|
| 511 |
+
"from": "Prop11",
|
| 512 |
+
"to": "Prop13"
|
| 513 |
+
},
|
| 514 |
+
{
|
| 515 |
+
"from": "BookI",
|
| 516 |
+
"to": "Prop14"
|
| 517 |
+
},
|
| 518 |
+
{
|
| 519 |
+
"from": "BookIII",
|
| 520 |
+
"to": "Prop14"
|
| 521 |
+
},
|
| 522 |
+
{
|
| 523 |
+
"from": "Prop11",
|
| 524 |
+
"to": "Prop14"
|
| 525 |
+
},
|
| 526 |
+
{
|
| 527 |
+
"from": "BookI",
|
| 528 |
+
"to": "Prop15"
|
| 529 |
+
},
|
| 530 |
+
{
|
| 531 |
+
"from": "BookIII",
|
| 532 |
+
"to": "Prop15"
|
| 533 |
+
},
|
| 534 |
+
{
|
| 535 |
+
"from": "Prop1",
|
| 536 |
+
"to": "Prop15"
|
| 537 |
+
},
|
| 538 |
+
{
|
| 539 |
+
"from": "BookI",
|
| 540 |
+
"to": "Prop16"
|
| 541 |
+
},
|
| 542 |
+
{
|
| 543 |
+
"from": "BookIII",
|
| 544 |
+
"to": "Prop16"
|
| 545 |
+
},
|
| 546 |
+
{
|
| 547 |
+
"from": "Prop1",
|
| 548 |
+
"to": "Prop16"
|
| 549 |
+
},
|
| 550 |
+
{
|
| 551 |
+
"from": "Prop2",
|
| 552 |
+
"to": "Prop16"
|
| 553 |
+
},
|
| 554 |
+
{
|
| 555 |
+
"from": "Prop11",
|
| 556 |
+
"to": "Prop16"
|
| 557 |
+
}
|
| 558 |
+
],
|
| 559 |
+
"colorScheme": {
|
| 560 |
+
"foundation": {
|
| 561 |
+
"fill": "#95a5a6",
|
| 562 |
+
"stroke": "#7f8c8d"
|
| 563 |
+
},
|
| 564 |
+
"definition": {
|
| 565 |
+
"fill": "#3498db",
|
| 566 |
+
"stroke": "#2980b9"
|
| 567 |
+
},
|
| 568 |
+
"proposition": {
|
| 569 |
+
"fill": "#1abc9c",
|
| 570 |
+
"stroke": "#16a085"
|
| 571 |
+
}
|
| 572 |
+
}
|
| 573 |
+
}
|
data/euclid-elements-book-ix.json
ADDED
|
@@ -0,0 +1,728 @@
|
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|
| 1 |
+
{
|
| 2 |
+
"schemaVersion": "1.0",
|
| 3 |
+
"discourse": {
|
| 4 |
+
"id": "euclid-elements-book-ix",
|
| 5 |
+
"name": "Euclid's Elements, Book IX",
|
| 6 |
+
"subject": "number_theory",
|
| 7 |
+
"variant": "classical",
|
| 8 |
+
"description": "Primes, perfect numbers, odd/even. 36 propositions. Depends on Books VII and VIII. Source: David E. Joyce.",
|
| 9 |
+
"structure": {
|
| 10 |
+
"books": 9,
|
| 11 |
+
"propositions": 36,
|
| 12 |
+
"foundationTypes": [
|
| 13 |
+
"foundation"
|
| 14 |
+
]
|
| 15 |
+
}
|
| 16 |
+
},
|
| 17 |
+
"metadata": {
|
| 18 |
+
"created": "2026-03-18",
|
| 19 |
+
"lastUpdated": "2026-03-18",
|
| 20 |
+
"version": "1.0.0",
|
| 21 |
+
"license": "CC BY 4.0",
|
| 22 |
+
"authors": [
|
| 23 |
+
"Welz, G."
|
| 24 |
+
],
|
| 25 |
+
"methodology": "Programming Framework",
|
| 26 |
+
"citation": "Welz, G. (2026). Euclid's Elements Book IX Dependency Graph. Programming Framework.",
|
| 27 |
+
"keywords": [
|
| 28 |
+
"Euclid",
|
| 29 |
+
"Elements",
|
| 30 |
+
"Book IX",
|
| 31 |
+
"prime",
|
| 32 |
+
"perfect",
|
| 33 |
+
"odd",
|
| 34 |
+
"even"
|
| 35 |
+
]
|
| 36 |
+
},
|
| 37 |
+
"sources": [
|
| 38 |
+
{
|
| 39 |
+
"id": "joyce",
|
| 40 |
+
"type": "digital",
|
| 41 |
+
"authors": "Joyce, David E.",
|
| 42 |
+
"title": "Euclid's Elements, Book IX",
|
| 43 |
+
"year": "1996",
|
| 44 |
+
"url": "https://mathcs.clarku.edu/~djoyce/java/elements/bookIX/bookIX.html",
|
| 45 |
+
"notes": "Clark University; IX.20 infinitude of primes"
|
| 46 |
+
}
|
| 47 |
+
],
|
| 48 |
+
"nodes": [
|
| 49 |
+
{
|
| 50 |
+
"id": "BookVII",
|
| 51 |
+
"type": "foundation",
|
| 52 |
+
"label": "Book VII — Number theory",
|
| 53 |
+
"shortLabel": "Book VII",
|
| 54 |
+
"short": "Foundation",
|
| 55 |
+
"book": 7,
|
| 56 |
+
"colorClass": "foundation"
|
| 57 |
+
},
|
| 58 |
+
{
|
| 59 |
+
"id": "BookVIII",
|
| 60 |
+
"type": "foundation",
|
| 61 |
+
"label": "Book VIII — Continued proportions",
|
| 62 |
+
"shortLabel": "Book VIII",
|
| 63 |
+
"short": "Foundation",
|
| 64 |
+
"book": 8,
|
| 65 |
+
"colorClass": "foundation"
|
| 66 |
+
},
|
| 67 |
+
{
|
| 68 |
+
"id": "Prop1",
|
| 69 |
+
"type": "proposition",
|
| 70 |
+
"label": "Two similar plane numbers multiplied: product is square",
|
| 71 |
+
"shortLabel": "Prop. IX.1",
|
| 72 |
+
"short": "Similar plane product square",
|
| 73 |
+
"book": 9,
|
| 74 |
+
"number": 1,
|
| 75 |
+
"colorClass": "proposition"
|
| 76 |
+
},
|
| 77 |
+
{
|
| 78 |
+
"id": "Prop2",
|
| 79 |
+
"type": "proposition",
|
| 80 |
+
"label": "Two numbers product square: they are similar plane",
|
| 81 |
+
"shortLabel": "Prop. IX.2",
|
| 82 |
+
"short": "Product square: similar plane",
|
| 83 |
+
"book": 9,
|
| 84 |
+
"number": 2,
|
| 85 |
+
"colorClass": "proposition"
|
| 86 |
+
},
|
| 87 |
+
{
|
| 88 |
+
"id": "Prop3",
|
| 89 |
+
"type": "proposition",
|
| 90 |
+
"label": "Cubic number multiplied by itself: product is cube",
|
| 91 |
+
"shortLabel": "Prop. IX.3",
|
| 92 |
+
"short": "Cube times itself",
|
| 93 |
+
"book": 9,
|
| 94 |
+
"number": 3,
|
| 95 |
+
"colorClass": "proposition"
|
| 96 |
+
},
|
| 97 |
+
{
|
| 98 |
+
"id": "Prop4",
|
| 99 |
+
"type": "proposition",
|
| 100 |
+
"label": "Cubic times cubic: product is cube",
|
| 101 |
+
"shortLabel": "Prop. IX.4",
|
| 102 |
+
"short": "Cube times cube",
|
| 103 |
+
"book": 9,
|
| 104 |
+
"number": 4,
|
| 105 |
+
"colorClass": "proposition"
|
| 106 |
+
},
|
| 107 |
+
{
|
| 108 |
+
"id": "Prop5",
|
| 109 |
+
"type": "proposition",
|
| 110 |
+
"label": "If cube times any makes cube, the multiplied is cubic",
|
| 111 |
+
"shortLabel": "Prop. IX.5",
|
| 112 |
+
"short": "Cube times any makes cube",
|
| 113 |
+
"book": 9,
|
| 114 |
+
"number": 5,
|
| 115 |
+
"colorClass": "proposition"
|
| 116 |
+
},
|
| 117 |
+
{
|
| 118 |
+
"id": "Prop6",
|
| 119 |
+
"type": "proposition",
|
| 120 |
+
"label": "If number times itself makes cubic, it is cubic",
|
| 121 |
+
"shortLabel": "Prop. IX.6",
|
| 122 |
+
"short": "Number times itself cubic",
|
| 123 |
+
"book": 9,
|
| 124 |
+
"number": 6,
|
| 125 |
+
"colorClass": "proposition"
|
| 126 |
+
},
|
| 127 |
+
{
|
| 128 |
+
"id": "Prop7",
|
| 129 |
+
"type": "proposition",
|
| 130 |
+
"label": "Composite times any: product is solid",
|
| 131 |
+
"shortLabel": "Prop. IX.7",
|
| 132 |
+
"short": "Composite times any: solid",
|
| 133 |
+
"book": 9,
|
| 134 |
+
"number": 7,
|
| 135 |
+
"colorClass": "proposition"
|
| 136 |
+
},
|
| 137 |
+
{
|
| 138 |
+
"id": "Prop8",
|
| 139 |
+
"type": "proposition",
|
| 140 |
+
"label": "Numbers from unit in continued proportion: 3rd square, 4th cube, 7th both",
|
| 141 |
+
"shortLabel": "Prop. IX.8",
|
| 142 |
+
"short": "Continued proportion from unit",
|
| 143 |
+
"book": 9,
|
| 144 |
+
"number": 8,
|
| 145 |
+
"colorClass": "proposition"
|
| 146 |
+
},
|
| 147 |
+
{
|
| 148 |
+
"id": "Prop9",
|
| 149 |
+
"type": "proposition",
|
| 150 |
+
"label": "If second from unit square, all square; if cubic, all cubic",
|
| 151 |
+
"shortLabel": "Prop. IX.9",
|
| 152 |
+
"short": "Second square: all square",
|
| 153 |
+
"book": 9,
|
| 154 |
+
"number": 9,
|
| 155 |
+
"colorClass": "proposition"
|
| 156 |
+
},
|
| 157 |
+
{
|
| 158 |
+
"id": "Prop10",
|
| 159 |
+
"type": "proposition",
|
| 160 |
+
"label": "If second not square, only 3rd and every other square; similar for cube",
|
| 161 |
+
"shortLabel": "Prop. IX.10",
|
| 162 |
+
"short": "Second not square",
|
| 163 |
+
"book": 9,
|
| 164 |
+
"number": 10,
|
| 165 |
+
"colorClass": "proposition"
|
| 166 |
+
},
|
| 167 |
+
{
|
| 168 |
+
"id": "Prop11",
|
| 169 |
+
"type": "proposition",
|
| 170 |
+
"label": "Continued proportion from unit: less measures greater",
|
| 171 |
+
"shortLabel": "Prop. IX.11",
|
| 172 |
+
"short": "Less measures greater",
|
| 173 |
+
"book": 9,
|
| 174 |
+
"number": 11,
|
| 175 |
+
"colorClass": "proposition"
|
| 176 |
+
},
|
| 177 |
+
{
|
| 178 |
+
"id": "Prop12",
|
| 179 |
+
"type": "proposition",
|
| 180 |
+
"label": "If prime measures last, it measures second from unit",
|
| 181 |
+
"shortLabel": "Prop. IX.12",
|
| 182 |
+
"short": "Prime measures last",
|
| 183 |
+
"book": 9,
|
| 184 |
+
"number": 12,
|
| 185 |
+
"colorClass": "proposition"
|
| 186 |
+
},
|
| 187 |
+
{
|
| 188 |
+
"id": "Prop13",
|
| 189 |
+
"type": "proposition",
|
| 190 |
+
"label": "Continued proportion, second prime: only proportional numbers measure last",
|
| 191 |
+
"shortLabel": "Prop. IX.13",
|
| 192 |
+
"short": "Second prime: only those measure",
|
| 193 |
+
"book": 9,
|
| 194 |
+
"number": 13,
|
| 195 |
+
"colorClass": "proposition"
|
| 196 |
+
},
|
| 197 |
+
{
|
| 198 |
+
"id": "Prop14",
|
| 199 |
+
"type": "proposition",
|
| 200 |
+
"label": "Least measured by given primes: not measured by any other prime",
|
| 201 |
+
"shortLabel": "Prop. IX.14",
|
| 202 |
+
"short": "Least measured by primes",
|
| 203 |
+
"book": 9,
|
| 204 |
+
"number": 14,
|
| 205 |
+
"colorClass": "proposition"
|
| 206 |
+
},
|
| 207 |
+
{
|
| 208 |
+
"id": "Prop15",
|
| 209 |
+
"type": "proposition",
|
| 210 |
+
"label": "Three least in ratio: sum of any two prime to remainder",
|
| 211 |
+
"shortLabel": "Prop. IX.15",
|
| 212 |
+
"short": "Three in proportion",
|
| 213 |
+
"book": 9,
|
| 214 |
+
"number": 15,
|
| 215 |
+
"colorClass": "proposition"
|
| 216 |
+
},
|
| 217 |
+
{
|
| 218 |
+
"id": "Prop16",
|
| 219 |
+
"type": "proposition",
|
| 220 |
+
"label": "Two relatively prime: no third as first to second",
|
| 221 |
+
"shortLabel": "Prop. IX.16",
|
| 222 |
+
"short": "Relatively prime: no third",
|
| 223 |
+
"book": 9,
|
| 224 |
+
"number": 16,
|
| 225 |
+
"colorClass": "proposition"
|
| 226 |
+
},
|
| 227 |
+
{
|
| 228 |
+
"id": "Prop17",
|
| 229 |
+
"type": "proposition",
|
| 230 |
+
"label": "Continued proportion, extremes prime: last not to any as first to second",
|
| 231 |
+
"shortLabel": "Prop. IX.17",
|
| 232 |
+
"short": "Extremes prime: no extension",
|
| 233 |
+
"book": 9,
|
| 234 |
+
"number": 17,
|
| 235 |
+
"colorClass": "proposition"
|
| 236 |
+
},
|
| 237 |
+
{
|
| 238 |
+
"id": "Prop18",
|
| 239 |
+
"type": "proposition",
|
| 240 |
+
"label": "Given two numbers, investigate if third proportional exists",
|
| 241 |
+
"shortLabel": "Prop. IX.18",
|
| 242 |
+
"short": "Third proportional",
|
| 243 |
+
"book": 9,
|
| 244 |
+
"number": 18,
|
| 245 |
+
"colorClass": "proposition"
|
| 246 |
+
},
|
| 247 |
+
{
|
| 248 |
+
"id": "Prop19",
|
| 249 |
+
"type": "proposition",
|
| 250 |
+
"label": "Given three numbers, investigate when fourth proportional exists",
|
| 251 |
+
"shortLabel": "Prop. IX.19",
|
| 252 |
+
"short": "Fourth proportional",
|
| 253 |
+
"book": 9,
|
| 254 |
+
"number": 19,
|
| 255 |
+
"colorClass": "proposition"
|
| 256 |
+
},
|
| 257 |
+
{
|
| 258 |
+
"id": "Prop20",
|
| 259 |
+
"type": "proposition",
|
| 260 |
+
"label": "Prime numbers are more than any assigned multitude",
|
| 261 |
+
"shortLabel": "Prop. IX.20",
|
| 262 |
+
"short": "Infinitude of primes",
|
| 263 |
+
"book": 9,
|
| 264 |
+
"number": 20,
|
| 265 |
+
"colorClass": "proposition"
|
| 266 |
+
},
|
| 267 |
+
{
|
| 268 |
+
"id": "Prop21",
|
| 269 |
+
"type": "proposition",
|
| 270 |
+
"label": "Sum of even numbers is even",
|
| 271 |
+
"shortLabel": "Prop. IX.21",
|
| 272 |
+
"short": "Sum of evens even",
|
| 273 |
+
"book": 9,
|
| 274 |
+
"number": 21,
|
| 275 |
+
"colorClass": "proposition"
|
| 276 |
+
},
|
| 277 |
+
{
|
| 278 |
+
"id": "Prop22",
|
| 279 |
+
"type": "proposition",
|
| 280 |
+
"label": "Sum of odd numbers, even multitude: sum even",
|
| 281 |
+
"shortLabel": "Prop. IX.22",
|
| 282 |
+
"short": "Sum of odds (even count) even",
|
| 283 |
+
"book": 9,
|
| 284 |
+
"number": 22,
|
| 285 |
+
"colorClass": "proposition"
|
| 286 |
+
},
|
| 287 |
+
{
|
| 288 |
+
"id": "Prop23",
|
| 289 |
+
"type": "proposition",
|
| 290 |
+
"label": "Sum of odd numbers, odd multitude: sum odd",
|
| 291 |
+
"shortLabel": "Prop. IX.23",
|
| 292 |
+
"short": "Sum of odds (odd count) odd",
|
| 293 |
+
"book": 9,
|
| 294 |
+
"number": 23,
|
| 295 |
+
"colorClass": "proposition"
|
| 296 |
+
},
|
| 297 |
+
{
|
| 298 |
+
"id": "Prop24",
|
| 299 |
+
"type": "proposition",
|
| 300 |
+
"label": "Even minus even: remainder even",
|
| 301 |
+
"shortLabel": "Prop. IX.24",
|
| 302 |
+
"short": "Even minus even",
|
| 303 |
+
"book": 9,
|
| 304 |
+
"number": 24,
|
| 305 |
+
"colorClass": "proposition"
|
| 306 |
+
},
|
| 307 |
+
{
|
| 308 |
+
"id": "Prop25",
|
| 309 |
+
"type": "proposition",
|
| 310 |
+
"label": "Even minus odd: remainder odd",
|
| 311 |
+
"shortLabel": "Prop. IX.25",
|
| 312 |
+
"short": "Even minus odd",
|
| 313 |
+
"book": 9,
|
| 314 |
+
"number": 25,
|
| 315 |
+
"colorClass": "proposition"
|
| 316 |
+
},
|
| 317 |
+
{
|
| 318 |
+
"id": "Prop26",
|
| 319 |
+
"type": "proposition",
|
| 320 |
+
"label": "Odd minus odd: remainder even",
|
| 321 |
+
"shortLabel": "Prop. IX.26",
|
| 322 |
+
"short": "Odd minus odd",
|
| 323 |
+
"book": 9,
|
| 324 |
+
"number": 26,
|
| 325 |
+
"colorClass": "proposition"
|
| 326 |
+
},
|
| 327 |
+
{
|
| 328 |
+
"id": "Prop27",
|
| 329 |
+
"type": "proposition",
|
| 330 |
+
"label": "Odd minus even: remainder odd",
|
| 331 |
+
"shortLabel": "Prop. IX.27",
|
| 332 |
+
"short": "Odd minus even",
|
| 333 |
+
"book": 9,
|
| 334 |
+
"number": 27,
|
| 335 |
+
"colorClass": "proposition"
|
| 336 |
+
},
|
| 337 |
+
{
|
| 338 |
+
"id": "Prop28",
|
| 339 |
+
"type": "proposition",
|
| 340 |
+
"label": "Odd times even: product even",
|
| 341 |
+
"shortLabel": "Prop. IX.28",
|
| 342 |
+
"short": "Odd times even",
|
| 343 |
+
"book": 9,
|
| 344 |
+
"number": 28,
|
| 345 |
+
"colorClass": "proposition"
|
| 346 |
+
},
|
| 347 |
+
{
|
| 348 |
+
"id": "Prop29",
|
| 349 |
+
"type": "proposition",
|
| 350 |
+
"label": "Odd times odd: product odd",
|
| 351 |
+
"shortLabel": "Prop. IX.29",
|
| 352 |
+
"short": "Odd times odd",
|
| 353 |
+
"book": 9,
|
| 354 |
+
"number": 29,
|
| 355 |
+
"colorClass": "proposition"
|
| 356 |
+
},
|
| 357 |
+
{
|
| 358 |
+
"id": "Prop30",
|
| 359 |
+
"type": "proposition",
|
| 360 |
+
"label": "Odd measuring even: measures half",
|
| 361 |
+
"shortLabel": "Prop. IX.30",
|
| 362 |
+
"short": "Odd measures even",
|
| 363 |
+
"book": 9,
|
| 364 |
+
"number": 30,
|
| 365 |
+
"colorClass": "proposition"
|
| 366 |
+
},
|
| 367 |
+
{
|
| 368 |
+
"id": "Prop31",
|
| 369 |
+
"type": "proposition",
|
| 370 |
+
"label": "Odd relatively prime to any: also prime to its double",
|
| 371 |
+
"shortLabel": "Prop. IX.31",
|
| 372 |
+
"short": "Odd prime to double",
|
| 373 |
+
"book": 9,
|
| 374 |
+
"number": 31,
|
| 375 |
+
"colorClass": "proposition"
|
| 376 |
+
},
|
| 377 |
+
{
|
| 378 |
+
"id": "Prop32",
|
| 379 |
+
"type": "proposition",
|
| 380 |
+
"label": "Numbers doubled from 2: even-times even only",
|
| 381 |
+
"shortLabel": "Prop. IX.32",
|
| 382 |
+
"short": "Powers of 2",
|
| 383 |
+
"book": 9,
|
| 384 |
+
"number": 32,
|
| 385 |
+
"colorClass": "proposition"
|
| 386 |
+
},
|
| 387 |
+
{
|
| 388 |
+
"id": "Prop33",
|
| 389 |
+
"type": "proposition",
|
| 390 |
+
"label": "Number with half odd: even-times odd only",
|
| 391 |
+
"shortLabel": "Prop. IX.33",
|
| 392 |
+
"short": "Half odd",
|
| 393 |
+
"book": 9,
|
| 394 |
+
"number": 33,
|
| 395 |
+
"colorClass": "proposition"
|
| 396 |
+
},
|
| 397 |
+
{
|
| 398 |
+
"id": "Prop34",
|
| 399 |
+
"type": "proposition",
|
| 400 |
+
"label": "Number neither: both even-times even and even-times odd",
|
| 401 |
+
"shortLabel": "Prop. IX.34",
|
| 402 |
+
"short": "Neither",
|
| 403 |
+
"book": 9,
|
| 404 |
+
"number": 34,
|
| 405 |
+
"colorClass": "proposition"
|
| 406 |
+
},
|
| 407 |
+
{
|
| 408 |
+
"id": "Prop35",
|
| 409 |
+
"type": "proposition",
|
| 410 |
+
"label": "Continued proportion: (second−first):first = (last−first):sum of rest",
|
| 411 |
+
"shortLabel": "Prop. IX.35",
|
| 412 |
+
"short": "Geometric series",
|
| 413 |
+
"book": 9,
|
| 414 |
+
"number": 35,
|
| 415 |
+
"colorClass": "proposition"
|
| 416 |
+
},
|
| 417 |
+
{
|
| 418 |
+
"id": "Prop36",
|
| 419 |
+
"type": "proposition",
|
| 420 |
+
"label": "If sum of powers of 2 is prime, product with last is perfect",
|
| 421 |
+
"shortLabel": "Prop. IX.36",
|
| 422 |
+
"short": "Perfect numbers",
|
| 423 |
+
"book": 9,
|
| 424 |
+
"number": 36,
|
| 425 |
+
"colorClass": "proposition"
|
| 426 |
+
}
|
| 427 |
+
],
|
| 428 |
+
"edges": [
|
| 429 |
+
{
|
| 430 |
+
"from": "BookVII",
|
| 431 |
+
"to": "Prop1"
|
| 432 |
+
},
|
| 433 |
+
{
|
| 434 |
+
"from": "BookVIII",
|
| 435 |
+
"to": "Prop1"
|
| 436 |
+
},
|
| 437 |
+
{
|
| 438 |
+
"from": "BookVII",
|
| 439 |
+
"to": "Prop2"
|
| 440 |
+
},
|
| 441 |
+
{
|
| 442 |
+
"from": "BookVIII",
|
| 443 |
+
"to": "Prop2"
|
| 444 |
+
},
|
| 445 |
+
{
|
| 446 |
+
"from": "BookVII",
|
| 447 |
+
"to": "Prop3"
|
| 448 |
+
},
|
| 449 |
+
{
|
| 450 |
+
"from": "BookVIII",
|
| 451 |
+
"to": "Prop3"
|
| 452 |
+
},
|
| 453 |
+
{
|
| 454 |
+
"from": "BookVII",
|
| 455 |
+
"to": "Prop4"
|
| 456 |
+
},
|
| 457 |
+
{
|
| 458 |
+
"from": "BookVIII",
|
| 459 |
+
"to": "Prop4"
|
| 460 |
+
},
|
| 461 |
+
{
|
| 462 |
+
"from": "BookVII",
|
| 463 |
+
"to": "Prop5"
|
| 464 |
+
},
|
| 465 |
+
{
|
| 466 |
+
"from": "BookVIII",
|
| 467 |
+
"to": "Prop5"
|
| 468 |
+
},
|
| 469 |
+
{
|
| 470 |
+
"from": "BookVII",
|
| 471 |
+
"to": "Prop6"
|
| 472 |
+
},
|
| 473 |
+
{
|
| 474 |
+
"from": "BookVIII",
|
| 475 |
+
"to": "Prop6"
|
| 476 |
+
},
|
| 477 |
+
{
|
| 478 |
+
"from": "BookVII",
|
| 479 |
+
"to": "Prop7"
|
| 480 |
+
},
|
| 481 |
+
{
|
| 482 |
+
"from": "BookVIII",
|
| 483 |
+
"to": "Prop7"
|
| 484 |
+
},
|
| 485 |
+
{
|
| 486 |
+
"from": "BookVII",
|
| 487 |
+
"to": "Prop8"
|
| 488 |
+
},
|
| 489 |
+
{
|
| 490 |
+
"from": "BookVIII",
|
| 491 |
+
"to": "Prop8"
|
| 492 |
+
},
|
| 493 |
+
{
|
| 494 |
+
"from": "BookVII",
|
| 495 |
+
"to": "Prop9"
|
| 496 |
+
},
|
| 497 |
+
{
|
| 498 |
+
"from": "BookVIII",
|
| 499 |
+
"to": "Prop9"
|
| 500 |
+
},
|
| 501 |
+
{
|
| 502 |
+
"from": "BookVII",
|
| 503 |
+
"to": "Prop10"
|
| 504 |
+
},
|
| 505 |
+
{
|
| 506 |
+
"from": "BookVIII",
|
| 507 |
+
"to": "Prop10"
|
| 508 |
+
},
|
| 509 |
+
{
|
| 510 |
+
"from": "BookVII",
|
| 511 |
+
"to": "Prop11"
|
| 512 |
+
},
|
| 513 |
+
{
|
| 514 |
+
"from": "BookVIII",
|
| 515 |
+
"to": "Prop11"
|
| 516 |
+
},
|
| 517 |
+
{
|
| 518 |
+
"from": "BookVII",
|
| 519 |
+
"to": "Prop12"
|
| 520 |
+
},
|
| 521 |
+
{
|
| 522 |
+
"from": "BookVIII",
|
| 523 |
+
"to": "Prop12"
|
| 524 |
+
},
|
| 525 |
+
{
|
| 526 |
+
"from": "BookVII",
|
| 527 |
+
"to": "Prop13"
|
| 528 |
+
},
|
| 529 |
+
{
|
| 530 |
+
"from": "BookVIII",
|
| 531 |
+
"to": "Prop13"
|
| 532 |
+
},
|
| 533 |
+
{
|
| 534 |
+
"from": "BookVII",
|
| 535 |
+
"to": "Prop14"
|
| 536 |
+
},
|
| 537 |
+
{
|
| 538 |
+
"from": "BookVIII",
|
| 539 |
+
"to": "Prop14"
|
| 540 |
+
},
|
| 541 |
+
{
|
| 542 |
+
"from": "BookVII",
|
| 543 |
+
"to": "Prop15"
|
| 544 |
+
},
|
| 545 |
+
{
|
| 546 |
+
"from": "BookVIII",
|
| 547 |
+
"to": "Prop15"
|
| 548 |
+
},
|
| 549 |
+
{
|
| 550 |
+
"from": "BookVII",
|
| 551 |
+
"to": "Prop16"
|
| 552 |
+
},
|
| 553 |
+
{
|
| 554 |
+
"from": "BookVIII",
|
| 555 |
+
"to": "Prop16"
|
| 556 |
+
},
|
| 557 |
+
{
|
| 558 |
+
"from": "BookVII",
|
| 559 |
+
"to": "Prop17"
|
| 560 |
+
},
|
| 561 |
+
{
|
| 562 |
+
"from": "BookVIII",
|
| 563 |
+
"to": "Prop17"
|
| 564 |
+
},
|
| 565 |
+
{
|
| 566 |
+
"from": "BookVII",
|
| 567 |
+
"to": "Prop18"
|
| 568 |
+
},
|
| 569 |
+
{
|
| 570 |
+
"from": "BookVIII",
|
| 571 |
+
"to": "Prop18"
|
| 572 |
+
},
|
| 573 |
+
{
|
| 574 |
+
"from": "BookVII",
|
| 575 |
+
"to": "Prop19"
|
| 576 |
+
},
|
| 577 |
+
{
|
| 578 |
+
"from": "BookVIII",
|
| 579 |
+
"to": "Prop19"
|
| 580 |
+
},
|
| 581 |
+
{
|
| 582 |
+
"from": "BookVII",
|
| 583 |
+
"to": "Prop20"
|
| 584 |
+
},
|
| 585 |
+
{
|
| 586 |
+
"from": "BookVIII",
|
| 587 |
+
"to": "Prop20"
|
| 588 |
+
},
|
| 589 |
+
{
|
| 590 |
+
"from": "BookVII",
|
| 591 |
+
"to": "Prop21"
|
| 592 |
+
},
|
| 593 |
+
{
|
| 594 |
+
"from": "BookVIII",
|
| 595 |
+
"to": "Prop21"
|
| 596 |
+
},
|
| 597 |
+
{
|
| 598 |
+
"from": "BookVII",
|
| 599 |
+
"to": "Prop22"
|
| 600 |
+
},
|
| 601 |
+
{
|
| 602 |
+
"from": "BookVIII",
|
| 603 |
+
"to": "Prop22"
|
| 604 |
+
},
|
| 605 |
+
{
|
| 606 |
+
"from": "BookVII",
|
| 607 |
+
"to": "Prop23"
|
| 608 |
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|
| 609 |
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{
|
| 610 |
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|
| 611 |
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|
| 612 |
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|
| 613 |
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{
|
| 614 |
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|
| 615 |
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"to": "Prop24"
|
| 616 |
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|
| 617 |
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{
|
| 618 |
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|
| 619 |
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|
| 620 |
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|
| 621 |
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|
| 622 |
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|
| 623 |
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"to": "Prop25"
|
| 624 |
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|
| 625 |
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{
|
| 626 |
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|
| 627 |
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|
| 628 |
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|
| 629 |
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|
| 630 |
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|
| 631 |
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"to": "Prop26"
|
| 632 |
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|
| 633 |
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{
|
| 634 |
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|
| 635 |
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|
| 636 |
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| 637 |
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| 638 |
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|
| 639 |
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|
| 640 |
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| 641 |
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|
| 642 |
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| 643 |
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|
| 644 |
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| 645 |
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|
| 646 |
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| 647 |
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|
| 648 |
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| 649 |
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| 650 |
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|
| 652 |
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| 653 |
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|
| 654 |
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|
| 655 |
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|
| 656 |
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| 657 |
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|
| 658 |
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|
| 659 |
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| 660 |
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| 661 |
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|
| 662 |
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|
| 663 |
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|
| 664 |
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| 665 |
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|
| 666 |
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|
| 667 |
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|
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| 669 |
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|
| 670 |
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|
| 671 |
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|
| 672 |
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|
| 673 |
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{
|
| 674 |
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"from": "BookVIII",
|
| 675 |
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"to": "Prop31"
|
| 676 |
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|
| 677 |
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{
|
| 678 |
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"from": "BookVII",
|
| 679 |
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"to": "Prop32"
|
| 680 |
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|
| 681 |
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{
|
| 682 |
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"from": "BookVIII",
|
| 683 |
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"to": "Prop32"
|
| 684 |
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|
| 685 |
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{
|
| 686 |
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|
| 687 |
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"to": "Prop33"
|
| 688 |
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|
| 689 |
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{
|
| 690 |
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"from": "BookVIII",
|
| 691 |
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|
| 692 |
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|
| 693 |
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{
|
| 694 |
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"from": "BookVII",
|
| 695 |
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"to": "Prop34"
|
| 696 |
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|
| 697 |
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{
|
| 698 |
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|
| 699 |
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|
| 700 |
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|
| 701 |
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{
|
| 702 |
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"from": "BookVII",
|
| 703 |
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"to": "Prop35"
|
| 704 |
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|
| 705 |
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{
|
| 706 |
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|
| 707 |
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"to": "Prop35"
|
| 708 |
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|
| 709 |
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{
|
| 710 |
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"from": "BookVII",
|
| 711 |
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"to": "Prop36"
|
| 712 |
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|
| 713 |
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{
|
| 714 |
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"from": "BookVIII",
|
| 715 |
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"to": "Prop36"
|
| 716 |
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}
|
| 717 |
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],
|
| 718 |
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"colorScheme": {
|
| 719 |
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"foundation": {
|
| 720 |
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"fill": "#95a5a6",
|
| 721 |
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"stroke": "#7f8c8d"
|
| 722 |
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|
| 723 |
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"proposition": {
|
| 724 |
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|
| 725 |
+
"stroke": "#16a085"
|
| 726 |
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}
|
| 727 |
+
}
|
| 728 |
+
}
|
data/euclid-elements-book-v.json
ADDED
|
@@ -0,0 +1,676 @@
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| 1 |
+
{
|
| 2 |
+
"schemaVersion": "1.0",
|
| 3 |
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"discourse": {
|
| 4 |
+
"id": "euclid-elements-book-v",
|
| 5 |
+
"name": "Euclid's Elements, Book V",
|
| 6 |
+
"subject": "geometry",
|
| 7 |
+
"variant": "classical",
|
| 8 |
+
"description": "Theory of ratio and proportion (Eudoxus). 18 definitions, 25 propositions. Does not depend on previous books. Source: David E. Joyce.",
|
| 9 |
+
"structure": {
|
| 10 |
+
"books": 5,
|
| 11 |
+
"definitions": 18,
|
| 12 |
+
"propositions": 25,
|
| 13 |
+
"foundationTypes": [
|
| 14 |
+
"definition"
|
| 15 |
+
]
|
| 16 |
+
}
|
| 17 |
+
},
|
| 18 |
+
"metadata": {
|
| 19 |
+
"created": "2026-03-15",
|
| 20 |
+
"lastUpdated": "2026-03-15",
|
| 21 |
+
"version": "1.0.0",
|
| 22 |
+
"license": "CC BY 4.0",
|
| 23 |
+
"authors": [
|
| 24 |
+
"Welz, G."
|
| 25 |
+
],
|
| 26 |
+
"methodology": "Programming Framework",
|
| 27 |
+
"citation": "Welz, G. (2026). Euclid's Elements Book V Dependency Graph. Programming Framework.",
|
| 28 |
+
"keywords": [
|
| 29 |
+
"Euclid",
|
| 30 |
+
"Elements",
|
| 31 |
+
"Book V",
|
| 32 |
+
"proportion",
|
| 33 |
+
"ratio",
|
| 34 |
+
"Eudoxus"
|
| 35 |
+
]
|
| 36 |
+
},
|
| 37 |
+
"sources": [
|
| 38 |
+
{
|
| 39 |
+
"id": "joyce",
|
| 40 |
+
"type": "digital",
|
| 41 |
+
"authors": "Joyce, David E.",
|
| 42 |
+
"title": "Euclid's Elements, Book V",
|
| 43 |
+
"year": "1996",
|
| 44 |
+
"url": "https://mathcs.clarku.edu/~djoyce/java/elements/bookV/bookV.html",
|
| 45 |
+
"notes": "Clark University; Logical structure"
|
| 46 |
+
}
|
| 47 |
+
],
|
| 48 |
+
"nodes": [
|
| 49 |
+
{
|
| 50 |
+
"id": "Def1",
|
| 51 |
+
"type": "definition",
|
| 52 |
+
"label": "A magnitude is a part of a magnitude when it measures it",
|
| 53 |
+
"shortLabel": "Def. V.1",
|
| 54 |
+
"short": "Part",
|
| 55 |
+
"book": 5,
|
| 56 |
+
"number": 1,
|
| 57 |
+
"colorClass": "definition"
|
| 58 |
+
},
|
| 59 |
+
{
|
| 60 |
+
"id": "Def2",
|
| 61 |
+
"type": "definition",
|
| 62 |
+
"label": "The greater is a multiple of the less when it is measured by the less",
|
| 63 |
+
"shortLabel": "Def. V.2",
|
| 64 |
+
"short": "Multiple",
|
| 65 |
+
"book": 5,
|
| 66 |
+
"number": 2,
|
| 67 |
+
"colorClass": "definition"
|
| 68 |
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},
|
| 69 |
+
{
|
| 70 |
+
"id": "Def3",
|
| 71 |
+
"type": "definition",
|
| 72 |
+
"label": "A ratio is a sort of relation in respect of size between two magnitudes",
|
| 73 |
+
"shortLabel": "Def. V.3",
|
| 74 |
+
"short": "Ratio",
|
| 75 |
+
"book": 5,
|
| 76 |
+
"number": 3,
|
| 77 |
+
"colorClass": "definition"
|
| 78 |
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},
|
| 79 |
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{
|
| 80 |
+
"id": "Def4",
|
| 81 |
+
"type": "definition",
|
| 82 |
+
"label": "Magnitudes have a ratio when the less can be multiplied to exceed the greater",
|
| 83 |
+
"shortLabel": "Def. V.4",
|
| 84 |
+
"short": "Same ratio",
|
| 85 |
+
"book": 5,
|
| 86 |
+
"number": 4,
|
| 87 |
+
"colorClass": "definition"
|
| 88 |
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},
|
| 89 |
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{
|
| 90 |
+
"id": "Def5",
|
| 91 |
+
"type": "definition",
|
| 92 |
+
"label": "Magnitudes in same ratio when equimultiples alike exceed, equal, or fall short",
|
| 93 |
+
"shortLabel": "Def. V.5",
|
| 94 |
+
"short": "In same ratio (Eudoxus)",
|
| 95 |
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"book": 5,
|
| 96 |
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"number": 5,
|
| 97 |
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"colorClass": "definition"
|
| 98 |
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},
|
| 99 |
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{
|
| 100 |
+
"id": "Def6",
|
| 101 |
+
"type": "definition",
|
| 102 |
+
"label": "Magnitudes which have the same ratio are proportional",
|
| 103 |
+
"shortLabel": "Def. V.6",
|
| 104 |
+
"short": "Proportional",
|
| 105 |
+
"book": 5,
|
| 106 |
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"number": 6,
|
| 107 |
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"colorClass": "definition"
|
| 108 |
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},
|
| 109 |
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{
|
| 110 |
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"id": "Def7",
|
| 111 |
+
"type": "definition",
|
| 112 |
+
"label": "When of equimultiples first exceeds second, third does not exceed fourth",
|
| 113 |
+
"shortLabel": "Def. V.7",
|
| 114 |
+
"short": "Greater ratio",
|
| 115 |
+
"book": 5,
|
| 116 |
+
"number": 7,
|
| 117 |
+
"colorClass": "definition"
|
| 118 |
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},
|
| 119 |
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{
|
| 120 |
+
"id": "Def8",
|
| 121 |
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"type": "definition",
|
| 122 |
+
"label": "Compound ratio is the ratio of the products of corresponding terms",
|
| 123 |
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"shortLabel": "Def. V.8",
|
| 124 |
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"short": "Compound ratio",
|
| 125 |
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"book": 5,
|
| 126 |
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"number": 8,
|
| 127 |
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"colorClass": "definition"
|
| 128 |
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},
|
| 129 |
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{
|
| 130 |
+
"id": "Def9",
|
| 131 |
+
"type": "definition",
|
| 132 |
+
"label": "Duplicate ratio is the ratio of the squares",
|
| 133 |
+
"shortLabel": "Def. V.9",
|
| 134 |
+
"short": "Duplicate ratio",
|
| 135 |
+
"book": 5,
|
| 136 |
+
"number": 9,
|
| 137 |
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"colorClass": "definition"
|
| 138 |
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},
|
| 139 |
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{
|
| 140 |
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"id": "Def10",
|
| 141 |
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"type": "definition",
|
| 142 |
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"label": "Triplicate ratio is the ratio of the cubes",
|
| 143 |
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"shortLabel": "Def. V.10",
|
| 144 |
+
"short": "Triplicate ratio",
|
| 145 |
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"book": 5,
|
| 146 |
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"number": 10,
|
| 147 |
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"colorClass": "definition"
|
| 148 |
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},
|
| 149 |
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{
|
| 150 |
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"id": "Def11",
|
| 151 |
+
"type": "definition",
|
| 152 |
+
"label": "Corresponding magnitudes in proportion",
|
| 153 |
+
"shortLabel": "Def. V.11",
|
| 154 |
+
"short": "Corresponding magnitudes",
|
| 155 |
+
"book": 5,
|
| 156 |
+
"number": 11,
|
| 157 |
+
"colorClass": "definition"
|
| 158 |
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},
|
| 159 |
+
{
|
| 160 |
+
"id": "Def12",
|
| 161 |
+
"type": "definition",
|
| 162 |
+
"label": "Alternate: first to third as second to fourth",
|
| 163 |
+
"shortLabel": "Def. V.12",
|
| 164 |
+
"short": "Alternate ratio",
|
| 165 |
+
"book": 5,
|
| 166 |
+
"number": 12,
|
| 167 |
+
"colorClass": "definition"
|
| 168 |
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},
|
| 169 |
+
{
|
| 170 |
+
"id": "Def13",
|
| 171 |
+
"type": "definition",
|
| 172 |
+
"label": "Inverse: second to first as fourth to third",
|
| 173 |
+
"shortLabel": "Def. V.13",
|
| 174 |
+
"short": "Inverse ratio",
|
| 175 |
+
"book": 5,
|
| 176 |
+
"number": 13,
|
| 177 |
+
"colorClass": "definition"
|
| 178 |
+
},
|
| 179 |
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{
|
| 180 |
+
"id": "Def14",
|
| 181 |
+
"type": "definition",
|
| 182 |
+
"label": "Composition: first+second to second as third+fourth to fourth",
|
| 183 |
+
"shortLabel": "Def. V.14",
|
| 184 |
+
"short": "Composition of ratio",
|
| 185 |
+
"book": 5,
|
| 186 |
+
"number": 14,
|
| 187 |
+
"colorClass": "definition"
|
| 188 |
+
},
|
| 189 |
+
{
|
| 190 |
+
"id": "Def15",
|
| 191 |
+
"type": "definition",
|
| 192 |
+
"label": "Separation: first−second to second as third−fourth to fourth",
|
| 193 |
+
"shortLabel": "Def. V.15",
|
| 194 |
+
"short": "Separation of ratio",
|
| 195 |
+
"book": 5,
|
| 196 |
+
"number": 15,
|
| 197 |
+
"colorClass": "definition"
|
| 198 |
+
},
|
| 199 |
+
{
|
| 200 |
+
"id": "Def16",
|
| 201 |
+
"type": "definition",
|
| 202 |
+
"label": "Conversion: first to first−second as third to third−fourth",
|
| 203 |
+
"shortLabel": "Def. V.16",
|
| 204 |
+
"short": "Conversion of ratio",
|
| 205 |
+
"book": 5,
|
| 206 |
+
"number": 16,
|
| 207 |
+
"colorClass": "definition"
|
| 208 |
+
},
|
| 209 |
+
{
|
| 210 |
+
"id": "Def17",
|
| 211 |
+
"type": "definition",
|
| 212 |
+
"label": "Ex aequali: when first to second as second to third",
|
| 213 |
+
"shortLabel": "Def. V.17",
|
| 214 |
+
"short": "Ex aequali",
|
| 215 |
+
"book": 5,
|
| 216 |
+
"number": 17,
|
| 217 |
+
"colorClass": "definition"
|
| 218 |
+
},
|
| 219 |
+
{
|
| 220 |
+
"id": "Def18",
|
| 221 |
+
"type": "definition",
|
| 222 |
+
"label": "Ex aequali perturbed: when ratios are in perturbed order",
|
| 223 |
+
"shortLabel": "Def. V.18",
|
| 224 |
+
"short": "Ex aequali perturbed",
|
| 225 |
+
"book": 5,
|
| 226 |
+
"number": 18,
|
| 227 |
+
"colorClass": "definition"
|
| 228 |
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},
|
| 229 |
+
{
|
| 230 |
+
"id": "Prop1",
|
| 231 |
+
"type": "proposition",
|
| 232 |
+
"label": "If magnitudes each same multiple of others, sum is that multiple of sum",
|
| 233 |
+
"shortLabel": "Prop. V.1",
|
| 234 |
+
"short": "Sum of multiples",
|
| 235 |
+
"book": 5,
|
| 236 |
+
"number": 1,
|
| 237 |
+
"colorClass": "proposition"
|
| 238 |
+
},
|
| 239 |
+
{
|
| 240 |
+
"id": "Prop2",
|
| 241 |
+
"type": "proposition",
|
| 242 |
+
"label": "If first:second as third:fourth, sum of first and fifth as sum of third and sixth",
|
| 243 |
+
"shortLabel": "Prop. V.2",
|
| 244 |
+
"short": "Equimultiples sum",
|
| 245 |
+
"book": 5,
|
| 246 |
+
"number": 2,
|
| 247 |
+
"colorClass": "proposition"
|
| 248 |
+
},
|
| 249 |
+
{
|
| 250 |
+
"id": "Prop3",
|
| 251 |
+
"type": "proposition",
|
| 252 |
+
"label": "Equimultiples of equimultiples are equimultiples",
|
| 253 |
+
"shortLabel": "Prop. V.3",
|
| 254 |
+
"short": "Equimultiples of equimultiples",
|
| 255 |
+
"book": 5,
|
| 256 |
+
"number": 3,
|
| 257 |
+
"colorClass": "proposition"
|
| 258 |
+
},
|
| 259 |
+
{
|
| 260 |
+
"id": "Prop4",
|
| 261 |
+
"type": "proposition",
|
| 262 |
+
"label": "If a:b = c:d, then ma:nb = mc:nd",
|
| 263 |
+
"shortLabel": "Prop. V.4",
|
| 264 |
+
"short": "Equimultiples preserve ratio",
|
| 265 |
+
"book": 5,
|
| 266 |
+
"number": 4,
|
| 267 |
+
"colorClass": "proposition"
|
| 268 |
+
},
|
| 269 |
+
{
|
| 270 |
+
"id": "Prop5",
|
| 271 |
+
"type": "proposition",
|
| 272 |
+
"label": "Multiple of whole minus multiple of part = multiple of remainder",
|
| 273 |
+
"shortLabel": "Prop. V.5",
|
| 274 |
+
"short": "Multiple of difference",
|
| 275 |
+
"book": 5,
|
| 276 |
+
"number": 5,
|
| 277 |
+
"colorClass": "proposition"
|
| 278 |
+
},
|
| 279 |
+
{
|
| 280 |
+
"id": "Prop6",
|
| 281 |
+
"type": "proposition",
|
| 282 |
+
"label": "Equimultiples minus equimultiples equal or equimultiples",
|
| 283 |
+
"shortLabel": "Prop. V.6",
|
| 284 |
+
"short": "Equimultiples minus equimultiples",
|
| 285 |
+
"book": 5,
|
| 286 |
+
"number": 6,
|
| 287 |
+
"colorClass": "proposition"
|
| 288 |
+
},
|
| 289 |
+
{
|
| 290 |
+
"id": "Prop7",
|
| 291 |
+
"type": "proposition",
|
| 292 |
+
"label": "Equal magnitudes have same ratio to same; same to equals",
|
| 293 |
+
"shortLabel": "Prop. V.7",
|
| 294 |
+
"short": "Equals in ratio",
|
| 295 |
+
"book": 5,
|
| 296 |
+
"number": 7,
|
| 297 |
+
"colorClass": "proposition"
|
| 298 |
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},
|
| 299 |
+
{
|
| 300 |
+
"id": "Prop8",
|
| 301 |
+
"type": "proposition",
|
| 302 |
+
"label": "Of unequal magnitudes, greater has greater ratio to same",
|
| 303 |
+
"shortLabel": "Prop. V.8",
|
| 304 |
+
"short": "Greater has greater ratio",
|
| 305 |
+
"book": 5,
|
| 306 |
+
"number": 8,
|
| 307 |
+
"colorClass": "proposition"
|
| 308 |
+
},
|
| 309 |
+
{
|
| 310 |
+
"id": "Prop9",
|
| 311 |
+
"type": "proposition",
|
| 312 |
+
"label": "Magnitudes with same ratio to same are equal",
|
| 313 |
+
"shortLabel": "Prop. V.9",
|
| 314 |
+
"short": "Same ratio implies equal",
|
| 315 |
+
"book": 5,
|
| 316 |
+
"number": 9,
|
| 317 |
+
"colorClass": "proposition"
|
| 318 |
+
},
|
| 319 |
+
{
|
| 320 |
+
"id": "Prop10",
|
| 321 |
+
"type": "proposition",
|
| 322 |
+
"label": "Of magnitudes with ratio to same, greater ratio implies greater",
|
| 323 |
+
"shortLabel": "Prop. V.10",
|
| 324 |
+
"short": "Greater ratio implies greater",
|
| 325 |
+
"book": 5,
|
| 326 |
+
"number": 10,
|
| 327 |
+
"colorClass": "proposition"
|
| 328 |
+
},
|
| 329 |
+
{
|
| 330 |
+
"id": "Prop11",
|
| 331 |
+
"type": "proposition",
|
| 332 |
+
"label": "Ratios same with same ratio are same with one another",
|
| 333 |
+
"shortLabel": "Prop. V.11",
|
| 334 |
+
"short": "Transitivity of ratios",
|
| 335 |
+
"book": 5,
|
| 336 |
+
"number": 11,
|
| 337 |
+
"colorClass": "proposition"
|
| 338 |
+
},
|
| 339 |
+
{
|
| 340 |
+
"id": "Prop12",
|
| 341 |
+
"type": "proposition",
|
| 342 |
+
"label": "Proportional: one antecedent to one consequent as sum to sum",
|
| 343 |
+
"shortLabel": "Prop. V.12",
|
| 344 |
+
"short": "Sum of antecedents/consequents",
|
| 345 |
+
"book": 5,
|
| 346 |
+
"number": 12,
|
| 347 |
+
"colorClass": "proposition"
|
| 348 |
+
},
|
| 349 |
+
{
|
| 350 |
+
"id": "Prop13",
|
| 351 |
+
"type": "proposition",
|
| 352 |
+
"label": "If a:b = c:d and c:d > e:f, then a:b > e:f",
|
| 353 |
+
"shortLabel": "Prop. V.13",
|
| 354 |
+
"short": "Substitution in ratio inequality",
|
| 355 |
+
"book": 5,
|
| 356 |
+
"number": 13,
|
| 357 |
+
"colorClass": "proposition"
|
| 358 |
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},
|
| 359 |
+
{
|
| 360 |
+
"id": "Prop14",
|
| 361 |
+
"type": "proposition",
|
| 362 |
+
"label": "If a:b = c:d and a>c, then b>d",
|
| 363 |
+
"shortLabel": "Prop. V.14",
|
| 364 |
+
"short": "Equal ratios, equal magnitudes",
|
| 365 |
+
"book": 5,
|
| 366 |
+
"number": 14,
|
| 367 |
+
"colorClass": "proposition"
|
| 368 |
+
},
|
| 369 |
+
{
|
| 370 |
+
"id": "Prop15",
|
| 371 |
+
"type": "proposition",
|
| 372 |
+
"label": "Parts have same ratio as their equimultiples",
|
| 373 |
+
"shortLabel": "Prop. V.15",
|
| 374 |
+
"short": "Parts as equimultiples",
|
| 375 |
+
"book": 5,
|
| 376 |
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"number": 15,
|
| 377 |
+
"colorClass": "proposition"
|
| 378 |
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},
|
| 379 |
+
{
|
| 380 |
+
"id": "Prop16",
|
| 381 |
+
"type": "proposition",
|
| 382 |
+
"label": "If a:b = c:d, then a:c = b:d",
|
| 383 |
+
"shortLabel": "Prop. V.16",
|
| 384 |
+
"short": "Alternate proportion",
|
| 385 |
+
"book": 5,
|
| 386 |
+
"number": 16,
|
| 387 |
+
"colorClass": "proposition"
|
| 388 |
+
},
|
| 389 |
+
{
|
| 390 |
+
"id": "Prop17",
|
| 391 |
+
"type": "proposition",
|
| 392 |
+
"label": "If (a+b):b = (c+d):d, then a:b = c:d",
|
| 393 |
+
"shortLabel": "Prop. V.17",
|
| 394 |
+
"short": "Jointly implies separately",
|
| 395 |
+
"book": 5,
|
| 396 |
+
"number": 17,
|
| 397 |
+
"colorClass": "proposition"
|
| 398 |
+
},
|
| 399 |
+
{
|
| 400 |
+
"id": "Prop18",
|
| 401 |
+
"type": "proposition",
|
| 402 |
+
"label": "If a:b = c:d, then (a+b):b = (c+d):d",
|
| 403 |
+
"shortLabel": "Prop. V.18",
|
| 404 |
+
"short": "Separately implies jointly",
|
| 405 |
+
"book": 5,
|
| 406 |
+
"number": 18,
|
| 407 |
+
"colorClass": "proposition"
|
| 408 |
+
},
|
| 409 |
+
{
|
| 410 |
+
"id": "Prop19",
|
| 411 |
+
"type": "proposition",
|
| 412 |
+
"label": "If (a+b):(c+d) = a:c, then also = b:d",
|
| 413 |
+
"shortLabel": "Prop. V.19",
|
| 414 |
+
"short": "Whole to whole as part to part",
|
| 415 |
+
"book": 5,
|
| 416 |
+
"number": 19,
|
| 417 |
+
"colorClass": "proposition"
|
| 418 |
+
},
|
| 419 |
+
{
|
| 420 |
+
"id": "Prop20",
|
| 421 |
+
"type": "proposition",
|
| 422 |
+
"label": "If a:b = d:e and b:c = e:f and a>c, then d>f",
|
| 423 |
+
"shortLabel": "Prop. V.20",
|
| 424 |
+
"short": "Ex aequali (direct)",
|
| 425 |
+
"book": 5,
|
| 426 |
+
"number": 20,
|
| 427 |
+
"colorClass": "proposition"
|
| 428 |
+
},
|
| 429 |
+
{
|
| 430 |
+
"id": "Prop21",
|
| 431 |
+
"type": "proposition",
|
| 432 |
+
"label": "If a:b = e:f and b:c = d:e and a>c, then d>f",
|
| 433 |
+
"shortLabel": "Prop. V.21",
|
| 434 |
+
"short": "Ex aequali (perturbed)",
|
| 435 |
+
"book": 5,
|
| 436 |
+
"number": 21,
|
| 437 |
+
"colorClass": "proposition"
|
| 438 |
+
},
|
| 439 |
+
{
|
| 440 |
+
"id": "Prop22",
|
| 441 |
+
"type": "proposition",
|
| 442 |
+
"label": "If a1:a2 = b1:b2, a2:a3 = b2:b3, ..., then a1:an = b1:bn",
|
| 443 |
+
"shortLabel": "Prop. V.22",
|
| 444 |
+
"short": "Ex aequali chain",
|
| 445 |
+
"book": 5,
|
| 446 |
+
"number": 22,
|
| 447 |
+
"colorClass": "proposition"
|
| 448 |
+
},
|
| 449 |
+
{
|
| 450 |
+
"id": "Prop23",
|
| 451 |
+
"type": "proposition",
|
| 452 |
+
"label": "If a:b = y:z and b:c = x:y, then a:c = x:z",
|
| 453 |
+
"shortLabel": "Prop. V.23",
|
| 454 |
+
"short": "Ex aequali perturbed chain",
|
| 455 |
+
"book": 5,
|
| 456 |
+
"number": 23,
|
| 457 |
+
"colorClass": "proposition"
|
| 458 |
+
},
|
| 459 |
+
{
|
| 460 |
+
"id": "Prop24",
|
| 461 |
+
"type": "proposition",
|
| 462 |
+
"label": "If a:b = c:d and e:b = f:d, then (a+e):b = (c+f):d",
|
| 463 |
+
"shortLabel": "Prop. V.24",
|
| 464 |
+
"short": "Sum of ratios",
|
| 465 |
+
"book": 5,
|
| 466 |
+
"number": 24,
|
| 467 |
+
"colorClass": "proposition"
|
| 468 |
+
},
|
| 469 |
+
{
|
| 470 |
+
"id": "Prop25",
|
| 471 |
+
"type": "proposition",
|
| 472 |
+
"label": "If a:b = c:d and a greatest, d least, then a+d > b+c",
|
| 473 |
+
"shortLabel": "Prop. V.25",
|
| 474 |
+
"short": "Sum of extremes > sum of means",
|
| 475 |
+
"book": 5,
|
| 476 |
+
"number": 25,
|
| 477 |
+
"colorClass": "proposition"
|
| 478 |
+
}
|
| 479 |
+
],
|
| 480 |
+
"edges": [
|
| 481 |
+
{
|
| 482 |
+
"from": "Prop2",
|
| 483 |
+
"to": "Prop3"
|
| 484 |
+
},
|
| 485 |
+
{
|
| 486 |
+
"from": "Prop3",
|
| 487 |
+
"to": "Prop4"
|
| 488 |
+
},
|
| 489 |
+
{
|
| 490 |
+
"from": "Prop1",
|
| 491 |
+
"to": "Prop5"
|
| 492 |
+
},
|
| 493 |
+
{
|
| 494 |
+
"from": "Prop2",
|
| 495 |
+
"to": "Prop6"
|
| 496 |
+
},
|
| 497 |
+
{
|
| 498 |
+
"from": "Prop1",
|
| 499 |
+
"to": "Prop8"
|
| 500 |
+
},
|
| 501 |
+
{
|
| 502 |
+
"from": "Prop8",
|
| 503 |
+
"to": "Prop9"
|
| 504 |
+
},
|
| 505 |
+
{
|
| 506 |
+
"from": "Prop7",
|
| 507 |
+
"to": "Prop10"
|
| 508 |
+
},
|
| 509 |
+
{
|
| 510 |
+
"from": "Prop8",
|
| 511 |
+
"to": "Prop10"
|
| 512 |
+
},
|
| 513 |
+
{
|
| 514 |
+
"from": "Prop1",
|
| 515 |
+
"to": "Prop12"
|
| 516 |
+
},
|
| 517 |
+
{
|
| 518 |
+
"from": "Prop8",
|
| 519 |
+
"to": "Prop14"
|
| 520 |
+
},
|
| 521 |
+
{
|
| 522 |
+
"from": "Prop10",
|
| 523 |
+
"to": "Prop14"
|
| 524 |
+
},
|
| 525 |
+
{
|
| 526 |
+
"from": "Prop13",
|
| 527 |
+
"to": "Prop14"
|
| 528 |
+
},
|
| 529 |
+
{
|
| 530 |
+
"from": "Prop7",
|
| 531 |
+
"to": "Prop15"
|
| 532 |
+
},
|
| 533 |
+
{
|
| 534 |
+
"from": "Prop12",
|
| 535 |
+
"to": "Prop15"
|
| 536 |
+
},
|
| 537 |
+
{
|
| 538 |
+
"from": "Prop11",
|
| 539 |
+
"to": "Prop16"
|
| 540 |
+
},
|
| 541 |
+
{
|
| 542 |
+
"from": "Prop14",
|
| 543 |
+
"to": "Prop16"
|
| 544 |
+
},
|
| 545 |
+
{
|
| 546 |
+
"from": "Prop15",
|
| 547 |
+
"to": "Prop16"
|
| 548 |
+
},
|
| 549 |
+
{
|
| 550 |
+
"from": "Prop1",
|
| 551 |
+
"to": "Prop17"
|
| 552 |
+
},
|
| 553 |
+
{
|
| 554 |
+
"from": "Prop2",
|
| 555 |
+
"to": "Prop17"
|
| 556 |
+
},
|
| 557 |
+
{
|
| 558 |
+
"from": "Prop11",
|
| 559 |
+
"to": "Prop18"
|
| 560 |
+
},
|
| 561 |
+
{
|
| 562 |
+
"from": "Prop14",
|
| 563 |
+
"to": "Prop18"
|
| 564 |
+
},
|
| 565 |
+
{
|
| 566 |
+
"from": "Prop17",
|
| 567 |
+
"to": "Prop18"
|
| 568 |
+
},
|
| 569 |
+
{
|
| 570 |
+
"from": "Prop11",
|
| 571 |
+
"to": "Prop19"
|
| 572 |
+
},
|
| 573 |
+
{
|
| 574 |
+
"from": "Prop16",
|
| 575 |
+
"to": "Prop19"
|
| 576 |
+
},
|
| 577 |
+
{
|
| 578 |
+
"from": "Prop17",
|
| 579 |
+
"to": "Prop19"
|
| 580 |
+
},
|
| 581 |
+
{
|
| 582 |
+
"from": "Prop7",
|
| 583 |
+
"to": "Prop20"
|
| 584 |
+
},
|
| 585 |
+
{
|
| 586 |
+
"from": "Prop8",
|
| 587 |
+
"to": "Prop20"
|
| 588 |
+
},
|
| 589 |
+
{
|
| 590 |
+
"from": "Prop10",
|
| 591 |
+
"to": "Prop20"
|
| 592 |
+
},
|
| 593 |
+
{
|
| 594 |
+
"from": "Prop13",
|
| 595 |
+
"to": "Prop20"
|
| 596 |
+
},
|
| 597 |
+
{
|
| 598 |
+
"from": "Prop7",
|
| 599 |
+
"to": "Prop21"
|
| 600 |
+
},
|
| 601 |
+
{
|
| 602 |
+
"from": "Prop8",
|
| 603 |
+
"to": "Prop21"
|
| 604 |
+
},
|
| 605 |
+
{
|
| 606 |
+
"from": "Prop10",
|
| 607 |
+
"to": "Prop21"
|
| 608 |
+
},
|
| 609 |
+
{
|
| 610 |
+
"from": "Prop13",
|
| 611 |
+
"to": "Prop21"
|
| 612 |
+
},
|
| 613 |
+
{
|
| 614 |
+
"from": "Prop4",
|
| 615 |
+
"to": "Prop22"
|
| 616 |
+
},
|
| 617 |
+
{
|
| 618 |
+
"from": "Prop20",
|
| 619 |
+
"to": "Prop22"
|
| 620 |
+
},
|
| 621 |
+
{
|
| 622 |
+
"from": "Prop11",
|
| 623 |
+
"to": "Prop23"
|
| 624 |
+
},
|
| 625 |
+
{
|
| 626 |
+
"from": "Prop15",
|
| 627 |
+
"to": "Prop23"
|
| 628 |
+
},
|
| 629 |
+
{
|
| 630 |
+
"from": "Prop16",
|
| 631 |
+
"to": "Prop23"
|
| 632 |
+
},
|
| 633 |
+
{
|
| 634 |
+
"from": "Prop21",
|
| 635 |
+
"to": "Prop23"
|
| 636 |
+
},
|
| 637 |
+
{
|
| 638 |
+
"from": "Prop7",
|
| 639 |
+
"to": "Prop24"
|
| 640 |
+
},
|
| 641 |
+
{
|
| 642 |
+
"from": "Prop18",
|
| 643 |
+
"to": "Prop24"
|
| 644 |
+
},
|
| 645 |
+
{
|
| 646 |
+
"from": "Prop22",
|
| 647 |
+
"to": "Prop24"
|
| 648 |
+
},
|
| 649 |
+
{
|
| 650 |
+
"from": "Prop7",
|
| 651 |
+
"to": "Prop25"
|
| 652 |
+
},
|
| 653 |
+
{
|
| 654 |
+
"from": "Prop11",
|
| 655 |
+
"to": "Prop25"
|
| 656 |
+
},
|
| 657 |
+
{
|
| 658 |
+
"from": "Prop14",
|
| 659 |
+
"to": "Prop25"
|
| 660 |
+
},
|
| 661 |
+
{
|
| 662 |
+
"from": "Prop19",
|
| 663 |
+
"to": "Prop25"
|
| 664 |
+
}
|
| 665 |
+
],
|
| 666 |
+
"colorScheme": {
|
| 667 |
+
"definition": {
|
| 668 |
+
"fill": "#3498db",
|
| 669 |
+
"stroke": "#2980b9"
|
| 670 |
+
},
|
| 671 |
+
"proposition": {
|
| 672 |
+
"fill": "#1abc9c",
|
| 673 |
+
"stroke": "#16a085"
|
| 674 |
+
}
|
| 675 |
+
}
|
| 676 |
+
}
|
data/euclid-elements-book-vi.json
ADDED
|
@@ -0,0 +1,875 @@
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|
| 1 |
+
{
|
| 2 |
+
"schemaVersion": "1.0",
|
| 3 |
+
"discourse": {
|
| 4 |
+
"id": "euclid-elements-book-vi",
|
| 5 |
+
"name": "Euclid's Elements, Book VI",
|
| 6 |
+
"subject": "geometry",
|
| 7 |
+
"variant": "classical",
|
| 8 |
+
"description": "Similar figures. 4 definitions, 33 propositions. Depends on Book I and Book V. VI.1 is basis for most. Source: David E. Joyce.",
|
| 9 |
+
"structure": {
|
| 10 |
+
"books": 6,
|
| 11 |
+
"definitions": 4,
|
| 12 |
+
"propositions": 33,
|
| 13 |
+
"foundationTypes": [
|
| 14 |
+
"definition",
|
| 15 |
+
"foundation"
|
| 16 |
+
]
|
| 17 |
+
}
|
| 18 |
+
},
|
| 19 |
+
"metadata": {
|
| 20 |
+
"created": "2026-03-15",
|
| 21 |
+
"lastUpdated": "2026-03-15",
|
| 22 |
+
"version": "1.0.0",
|
| 23 |
+
"license": "CC BY 4.0",
|
| 24 |
+
"authors": [
|
| 25 |
+
"Welz, G."
|
| 26 |
+
],
|
| 27 |
+
"methodology": "Programming Framework",
|
| 28 |
+
"citation": "Welz, G. (2026). Euclid's Elements Book VI Dependency Graph. Programming Framework.",
|
| 29 |
+
"keywords": [
|
| 30 |
+
"Euclid",
|
| 31 |
+
"Elements",
|
| 32 |
+
"Book VI",
|
| 33 |
+
"similar",
|
| 34 |
+
"proportion",
|
| 35 |
+
"triangles"
|
| 36 |
+
]
|
| 37 |
+
},
|
| 38 |
+
"sources": [
|
| 39 |
+
{
|
| 40 |
+
"id": "joyce",
|
| 41 |
+
"type": "digital",
|
| 42 |
+
"authors": "Joyce, David E.",
|
| 43 |
+
"title": "Euclid's Elements, Book VI",
|
| 44 |
+
"year": "1996",
|
| 45 |
+
"url": "https://mathcs.clarku.edu/~djoyce/java/elements/bookVI/bookVI.html",
|
| 46 |
+
"notes": "Clark University; VI.1 basis for most"
|
| 47 |
+
}
|
| 48 |
+
],
|
| 49 |
+
"nodes": [
|
| 50 |
+
{
|
| 51 |
+
"id": "BookI",
|
| 52 |
+
"type": "foundation",
|
| 53 |
+
"label": "Book I — Fundamentals of plane geometry",
|
| 54 |
+
"shortLabel": "Book I",
|
| 55 |
+
"short": "Foundation",
|
| 56 |
+
"book": 1,
|
| 57 |
+
"colorClass": "foundation"
|
| 58 |
+
},
|
| 59 |
+
{
|
| 60 |
+
"id": "BookV",
|
| 61 |
+
"type": "foundation",
|
| 62 |
+
"label": "Book V — Theory of proportions",
|
| 63 |
+
"shortLabel": "Book V",
|
| 64 |
+
"short": "Foundation",
|
| 65 |
+
"book": 5,
|
| 66 |
+
"colorClass": "foundation"
|
| 67 |
+
},
|
| 68 |
+
{
|
| 69 |
+
"id": "Def1",
|
| 70 |
+
"type": "definition",
|
| 71 |
+
"label": "Similar rectilinear figures have equal angles and proportional sides",
|
| 72 |
+
"shortLabel": "Def. VI.1",
|
| 73 |
+
"short": "Similar rectilinear",
|
| 74 |
+
"book": 6,
|
| 75 |
+
"number": 1,
|
| 76 |
+
"colorClass": "definition"
|
| 77 |
+
},
|
| 78 |
+
{
|
| 79 |
+
"id": "Def2",
|
| 80 |
+
"type": "definition",
|
| 81 |
+
"label": "Figures reciprocally proportional when sides are proportional inversely",
|
| 82 |
+
"shortLabel": "Def. VI.2",
|
| 83 |
+
"short": "Reciprocally proportional",
|
| 84 |
+
"book": 6,
|
| 85 |
+
"number": 2,
|
| 86 |
+
"colorClass": "definition"
|
| 87 |
+
},
|
| 88 |
+
{
|
| 89 |
+
"id": "Def3",
|
| 90 |
+
"type": "definition",
|
| 91 |
+
"label": "Straight line is mean proportional when first to it as it to third",
|
| 92 |
+
"shortLabel": "Def. VI.3",
|
| 93 |
+
"short": "Mean proportional",
|
| 94 |
+
"book": 6,
|
| 95 |
+
"number": 3,
|
| 96 |
+
"colorClass": "definition"
|
| 97 |
+
},
|
| 98 |
+
{
|
| 99 |
+
"id": "Def4",
|
| 100 |
+
"type": "definition",
|
| 101 |
+
"label": "Duplicate ratio is the ratio of the squares on corresponding sides",
|
| 102 |
+
"shortLabel": "Def. VI.4",
|
| 103 |
+
"short": "Duplicate ratio",
|
| 104 |
+
"book": 6,
|
| 105 |
+
"number": 4,
|
| 106 |
+
"colorClass": "definition"
|
| 107 |
+
},
|
| 108 |
+
{
|
| 109 |
+
"id": "Prop1",
|
| 110 |
+
"type": "proposition",
|
| 111 |
+
"label": "Triangles and parallelograms under same height are as their bases",
|
| 112 |
+
"shortLabel": "Prop. VI.1",
|
| 113 |
+
"short": "Triangles under same height",
|
| 114 |
+
"book": 6,
|
| 115 |
+
"number": 1,
|
| 116 |
+
"colorClass": "proposition"
|
| 117 |
+
},
|
| 118 |
+
{
|
| 119 |
+
"id": "Prop2",
|
| 120 |
+
"type": "proposition",
|
| 121 |
+
"label": "Line parallel to side cuts sides proportionally; converse",
|
| 122 |
+
"shortLabel": "Prop. VI.2",
|
| 123 |
+
"short": "Parallel cuts sides proportionally",
|
| 124 |
+
"book": 6,
|
| 125 |
+
"number": 2,
|
| 126 |
+
"colorClass": "proposition"
|
| 127 |
+
},
|
| 128 |
+
{
|
| 129 |
+
"id": "Prop3",
|
| 130 |
+
"type": "proposition",
|
| 131 |
+
"label": "Angle bisector: segments of base proportionally as remaining sides",
|
| 132 |
+
"shortLabel": "Prop. VI.3",
|
| 133 |
+
"short": "Angle bisector divides base",
|
| 134 |
+
"book": 6,
|
| 135 |
+
"number": 3,
|
| 136 |
+
"colorClass": "proposition"
|
| 137 |
+
},
|
| 138 |
+
{
|
| 139 |
+
"id": "Prop4",
|
| 140 |
+
"type": "proposition",
|
| 141 |
+
"label": "Equiangular triangles: sides about equal angles proportional",
|
| 142 |
+
"shortLabel": "Prop. VI.4",
|
| 143 |
+
"short": "Equiangular: sides proportional",
|
| 144 |
+
"book": 6,
|
| 145 |
+
"number": 4,
|
| 146 |
+
"colorClass": "proposition"
|
| 147 |
+
},
|
| 148 |
+
{
|
| 149 |
+
"id": "Prop5",
|
| 150 |
+
"type": "proposition",
|
| 151 |
+
"label": "If sides proportional, triangles equiangular",
|
| 152 |
+
"shortLabel": "Prop. VI.5",
|
| 153 |
+
"short": "Sides proportional: equiangular",
|
| 154 |
+
"book": 6,
|
| 155 |
+
"number": 5,
|
| 156 |
+
"colorClass": "proposition"
|
| 157 |
+
},
|
| 158 |
+
{
|
| 159 |
+
"id": "Prop6",
|
| 160 |
+
"type": "proposition",
|
| 161 |
+
"label": "One angle equal, sides about it proportional: equiangular",
|
| 162 |
+
"shortLabel": "Prop. VI.6",
|
| 163 |
+
"short": "One angle equal, sides proportional",
|
| 164 |
+
"book": 6,
|
| 165 |
+
"number": 6,
|
| 166 |
+
"colorClass": "proposition"
|
| 167 |
+
},
|
| 168 |
+
{
|
| 169 |
+
"id": "Prop7",
|
| 170 |
+
"type": "proposition",
|
| 171 |
+
"label": "One angle equal, sides about others proportional: equiangular",
|
| 172 |
+
"shortLabel": "Prop. VI.7",
|
| 173 |
+
"short": "One angle equal, other sides proportional",
|
| 174 |
+
"book": 6,
|
| 175 |
+
"number": 7,
|
| 176 |
+
"colorClass": "proposition"
|
| 177 |
+
},
|
| 178 |
+
{
|
| 179 |
+
"id": "Prop8",
|
| 180 |
+
"type": "proposition",
|
| 181 |
+
"label": "Perpendicular from right angle: triangles similar to whole",
|
| 182 |
+
"shortLabel": "Prop. VI.8",
|
| 183 |
+
"short": "Altitude in right triangle",
|
| 184 |
+
"book": 6,
|
| 185 |
+
"number": 8,
|
| 186 |
+
"colorClass": "proposition"
|
| 187 |
+
},
|
| 188 |
+
{
|
| 189 |
+
"id": "Prop9",
|
| 190 |
+
"type": "proposition",
|
| 191 |
+
"label": "To cut off a prescribed part from a given straight line",
|
| 192 |
+
"shortLabel": "Prop. VI.9",
|
| 193 |
+
"short": "Cut off prescribed part",
|
| 194 |
+
"book": 6,
|
| 195 |
+
"number": 9,
|
| 196 |
+
"colorClass": "proposition"
|
| 197 |
+
},
|
| 198 |
+
{
|
| 199 |
+
"id": "Prop10",
|
| 200 |
+
"type": "proposition",
|
| 201 |
+
"label": "To cut a given line similarly to a given cut line",
|
| 202 |
+
"shortLabel": "Prop. VI.10",
|
| 203 |
+
"short": "Cut line similarly",
|
| 204 |
+
"book": 6,
|
| 205 |
+
"number": 10,
|
| 206 |
+
"colorClass": "proposition"
|
| 207 |
+
},
|
| 208 |
+
{
|
| 209 |
+
"id": "Prop11",
|
| 210 |
+
"type": "proposition",
|
| 211 |
+
"label": "To find a third proportional to two given lines",
|
| 212 |
+
"shortLabel": "Prop. VI.11",
|
| 213 |
+
"short": "Third proportional",
|
| 214 |
+
"book": 6,
|
| 215 |
+
"number": 11,
|
| 216 |
+
"colorClass": "proposition"
|
| 217 |
+
},
|
| 218 |
+
{
|
| 219 |
+
"id": "Prop12",
|
| 220 |
+
"type": "proposition",
|
| 221 |
+
"label": "To find a fourth proportional to three given lines",
|
| 222 |
+
"shortLabel": "Prop. VI.12",
|
| 223 |
+
"short": "Fourth proportional",
|
| 224 |
+
"book": 6,
|
| 225 |
+
"number": 12,
|
| 226 |
+
"colorClass": "proposition"
|
| 227 |
+
},
|
| 228 |
+
{
|
| 229 |
+
"id": "Prop13",
|
| 230 |
+
"type": "proposition",
|
| 231 |
+
"label": "To find a mean proportional to two given lines",
|
| 232 |
+
"shortLabel": "Prop. VI.13",
|
| 233 |
+
"short": "Mean proportional",
|
| 234 |
+
"book": 6,
|
| 235 |
+
"number": 13,
|
| 236 |
+
"colorClass": "proposition"
|
| 237 |
+
},
|
| 238 |
+
{
|
| 239 |
+
"id": "Prop14",
|
| 240 |
+
"type": "proposition",
|
| 241 |
+
"label": "Equal equiangular parallelograms: sides reciprocally proportional",
|
| 242 |
+
"shortLabel": "Prop. VI.14",
|
| 243 |
+
"short": "Parallelograms reciprocally proportional",
|
| 244 |
+
"book": 6,
|
| 245 |
+
"number": 14,
|
| 246 |
+
"colorClass": "proposition"
|
| 247 |
+
},
|
| 248 |
+
{
|
| 249 |
+
"id": "Prop15",
|
| 250 |
+
"type": "proposition",
|
| 251 |
+
"label": "Equal triangles, one angle equal: sides reciprocally proportional",
|
| 252 |
+
"shortLabel": "Prop. VI.15",
|
| 253 |
+
"short": "Triangles reciprocally proportional",
|
| 254 |
+
"book": 6,
|
| 255 |
+
"number": 15,
|
| 256 |
+
"colorClass": "proposition"
|
| 257 |
+
},
|
| 258 |
+
{
|
| 259 |
+
"id": "Prop16",
|
| 260 |
+
"type": "proposition",
|
| 261 |
+
"label": "Four lines proportional iff rectangle extremes = rectangle means",
|
| 262 |
+
"shortLabel": "Prop. VI.16",
|
| 263 |
+
"short": "Four lines proportional: rectangle",
|
| 264 |
+
"book": 6,
|
| 265 |
+
"number": 16,
|
| 266 |
+
"colorClass": "proposition"
|
| 267 |
+
},
|
| 268 |
+
{
|
| 269 |
+
"id": "Prop17",
|
| 270 |
+
"type": "proposition",
|
| 271 |
+
"label": "Three lines proportional iff rectangle extremes = square on mean",
|
| 272 |
+
"shortLabel": "Prop. VI.17",
|
| 273 |
+
"short": "Three lines proportional: rectangle",
|
| 274 |
+
"book": 6,
|
| 275 |
+
"number": 17,
|
| 276 |
+
"colorClass": "proposition"
|
| 277 |
+
},
|
| 278 |
+
{
|
| 279 |
+
"id": "Prop18",
|
| 280 |
+
"type": "proposition",
|
| 281 |
+
"label": "To describe figure similar to given on given line",
|
| 282 |
+
"shortLabel": "Prop. VI.18",
|
| 283 |
+
"short": "Similar figure on given line",
|
| 284 |
+
"book": 6,
|
| 285 |
+
"number": 18,
|
| 286 |
+
"colorClass": "proposition"
|
| 287 |
+
},
|
| 288 |
+
{
|
| 289 |
+
"id": "Prop19",
|
| 290 |
+
"type": "proposition",
|
| 291 |
+
"label": "Similar triangles in duplicate ratio of corresponding sides",
|
| 292 |
+
"shortLabel": "Prop. VI.19",
|
| 293 |
+
"short": "Similar triangles: duplicate ratio",
|
| 294 |
+
"book": 6,
|
| 295 |
+
"number": 19,
|
| 296 |
+
"colorClass": "proposition"
|
| 297 |
+
},
|
| 298 |
+
{
|
| 299 |
+
"id": "Prop20",
|
| 300 |
+
"type": "proposition",
|
| 301 |
+
"label": "Similar polygons in duplicate ratio of corresponding sides",
|
| 302 |
+
"shortLabel": "Prop. VI.20",
|
| 303 |
+
"short": "Similar polygons: duplicate ratio",
|
| 304 |
+
"book": 6,
|
| 305 |
+
"number": 20,
|
| 306 |
+
"colorClass": "proposition"
|
| 307 |
+
},
|
| 308 |
+
{
|
| 309 |
+
"id": "Prop21",
|
| 310 |
+
"type": "proposition",
|
| 311 |
+
"label": "Figures similar to same rectilinear figure are similar",
|
| 312 |
+
"shortLabel": "Prop. VI.21",
|
| 313 |
+
"short": "Similar to same: similar",
|
| 314 |
+
"book": 6,
|
| 315 |
+
"number": 21,
|
| 316 |
+
"colorClass": "proposition"
|
| 317 |
+
},
|
| 318 |
+
{
|
| 319 |
+
"id": "Prop22",
|
| 320 |
+
"type": "proposition",
|
| 321 |
+
"label": "Four lines proportional iff similar figures on them proportional",
|
| 322 |
+
"shortLabel": "Prop. VI.22",
|
| 323 |
+
"short": "Four lines proportional: figures",
|
| 324 |
+
"book": 6,
|
| 325 |
+
"number": 22,
|
| 326 |
+
"colorClass": "proposition"
|
| 327 |
+
},
|
| 328 |
+
{
|
| 329 |
+
"id": "Prop23",
|
| 330 |
+
"type": "proposition",
|
| 331 |
+
"label": "Equiangular parallelograms: ratio compounded of sides",
|
| 332 |
+
"shortLabel": "Prop. VI.23",
|
| 333 |
+
"short": "Equiangular parallelograms: compound ratio",
|
| 334 |
+
"book": 6,
|
| 335 |
+
"number": 23,
|
| 336 |
+
"colorClass": "proposition"
|
| 337 |
+
},
|
| 338 |
+
{
|
| 339 |
+
"id": "Prop24",
|
| 340 |
+
"type": "proposition",
|
| 341 |
+
"label": "Parallelograms about diameter similar to whole",
|
| 342 |
+
"shortLabel": "Prop. VI.24",
|
| 343 |
+
"short": "Parallelograms about diameter",
|
| 344 |
+
"book": 6,
|
| 345 |
+
"number": 24,
|
| 346 |
+
"colorClass": "proposition"
|
| 347 |
+
},
|
| 348 |
+
{
|
| 349 |
+
"id": "Prop25",
|
| 350 |
+
"type": "proposition",
|
| 351 |
+
"label": "To construct figure similar to one and equal to another",
|
| 352 |
+
"shortLabel": "Prop. VI.25",
|
| 353 |
+
"short": "Similar and equal to another",
|
| 354 |
+
"book": 6,
|
| 355 |
+
"number": 25,
|
| 356 |
+
"colorClass": "proposition"
|
| 357 |
+
},
|
| 358 |
+
{
|
| 359 |
+
"id": "Prop26",
|
| 360 |
+
"type": "proposition",
|
| 361 |
+
"label": "Parallelogram similar to whole, common angle: about same diameter",
|
| 362 |
+
"shortLabel": "Prop. VI.26",
|
| 363 |
+
"short": "Parallelogram similar to difference",
|
| 364 |
+
"book": 6,
|
| 365 |
+
"number": 26,
|
| 366 |
+
"colorClass": "proposition"
|
| 367 |
+
},
|
| 368 |
+
{
|
| 369 |
+
"id": "Prop27",
|
| 370 |
+
"type": "proposition",
|
| 371 |
+
"label": "Of parallelograms applied to line, greatest is on half",
|
| 372 |
+
"shortLabel": "Prop. VI.27",
|
| 373 |
+
"short": "Greatest parallelogram applied",
|
| 374 |
+
"book": 6,
|
| 375 |
+
"number": 27,
|
| 376 |
+
"colorClass": "proposition"
|
| 377 |
+
},
|
| 378 |
+
{
|
| 379 |
+
"id": "Prop28",
|
| 380 |
+
"type": "proposition",
|
| 381 |
+
"label": "To apply parallelogram equal to figure, deficient by similar",
|
| 382 |
+
"shortLabel": "Prop. VI.28",
|
| 383 |
+
"short": "Apply parallelogram: deficient",
|
| 384 |
+
"book": 6,
|
| 385 |
+
"number": 28,
|
| 386 |
+
"colorClass": "proposition"
|
| 387 |
+
},
|
| 388 |
+
{
|
| 389 |
+
"id": "Prop29",
|
| 390 |
+
"type": "proposition",
|
| 391 |
+
"label": "To apply parallelogram equal to figure, exceeding by similar",
|
| 392 |
+
"shortLabel": "Prop. VI.29",
|
| 393 |
+
"short": "Apply parallelogram: exceeding",
|
| 394 |
+
"book": 6,
|
| 395 |
+
"number": 29,
|
| 396 |
+
"colorClass": "proposition"
|
| 397 |
+
},
|
| 398 |
+
{
|
| 399 |
+
"id": "Prop30",
|
| 400 |
+
"type": "proposition",
|
| 401 |
+
"label": "To cut a given line in extreme and mean ratio",
|
| 402 |
+
"shortLabel": "Prop. VI.30",
|
| 403 |
+
"short": "Extreme and mean ratio",
|
| 404 |
+
"book": 6,
|
| 405 |
+
"number": 30,
|
| 406 |
+
"colorClass": "proposition"
|
| 407 |
+
},
|
| 408 |
+
{
|
| 409 |
+
"id": "Prop31",
|
| 410 |
+
"type": "proposition",
|
| 411 |
+
"label": "In right triangle, figure on hypotenuse = sum of similar on sides",
|
| 412 |
+
"shortLabel": "Prop. VI.31",
|
| 413 |
+
"short": "Right triangle: similar figures",
|
| 414 |
+
"book": 6,
|
| 415 |
+
"number": 31,
|
| 416 |
+
"colorClass": "proposition"
|
| 417 |
+
},
|
| 418 |
+
{
|
| 419 |
+
"id": "Prop32",
|
| 420 |
+
"type": "proposition",
|
| 421 |
+
"label": "Two triangles, two sides proportional, placed with parallel sides",
|
| 422 |
+
"shortLabel": "Prop. VI.32",
|
| 423 |
+
"short": "Two triangles: sides parallel",
|
| 424 |
+
"book": 6,
|
| 425 |
+
"number": 32,
|
| 426 |
+
"colorClass": "proposition"
|
| 427 |
+
},
|
| 428 |
+
{
|
| 429 |
+
"id": "Prop33",
|
| 430 |
+
"type": "proposition",
|
| 431 |
+
"label": "Angles in equal circles have ratio of circumferences",
|
| 432 |
+
"shortLabel": "Prop. VI.33",
|
| 433 |
+
"short": "Angles in circles: ratio of arcs",
|
| 434 |
+
"book": 6,
|
| 435 |
+
"number": 33,
|
| 436 |
+
"colorClass": "proposition"
|
| 437 |
+
}
|
| 438 |
+
],
|
| 439 |
+
"edges": [
|
| 440 |
+
{
|
| 441 |
+
"from": "BookI",
|
| 442 |
+
"to": "Def1"
|
| 443 |
+
},
|
| 444 |
+
{
|
| 445 |
+
"from": "BookV",
|
| 446 |
+
"to": "Def1"
|
| 447 |
+
},
|
| 448 |
+
{
|
| 449 |
+
"from": "BookI",
|
| 450 |
+
"to": "Def2"
|
| 451 |
+
},
|
| 452 |
+
{
|
| 453 |
+
"from": "BookV",
|
| 454 |
+
"to": "Def2"
|
| 455 |
+
},
|
| 456 |
+
{
|
| 457 |
+
"from": "BookI",
|
| 458 |
+
"to": "Def3"
|
| 459 |
+
},
|
| 460 |
+
{
|
| 461 |
+
"from": "BookV",
|
| 462 |
+
"to": "Def3"
|
| 463 |
+
},
|
| 464 |
+
{
|
| 465 |
+
"from": "BookI",
|
| 466 |
+
"to": "Def4"
|
| 467 |
+
},
|
| 468 |
+
{
|
| 469 |
+
"from": "BookV",
|
| 470 |
+
"to": "Def4"
|
| 471 |
+
},
|
| 472 |
+
{
|
| 473 |
+
"from": "BookI",
|
| 474 |
+
"to": "Prop1"
|
| 475 |
+
},
|
| 476 |
+
{
|
| 477 |
+
"from": "BookV",
|
| 478 |
+
"to": "Prop1"
|
| 479 |
+
},
|
| 480 |
+
{
|
| 481 |
+
"from": "BookI",
|
| 482 |
+
"to": "Prop2"
|
| 483 |
+
},
|
| 484 |
+
{
|
| 485 |
+
"from": "BookV",
|
| 486 |
+
"to": "Prop2"
|
| 487 |
+
},
|
| 488 |
+
{
|
| 489 |
+
"from": "Prop1",
|
| 490 |
+
"to": "Prop2"
|
| 491 |
+
},
|
| 492 |
+
{
|
| 493 |
+
"from": "BookI",
|
| 494 |
+
"to": "Prop3"
|
| 495 |
+
},
|
| 496 |
+
{
|
| 497 |
+
"from": "BookV",
|
| 498 |
+
"to": "Prop3"
|
| 499 |
+
},
|
| 500 |
+
{
|
| 501 |
+
"from": "Prop1",
|
| 502 |
+
"to": "Prop3"
|
| 503 |
+
},
|
| 504 |
+
{
|
| 505 |
+
"from": "BookI",
|
| 506 |
+
"to": "Prop4"
|
| 507 |
+
},
|
| 508 |
+
{
|
| 509 |
+
"from": "BookV",
|
| 510 |
+
"to": "Prop4"
|
| 511 |
+
},
|
| 512 |
+
{
|
| 513 |
+
"from": "Prop1",
|
| 514 |
+
"to": "Prop4"
|
| 515 |
+
},
|
| 516 |
+
{
|
| 517 |
+
"from": "BookI",
|
| 518 |
+
"to": "Prop5"
|
| 519 |
+
},
|
| 520 |
+
{
|
| 521 |
+
"from": "BookV",
|
| 522 |
+
"to": "Prop5"
|
| 523 |
+
},
|
| 524 |
+
{
|
| 525 |
+
"from": "Prop1",
|
| 526 |
+
"to": "Prop5"
|
| 527 |
+
},
|
| 528 |
+
{
|
| 529 |
+
"from": "BookI",
|
| 530 |
+
"to": "Prop6"
|
| 531 |
+
},
|
| 532 |
+
{
|
| 533 |
+
"from": "BookV",
|
| 534 |
+
"to": "Prop6"
|
| 535 |
+
},
|
| 536 |
+
{
|
| 537 |
+
"from": "Prop1",
|
| 538 |
+
"to": "Prop6"
|
| 539 |
+
},
|
| 540 |
+
{
|
| 541 |
+
"from": "BookI",
|
| 542 |
+
"to": "Prop7"
|
| 543 |
+
},
|
| 544 |
+
{
|
| 545 |
+
"from": "BookV",
|
| 546 |
+
"to": "Prop7"
|
| 547 |
+
},
|
| 548 |
+
{
|
| 549 |
+
"from": "Prop1",
|
| 550 |
+
"to": "Prop7"
|
| 551 |
+
},
|
| 552 |
+
{
|
| 553 |
+
"from": "BookI",
|
| 554 |
+
"to": "Prop8"
|
| 555 |
+
},
|
| 556 |
+
{
|
| 557 |
+
"from": "BookV",
|
| 558 |
+
"to": "Prop8"
|
| 559 |
+
},
|
| 560 |
+
{
|
| 561 |
+
"from": "Prop1",
|
| 562 |
+
"to": "Prop8"
|
| 563 |
+
},
|
| 564 |
+
{
|
| 565 |
+
"from": "BookI",
|
| 566 |
+
"to": "Prop9"
|
| 567 |
+
},
|
| 568 |
+
{
|
| 569 |
+
"from": "BookV",
|
| 570 |
+
"to": "Prop9"
|
| 571 |
+
},
|
| 572 |
+
{
|
| 573 |
+
"from": "Prop1",
|
| 574 |
+
"to": "Prop9"
|
| 575 |
+
},
|
| 576 |
+
{
|
| 577 |
+
"from": "BookI",
|
| 578 |
+
"to": "Prop10"
|
| 579 |
+
},
|
| 580 |
+
{
|
| 581 |
+
"from": "BookV",
|
| 582 |
+
"to": "Prop10"
|
| 583 |
+
},
|
| 584 |
+
{
|
| 585 |
+
"from": "Prop1",
|
| 586 |
+
"to": "Prop10"
|
| 587 |
+
},
|
| 588 |
+
{
|
| 589 |
+
"from": "BookI",
|
| 590 |
+
"to": "Prop11"
|
| 591 |
+
},
|
| 592 |
+
{
|
| 593 |
+
"from": "BookV",
|
| 594 |
+
"to": "Prop11"
|
| 595 |
+
},
|
| 596 |
+
{
|
| 597 |
+
"from": "Prop1",
|
| 598 |
+
"to": "Prop11"
|
| 599 |
+
},
|
| 600 |
+
{
|
| 601 |
+
"from": "BookI",
|
| 602 |
+
"to": "Prop12"
|
| 603 |
+
},
|
| 604 |
+
{
|
| 605 |
+
"from": "BookV",
|
| 606 |
+
"to": "Prop12"
|
| 607 |
+
},
|
| 608 |
+
{
|
| 609 |
+
"from": "Prop1",
|
| 610 |
+
"to": "Prop12"
|
| 611 |
+
},
|
| 612 |
+
{
|
| 613 |
+
"from": "BookI",
|
| 614 |
+
"to": "Prop13"
|
| 615 |
+
},
|
| 616 |
+
{
|
| 617 |
+
"from": "BookV",
|
| 618 |
+
"to": "Prop13"
|
| 619 |
+
},
|
| 620 |
+
{
|
| 621 |
+
"from": "Prop1",
|
| 622 |
+
"to": "Prop13"
|
| 623 |
+
},
|
| 624 |
+
{
|
| 625 |
+
"from": "BookI",
|
| 626 |
+
"to": "Prop14"
|
| 627 |
+
},
|
| 628 |
+
{
|
| 629 |
+
"from": "BookV",
|
| 630 |
+
"to": "Prop14"
|
| 631 |
+
},
|
| 632 |
+
{
|
| 633 |
+
"from": "Prop1",
|
| 634 |
+
"to": "Prop14"
|
| 635 |
+
},
|
| 636 |
+
{
|
| 637 |
+
"from": "BookI",
|
| 638 |
+
"to": "Prop15"
|
| 639 |
+
},
|
| 640 |
+
{
|
| 641 |
+
"from": "BookV",
|
| 642 |
+
"to": "Prop15"
|
| 643 |
+
},
|
| 644 |
+
{
|
| 645 |
+
"from": "Prop1",
|
| 646 |
+
"to": "Prop15"
|
| 647 |
+
},
|
| 648 |
+
{
|
| 649 |
+
"from": "BookI",
|
| 650 |
+
"to": "Prop16"
|
| 651 |
+
},
|
| 652 |
+
{
|
| 653 |
+
"from": "BookV",
|
| 654 |
+
"to": "Prop16"
|
| 655 |
+
},
|
| 656 |
+
{
|
| 657 |
+
"from": "Prop1",
|
| 658 |
+
"to": "Prop16"
|
| 659 |
+
},
|
| 660 |
+
{
|
| 661 |
+
"from": "BookI",
|
| 662 |
+
"to": "Prop17"
|
| 663 |
+
},
|
| 664 |
+
{
|
| 665 |
+
"from": "BookV",
|
| 666 |
+
"to": "Prop17"
|
| 667 |
+
},
|
| 668 |
+
{
|
| 669 |
+
"from": "Prop1",
|
| 670 |
+
"to": "Prop17"
|
| 671 |
+
},
|
| 672 |
+
{
|
| 673 |
+
"from": "BookI",
|
| 674 |
+
"to": "Prop18"
|
| 675 |
+
},
|
| 676 |
+
{
|
| 677 |
+
"from": "BookV",
|
| 678 |
+
"to": "Prop18"
|
| 679 |
+
},
|
| 680 |
+
{
|
| 681 |
+
"from": "Prop1",
|
| 682 |
+
"to": "Prop18"
|
| 683 |
+
},
|
| 684 |
+
{
|
| 685 |
+
"from": "BookI",
|
| 686 |
+
"to": "Prop19"
|
| 687 |
+
},
|
| 688 |
+
{
|
| 689 |
+
"from": "BookV",
|
| 690 |
+
"to": "Prop19"
|
| 691 |
+
},
|
| 692 |
+
{
|
| 693 |
+
"from": "Prop1",
|
| 694 |
+
"to": "Prop19"
|
| 695 |
+
},
|
| 696 |
+
{
|
| 697 |
+
"from": "BookI",
|
| 698 |
+
"to": "Prop20"
|
| 699 |
+
},
|
| 700 |
+
{
|
| 701 |
+
"from": "BookV",
|
| 702 |
+
"to": "Prop20"
|
| 703 |
+
},
|
| 704 |
+
{
|
| 705 |
+
"from": "Prop1",
|
| 706 |
+
"to": "Prop20"
|
| 707 |
+
},
|
| 708 |
+
{
|
| 709 |
+
"from": "BookI",
|
| 710 |
+
"to": "Prop21"
|
| 711 |
+
},
|
| 712 |
+
{
|
| 713 |
+
"from": "BookV",
|
| 714 |
+
"to": "Prop21"
|
| 715 |
+
},
|
| 716 |
+
{
|
| 717 |
+
"from": "Prop1",
|
| 718 |
+
"to": "Prop21"
|
| 719 |
+
},
|
| 720 |
+
{
|
| 721 |
+
"from": "BookI",
|
| 722 |
+
"to": "Prop22"
|
| 723 |
+
},
|
| 724 |
+
{
|
| 725 |
+
"from": "BookV",
|
| 726 |
+
"to": "Prop22"
|
| 727 |
+
},
|
| 728 |
+
{
|
| 729 |
+
"from": "Prop1",
|
| 730 |
+
"to": "Prop22"
|
| 731 |
+
},
|
| 732 |
+
{
|
| 733 |
+
"from": "BookI",
|
| 734 |
+
"to": "Prop23"
|
| 735 |
+
},
|
| 736 |
+
{
|
| 737 |
+
"from": "BookV",
|
| 738 |
+
"to": "Prop23"
|
| 739 |
+
},
|
| 740 |
+
{
|
| 741 |
+
"from": "Prop1",
|
| 742 |
+
"to": "Prop23"
|
| 743 |
+
},
|
| 744 |
+
{
|
| 745 |
+
"from": "BookI",
|
| 746 |
+
"to": "Prop24"
|
| 747 |
+
},
|
| 748 |
+
{
|
| 749 |
+
"from": "BookV",
|
| 750 |
+
"to": "Prop24"
|
| 751 |
+
},
|
| 752 |
+
{
|
| 753 |
+
"from": "Prop1",
|
| 754 |
+
"to": "Prop24"
|
| 755 |
+
},
|
| 756 |
+
{
|
| 757 |
+
"from": "BookI",
|
| 758 |
+
"to": "Prop25"
|
| 759 |
+
},
|
| 760 |
+
{
|
| 761 |
+
"from": "BookV",
|
| 762 |
+
"to": "Prop25"
|
| 763 |
+
},
|
| 764 |
+
{
|
| 765 |
+
"from": "Prop1",
|
| 766 |
+
"to": "Prop25"
|
| 767 |
+
},
|
| 768 |
+
{
|
| 769 |
+
"from": "BookI",
|
| 770 |
+
"to": "Prop26"
|
| 771 |
+
},
|
| 772 |
+
{
|
| 773 |
+
"from": "BookV",
|
| 774 |
+
"to": "Prop26"
|
| 775 |
+
},
|
| 776 |
+
{
|
| 777 |
+
"from": "Prop1",
|
| 778 |
+
"to": "Prop26"
|
| 779 |
+
},
|
| 780 |
+
{
|
| 781 |
+
"from": "BookI",
|
| 782 |
+
"to": "Prop27"
|
| 783 |
+
},
|
| 784 |
+
{
|
| 785 |
+
"from": "BookV",
|
| 786 |
+
"to": "Prop27"
|
| 787 |
+
},
|
| 788 |
+
{
|
| 789 |
+
"from": "Prop1",
|
| 790 |
+
"to": "Prop27"
|
| 791 |
+
},
|
| 792 |
+
{
|
| 793 |
+
"from": "BookI",
|
| 794 |
+
"to": "Prop28"
|
| 795 |
+
},
|
| 796 |
+
{
|
| 797 |
+
"from": "BookV",
|
| 798 |
+
"to": "Prop28"
|
| 799 |
+
},
|
| 800 |
+
{
|
| 801 |
+
"from": "Prop1",
|
| 802 |
+
"to": "Prop28"
|
| 803 |
+
},
|
| 804 |
+
{
|
| 805 |
+
"from": "BookI",
|
| 806 |
+
"to": "Prop29"
|
| 807 |
+
},
|
| 808 |
+
{
|
| 809 |
+
"from": "BookV",
|
| 810 |
+
"to": "Prop29"
|
| 811 |
+
},
|
| 812 |
+
{
|
| 813 |
+
"from": "Prop1",
|
| 814 |
+
"to": "Prop29"
|
| 815 |
+
},
|
| 816 |
+
{
|
| 817 |
+
"from": "BookI",
|
| 818 |
+
"to": "Prop30"
|
| 819 |
+
},
|
| 820 |
+
{
|
| 821 |
+
"from": "BookV",
|
| 822 |
+
"to": "Prop30"
|
| 823 |
+
},
|
| 824 |
+
{
|
| 825 |
+
"from": "Prop1",
|
| 826 |
+
"to": "Prop30"
|
| 827 |
+
},
|
| 828 |
+
{
|
| 829 |
+
"from": "BookI",
|
| 830 |
+
"to": "Prop31"
|
| 831 |
+
},
|
| 832 |
+
{
|
| 833 |
+
"from": "BookV",
|
| 834 |
+
"to": "Prop31"
|
| 835 |
+
},
|
| 836 |
+
{
|
| 837 |
+
"from": "Prop1",
|
| 838 |
+
"to": "Prop31"
|
| 839 |
+
},
|
| 840 |
+
{
|
| 841 |
+
"from": "BookI",
|
| 842 |
+
"to": "Prop32"
|
| 843 |
+
},
|
| 844 |
+
{
|
| 845 |
+
"from": "BookV",
|
| 846 |
+
"to": "Prop32"
|
| 847 |
+
},
|
| 848 |
+
{
|
| 849 |
+
"from": "Prop1",
|
| 850 |
+
"to": "Prop32"
|
| 851 |
+
},
|
| 852 |
+
{
|
| 853 |
+
"from": "BookI",
|
| 854 |
+
"to": "Prop33"
|
| 855 |
+
},
|
| 856 |
+
{
|
| 857 |
+
"from": "BookV",
|
| 858 |
+
"to": "Prop33"
|
| 859 |
+
}
|
| 860 |
+
],
|
| 861 |
+
"colorScheme": {
|
| 862 |
+
"foundation": {
|
| 863 |
+
"fill": "#95a5a6",
|
| 864 |
+
"stroke": "#7f8c8d"
|
| 865 |
+
},
|
| 866 |
+
"definition": {
|
| 867 |
+
"fill": "#3498db",
|
| 868 |
+
"stroke": "#2980b9"
|
| 869 |
+
},
|
| 870 |
+
"proposition": {
|
| 871 |
+
"fill": "#1abc9c",
|
| 872 |
+
"stroke": "#16a085"
|
| 873 |
+
}
|
| 874 |
+
}
|
| 875 |
+
}
|
data/euclid-elements-book-vii.json
ADDED
|
@@ -0,0 +1,761 @@
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|
| 1 |
+
{
|
| 2 |
+
"schemaVersion": "1.0",
|
| 3 |
+
"discourse": {
|
| 4 |
+
"id": "euclid-elements-book-vii",
|
| 5 |
+
"name": "Euclid's Elements, Book VII",
|
| 6 |
+
"subject": "number_theory",
|
| 7 |
+
"variant": "classical",
|
| 8 |
+
"description": "Number theory: GCD (Euclidean algorithm), proportions, primes, LCM. 22 definitions, 39 propositions. Does not depend on previous books. Source: David E. Joyce.",
|
| 9 |
+
"structure": {
|
| 10 |
+
"books": 7,
|
| 11 |
+
"definitions": 22,
|
| 12 |
+
"propositions": 39,
|
| 13 |
+
"foundationTypes": [
|
| 14 |
+
"definition"
|
| 15 |
+
]
|
| 16 |
+
}
|
| 17 |
+
},
|
| 18 |
+
"metadata": {
|
| 19 |
+
"created": "2026-03-18",
|
| 20 |
+
"lastUpdated": "2026-03-18",
|
| 21 |
+
"version": "1.0.0",
|
| 22 |
+
"license": "CC BY 4.0",
|
| 23 |
+
"authors": [
|
| 24 |
+
"Welz, G."
|
| 25 |
+
],
|
| 26 |
+
"methodology": "Programming Framework",
|
| 27 |
+
"citation": "Welz, G. (2026). Euclid's Elements Book VII Dependency Graph. Programming Framework.",
|
| 28 |
+
"keywords": [
|
| 29 |
+
"Euclid",
|
| 30 |
+
"Elements",
|
| 31 |
+
"Book VII",
|
| 32 |
+
"number theory",
|
| 33 |
+
"GCD",
|
| 34 |
+
"prime",
|
| 35 |
+
"LCM"
|
| 36 |
+
]
|
| 37 |
+
},
|
| 38 |
+
"sources": [
|
| 39 |
+
{
|
| 40 |
+
"id": "joyce",
|
| 41 |
+
"type": "digital",
|
| 42 |
+
"authors": "Joyce, David E.",
|
| 43 |
+
"title": "Euclid's Elements, Book VII",
|
| 44 |
+
"year": "1996",
|
| 45 |
+
"url": "https://mathcs.clarku.edu/~djoyce/java/elements/bookVII/bookVII.html",
|
| 46 |
+
"notes": "Clark University"
|
| 47 |
+
}
|
| 48 |
+
],
|
| 49 |
+
"nodes": [
|
| 50 |
+
{
|
| 51 |
+
"id": "Def1",
|
| 52 |
+
"type": "definition",
|
| 53 |
+
"label": "A unit is that by virtue of which each of the things that exist is called one",
|
| 54 |
+
"shortLabel": "Def. VII.1",
|
| 55 |
+
"short": "Unit",
|
| 56 |
+
"book": 7,
|
| 57 |
+
"number": 1,
|
| 58 |
+
"colorClass": "definition"
|
| 59 |
+
},
|
| 60 |
+
{
|
| 61 |
+
"id": "Def2",
|
| 62 |
+
"type": "definition",
|
| 63 |
+
"label": "A number is a multitude composed of units",
|
| 64 |
+
"shortLabel": "Def. VII.2",
|
| 65 |
+
"short": "Number",
|
| 66 |
+
"book": 7,
|
| 67 |
+
"number": 2,
|
| 68 |
+
"colorClass": "definition"
|
| 69 |
+
},
|
| 70 |
+
{
|
| 71 |
+
"id": "Def3",
|
| 72 |
+
"type": "definition",
|
| 73 |
+
"label": "A number is part of a number when it measures it",
|
| 74 |
+
"shortLabel": "Def. VII.3",
|
| 75 |
+
"short": "Part",
|
| 76 |
+
"book": 7,
|
| 77 |
+
"number": 3,
|
| 78 |
+
"colorClass": "definition"
|
| 79 |
+
},
|
| 80 |
+
{
|
| 81 |
+
"id": "Def4",
|
| 82 |
+
"type": "definition",
|
| 83 |
+
"label": "Parts when it does not measure it",
|
| 84 |
+
"shortLabel": "Def. VII.4",
|
| 85 |
+
"short": "Parts",
|
| 86 |
+
"book": 7,
|
| 87 |
+
"number": 4,
|
| 88 |
+
"colorClass": "definition"
|
| 89 |
+
},
|
| 90 |
+
{
|
| 91 |
+
"id": "Def5",
|
| 92 |
+
"type": "definition",
|
| 93 |
+
"label": "The greater is a multiple of the less when measured by the less",
|
| 94 |
+
"shortLabel": "Def. VII.5",
|
| 95 |
+
"short": "Multiple",
|
| 96 |
+
"book": 7,
|
| 97 |
+
"number": 5,
|
| 98 |
+
"colorClass": "definition"
|
| 99 |
+
},
|
| 100 |
+
{
|
| 101 |
+
"id": "Def6",
|
| 102 |
+
"type": "definition",
|
| 103 |
+
"label": "An even number is that which is divisible into two equal parts",
|
| 104 |
+
"shortLabel": "Def. VII.6",
|
| 105 |
+
"short": "Even",
|
| 106 |
+
"book": 7,
|
| 107 |
+
"number": 6,
|
| 108 |
+
"colorClass": "definition"
|
| 109 |
+
},
|
| 110 |
+
{
|
| 111 |
+
"id": "Def7",
|
| 112 |
+
"type": "definition",
|
| 113 |
+
"label": "An odd number is that which is not divisible into two equal parts",
|
| 114 |
+
"shortLabel": "Def. VII.7",
|
| 115 |
+
"short": "Odd",
|
| 116 |
+
"book": 7,
|
| 117 |
+
"number": 7,
|
| 118 |
+
"colorClass": "definition"
|
| 119 |
+
},
|
| 120 |
+
{
|
| 121 |
+
"id": "Def8",
|
| 122 |
+
"type": "definition",
|
| 123 |
+
"label": "Even-times even: measured by an even number an even number of times",
|
| 124 |
+
"shortLabel": "Def. VII.8",
|
| 125 |
+
"short": "Even-times even",
|
| 126 |
+
"book": 7,
|
| 127 |
+
"number": 8,
|
| 128 |
+
"colorClass": "definition"
|
| 129 |
+
},
|
| 130 |
+
{
|
| 131 |
+
"id": "Def9",
|
| 132 |
+
"type": "definition",
|
| 133 |
+
"label": "Even-times odd: measured by an even number an odd number of times",
|
| 134 |
+
"shortLabel": "Def. VII.9",
|
| 135 |
+
"short": "Even-times odd",
|
| 136 |
+
"book": 7,
|
| 137 |
+
"number": 9,
|
| 138 |
+
"colorClass": "definition"
|
| 139 |
+
},
|
| 140 |
+
{
|
| 141 |
+
"id": "Def10",
|
| 142 |
+
"type": "definition",
|
| 143 |
+
"label": "Odd-times odd: measured by an odd number an odd number of times",
|
| 144 |
+
"shortLabel": "Def. VII.10",
|
| 145 |
+
"short": "Odd-times odd",
|
| 146 |
+
"book": 7,
|
| 147 |
+
"number": 10,
|
| 148 |
+
"colorClass": "definition"
|
| 149 |
+
},
|
| 150 |
+
{
|
| 151 |
+
"id": "Def11",
|
| 152 |
+
"type": "definition",
|
| 153 |
+
"label": "A prime number is that which is measured by a unit alone",
|
| 154 |
+
"shortLabel": "Def. VII.11",
|
| 155 |
+
"short": "Prime",
|
| 156 |
+
"book": 7,
|
| 157 |
+
"number": 11,
|
| 158 |
+
"colorClass": "definition"
|
| 159 |
+
},
|
| 160 |
+
{
|
| 161 |
+
"id": "Def12",
|
| 162 |
+
"type": "definition",
|
| 163 |
+
"label": "Numbers relatively prime when only a unit measures both",
|
| 164 |
+
"shortLabel": "Def. VII.12",
|
| 165 |
+
"short": "Relatively prime",
|
| 166 |
+
"book": 7,
|
| 167 |
+
"number": 12,
|
| 168 |
+
"colorClass": "definition"
|
| 169 |
+
},
|
| 170 |
+
{
|
| 171 |
+
"id": "Def13",
|
| 172 |
+
"type": "definition",
|
| 173 |
+
"label": "A composite number is that measured by some number",
|
| 174 |
+
"shortLabel": "Def. VII.13",
|
| 175 |
+
"short": "Composite",
|
| 176 |
+
"book": 7,
|
| 177 |
+
"number": 13,
|
| 178 |
+
"colorClass": "definition"
|
| 179 |
+
},
|
| 180 |
+
{
|
| 181 |
+
"id": "Def14",
|
| 182 |
+
"type": "definition",
|
| 183 |
+
"label": "Numbers composite to one another when some number measures both",
|
| 184 |
+
"shortLabel": "Def. VII.14",
|
| 185 |
+
"short": "Composite to one another",
|
| 186 |
+
"book": 7,
|
| 187 |
+
"number": 14,
|
| 188 |
+
"colorClass": "definition"
|
| 189 |
+
},
|
| 190 |
+
{
|
| 191 |
+
"id": "Def15",
|
| 192 |
+
"type": "definition",
|
| 193 |
+
"label": "A number multiplies a number when the latter is added as many times as units in the former",
|
| 194 |
+
"shortLabel": "Def. VII.15",
|
| 195 |
+
"short": "Multiply",
|
| 196 |
+
"book": 7,
|
| 197 |
+
"number": 15,
|
| 198 |
+
"colorClass": "definition"
|
| 199 |
+
},
|
| 200 |
+
{
|
| 201 |
+
"id": "Def16",
|
| 202 |
+
"type": "definition",
|
| 203 |
+
"label": "When two numbers multiplied produce a number, the product is plane",
|
| 204 |
+
"shortLabel": "Def. VII.16",
|
| 205 |
+
"short": "Product",
|
| 206 |
+
"book": 7,
|
| 207 |
+
"number": 16,
|
| 208 |
+
"colorClass": "definition"
|
| 209 |
+
},
|
| 210 |
+
{
|
| 211 |
+
"id": "Def17",
|
| 212 |
+
"type": "definition",
|
| 213 |
+
"label": "Sides of the product are the numbers multiplied",
|
| 214 |
+
"shortLabel": "Def. VII.17",
|
| 215 |
+
"short": "Side",
|
| 216 |
+
"book": 7,
|
| 217 |
+
"number": 17,
|
| 218 |
+
"colorClass": "definition"
|
| 219 |
+
},
|
| 220 |
+
{
|
| 221 |
+
"id": "Def18",
|
| 222 |
+
"type": "definition",
|
| 223 |
+
"label": "A plane number is that produced by two numbers",
|
| 224 |
+
"shortLabel": "Def. VII.18",
|
| 225 |
+
"short": "Plane number",
|
| 226 |
+
"book": 7,
|
| 227 |
+
"number": 18,
|
| 228 |
+
"colorClass": "definition"
|
| 229 |
+
},
|
| 230 |
+
{
|
| 231 |
+
"id": "Def19",
|
| 232 |
+
"type": "definition",
|
| 233 |
+
"label": "A solid number is that produced by three numbers",
|
| 234 |
+
"shortLabel": "Def. VII.19",
|
| 235 |
+
"short": "Solid number",
|
| 236 |
+
"book": 7,
|
| 237 |
+
"number": 19,
|
| 238 |
+
"colorClass": "definition"
|
| 239 |
+
},
|
| 240 |
+
{
|
| 241 |
+
"id": "Def20",
|
| 242 |
+
"type": "definition",
|
| 243 |
+
"label": "Similar plane numbers have sides proportional",
|
| 244 |
+
"shortLabel": "Def. VII.20",
|
| 245 |
+
"short": "Similar plane",
|
| 246 |
+
"book": 7,
|
| 247 |
+
"number": 20,
|
| 248 |
+
"colorClass": "definition"
|
| 249 |
+
},
|
| 250 |
+
{
|
| 251 |
+
"id": "Def21",
|
| 252 |
+
"type": "definition",
|
| 253 |
+
"label": "Similar solid numbers have sides proportional",
|
| 254 |
+
"shortLabel": "Def. VII.21",
|
| 255 |
+
"short": "Similar solid",
|
| 256 |
+
"book": 7,
|
| 257 |
+
"number": 21,
|
| 258 |
+
"colorClass": "definition"
|
| 259 |
+
},
|
| 260 |
+
{
|
| 261 |
+
"id": "Def22",
|
| 262 |
+
"type": "definition",
|
| 263 |
+
"label": "A perfect number is that which equals its own parts",
|
| 264 |
+
"shortLabel": "Def. VII.22",
|
| 265 |
+
"short": "Perfect",
|
| 266 |
+
"book": 7,
|
| 267 |
+
"number": 22,
|
| 268 |
+
"colorClass": "definition"
|
| 269 |
+
},
|
| 270 |
+
{
|
| 271 |
+
"id": "Prop1",
|
| 272 |
+
"type": "proposition",
|
| 273 |
+
"label": "Unequal numbers: repeated subtraction; if unit left, relatively prime",
|
| 274 |
+
"shortLabel": "Prop. VII.1",
|
| 275 |
+
"short": "Antenaresis, relatively prime",
|
| 276 |
+
"book": 7,
|
| 277 |
+
"number": 1,
|
| 278 |
+
"colorClass": "proposition"
|
| 279 |
+
},
|
| 280 |
+
{
|
| 281 |
+
"id": "Prop2",
|
| 282 |
+
"type": "proposition",
|
| 283 |
+
"label": "To find greatest common measure of two numbers not relatively prime",
|
| 284 |
+
"shortLabel": "Prop. VII.2",
|
| 285 |
+
"short": "GCD of two numbers",
|
| 286 |
+
"book": 7,
|
| 287 |
+
"number": 2,
|
| 288 |
+
"colorClass": "proposition"
|
| 289 |
+
},
|
| 290 |
+
{
|
| 291 |
+
"id": "Prop3",
|
| 292 |
+
"type": "proposition",
|
| 293 |
+
"label": "To find greatest common measure of three numbers",
|
| 294 |
+
"shortLabel": "Prop. VII.3",
|
| 295 |
+
"short": "GCD of three numbers",
|
| 296 |
+
"book": 7,
|
| 297 |
+
"number": 3,
|
| 298 |
+
"colorClass": "proposition"
|
| 299 |
+
},
|
| 300 |
+
{
|
| 301 |
+
"id": "Prop4",
|
| 302 |
+
"type": "proposition",
|
| 303 |
+
"label": "Any number is part or parts of any number, less of greater",
|
| 304 |
+
"shortLabel": "Prop. VII.4",
|
| 305 |
+
"short": "Part or parts",
|
| 306 |
+
"book": 7,
|
| 307 |
+
"number": 4,
|
| 308 |
+
"colorClass": "proposition"
|
| 309 |
+
},
|
| 310 |
+
{
|
| 311 |
+
"id": "Prop5",
|
| 312 |
+
"type": "proposition",
|
| 313 |
+
"label": "If a is same part of b as c of d, then a+c same part of b+d",
|
| 314 |
+
"shortLabel": "Prop. VII.5",
|
| 315 |
+
"short": "Same part: sum",
|
| 316 |
+
"book": 7,
|
| 317 |
+
"number": 5,
|
| 318 |
+
"colorClass": "proposition"
|
| 319 |
+
},
|
| 320 |
+
{
|
| 321 |
+
"id": "Prop6",
|
| 322 |
+
"type": "proposition",
|
| 323 |
+
"label": "If a is same parts of b as c of d, then a+c same parts of b+d",
|
| 324 |
+
"shortLabel": "Prop. VII.6",
|
| 325 |
+
"short": "Same parts: sum",
|
| 326 |
+
"book": 7,
|
| 327 |
+
"number": 6,
|
| 328 |
+
"colorClass": "proposition"
|
| 329 |
+
},
|
| 330 |
+
{
|
| 331 |
+
"id": "Prop7",
|
| 332 |
+
"type": "proposition",
|
| 333 |
+
"label": "If a part of b as c of d, remainder same part of remainder",
|
| 334 |
+
"shortLabel": "Prop. VII.7",
|
| 335 |
+
"short": "Same part: remainder",
|
| 336 |
+
"book": 7,
|
| 337 |
+
"number": 7,
|
| 338 |
+
"colorClass": "proposition"
|
| 339 |
+
},
|
| 340 |
+
{
|
| 341 |
+
"id": "Prop8",
|
| 342 |
+
"type": "proposition",
|
| 343 |
+
"label": "If a parts of b as c of d, remainder same parts of remainder",
|
| 344 |
+
"shortLabel": "Prop. VII.8",
|
| 345 |
+
"short": "Same parts: remainder",
|
| 346 |
+
"book": 7,
|
| 347 |
+
"number": 8,
|
| 348 |
+
"colorClass": "proposition"
|
| 349 |
+
},
|
| 350 |
+
{
|
| 351 |
+
"id": "Prop9",
|
| 352 |
+
"type": "proposition",
|
| 353 |
+
"label": "If a part of b as c of d, alternately a part/parts of c as b of d",
|
| 354 |
+
"shortLabel": "Prop. VII.9",
|
| 355 |
+
"short": "Same part: alternately",
|
| 356 |
+
"book": 7,
|
| 357 |
+
"number": 9,
|
| 358 |
+
"colorClass": "proposition"
|
| 359 |
+
},
|
| 360 |
+
{
|
| 361 |
+
"id": "Prop10",
|
| 362 |
+
"type": "proposition",
|
| 363 |
+
"label": "If a parts of b as c of d, alternately a part/parts of c as b of d",
|
| 364 |
+
"shortLabel": "Prop. VII.10",
|
| 365 |
+
"short": "Same parts: alternately",
|
| 366 |
+
"book": 7,
|
| 367 |
+
"number": 10,
|
| 368 |
+
"colorClass": "proposition"
|
| 369 |
+
},
|
| 370 |
+
{
|
| 371 |
+
"id": "Prop11",
|
| 372 |
+
"type": "proposition",
|
| 373 |
+
"label": "If whole:whole as subtracted:subtracted, remainder:remainder as whole:whole",
|
| 374 |
+
"shortLabel": "Prop. VII.11",
|
| 375 |
+
"short": "Proportion: remainder",
|
| 376 |
+
"book": 7,
|
| 377 |
+
"number": 11,
|
| 378 |
+
"colorClass": "proposition"
|
| 379 |
+
},
|
| 380 |
+
{
|
| 381 |
+
"id": "Prop12",
|
| 382 |
+
"type": "proposition",
|
| 383 |
+
"label": "Proportional: one antecedent to consequent as sum antecedents to sum consequents",
|
| 384 |
+
"shortLabel": "Prop. VII.12",
|
| 385 |
+
"short": "Proportional: sum",
|
| 386 |
+
"book": 7,
|
| 387 |
+
"number": 12,
|
| 388 |
+
"colorClass": "proposition"
|
| 389 |
+
},
|
| 390 |
+
{
|
| 391 |
+
"id": "Prop13",
|
| 392 |
+
"type": "proposition",
|
| 393 |
+
"label": "If four numbers proportional, also proportional alternately",
|
| 394 |
+
"shortLabel": "Prop. VII.13",
|
| 395 |
+
"short": "Proportional: alternately",
|
| 396 |
+
"book": 7,
|
| 397 |
+
"number": 13,
|
| 398 |
+
"colorClass": "proposition"
|
| 399 |
+
},
|
| 400 |
+
{
|
| 401 |
+
"id": "Prop14",
|
| 402 |
+
"type": "proposition",
|
| 403 |
+
"label": "If a:b = d:e and b:c = e:f, then a:c = d:f",
|
| 404 |
+
"shortLabel": "Prop. VII.14",
|
| 405 |
+
"short": "Ex aequali",
|
| 406 |
+
"book": 7,
|
| 407 |
+
"number": 14,
|
| 408 |
+
"colorClass": "proposition"
|
| 409 |
+
},
|
| 410 |
+
{
|
| 411 |
+
"id": "Prop15",
|
| 412 |
+
"type": "proposition",
|
| 413 |
+
"label": "If unit measures a, b measures c same times, alternately unit:c as b:d",
|
| 414 |
+
"shortLabel": "Prop. VII.15",
|
| 415 |
+
"short": "Unit measures",
|
| 416 |
+
"book": 7,
|
| 417 |
+
"number": 15,
|
| 418 |
+
"colorClass": "proposition"
|
| 419 |
+
},
|
| 420 |
+
{
|
| 421 |
+
"id": "Prop16",
|
| 422 |
+
"type": "proposition",
|
| 423 |
+
"label": "If a×b and c×d, then a×b = c×d (commutativity)",
|
| 424 |
+
"shortLabel": "Prop. VII.16",
|
| 425 |
+
"short": "Commutativity of product",
|
| 426 |
+
"book": 7,
|
| 427 |
+
"number": 16,
|
| 428 |
+
"colorClass": "proposition"
|
| 429 |
+
},
|
| 430 |
+
{
|
| 431 |
+
"id": "Prop17",
|
| 432 |
+
"type": "proposition",
|
| 433 |
+
"label": "a:b = (a×c):(b×c)",
|
| 434 |
+
"shortLabel": "Prop. VII.17",
|
| 435 |
+
"short": "Ratio of products",
|
| 436 |
+
"book": 7,
|
| 437 |
+
"number": 17,
|
| 438 |
+
"colorClass": "proposition"
|
| 439 |
+
},
|
| 440 |
+
{
|
| 441 |
+
"id": "Prop18",
|
| 442 |
+
"type": "proposition",
|
| 443 |
+
"label": "a×c : b×c = a:b",
|
| 444 |
+
"shortLabel": "Prop. VII.18",
|
| 445 |
+
"short": "Ratio: multipliers",
|
| 446 |
+
"book": 7,
|
| 447 |
+
"number": 18,
|
| 448 |
+
"colorClass": "proposition"
|
| 449 |
+
},
|
| 450 |
+
{
|
| 451 |
+
"id": "Prop19",
|
| 452 |
+
"type": "proposition",
|
| 453 |
+
"label": "a:b = c:d iff a×d = b×c",
|
| 454 |
+
"shortLabel": "Prop. VII.19",
|
| 455 |
+
"short": "Proportional iff product",
|
| 456 |
+
"book": 7,
|
| 457 |
+
"number": 19,
|
| 458 |
+
"colorClass": "proposition"
|
| 459 |
+
},
|
| 460 |
+
{
|
| 461 |
+
"id": "Prop20",
|
| 462 |
+
"type": "proposition",
|
| 463 |
+
"label": "Least numbers in ratio measure others same number of times",
|
| 464 |
+
"shortLabel": "Prop. VII.20",
|
| 465 |
+
"short": "Least in ratio",
|
| 466 |
+
"book": 7,
|
| 467 |
+
"number": 20,
|
| 468 |
+
"colorClass": "proposition"
|
| 469 |
+
},
|
| 470 |
+
{
|
| 471 |
+
"id": "Prop21",
|
| 472 |
+
"type": "proposition",
|
| 473 |
+
"label": "Relatively prime numbers are least in their ratio",
|
| 474 |
+
"shortLabel": "Prop. VII.21",
|
| 475 |
+
"short": "Relatively prime: least",
|
| 476 |
+
"book": 7,
|
| 477 |
+
"number": 21,
|
| 478 |
+
"colorClass": "proposition"
|
| 479 |
+
},
|
| 480 |
+
{
|
| 481 |
+
"id": "Prop22",
|
| 482 |
+
"type": "proposition",
|
| 483 |
+
"label": "Least numbers in ratio are relatively prime",
|
| 484 |
+
"shortLabel": "Prop. VII.22",
|
| 485 |
+
"short": "Least: relatively prime",
|
| 486 |
+
"book": 7,
|
| 487 |
+
"number": 22,
|
| 488 |
+
"colorClass": "proposition"
|
| 489 |
+
},
|
| 490 |
+
{
|
| 491 |
+
"id": "Prop23",
|
| 492 |
+
"type": "proposition",
|
| 493 |
+
"label": "If a,b relatively prime, divisor of a relatively prime to b",
|
| 494 |
+
"shortLabel": "Prop. VII.23",
|
| 495 |
+
"short": "Relatively prime: divisor",
|
| 496 |
+
"book": 7,
|
| 497 |
+
"number": 23,
|
| 498 |
+
"colorClass": "proposition"
|
| 499 |
+
},
|
| 500 |
+
{
|
| 501 |
+
"id": "Prop24",
|
| 502 |
+
"type": "proposition",
|
| 503 |
+
"label": "If a,b relatively prime to c, then a×b relatively prime to c",
|
| 504 |
+
"shortLabel": "Prop. VII.24",
|
| 505 |
+
"short": "Product relatively prime",
|
| 506 |
+
"book": 7,
|
| 507 |
+
"number": 24,
|
| 508 |
+
"colorClass": "proposition"
|
| 509 |
+
},
|
| 510 |
+
{
|
| 511 |
+
"id": "Prop25",
|
| 512 |
+
"type": "proposition",
|
| 513 |
+
"label": "If a,b relatively prime, a² relatively prime to b",
|
| 514 |
+
"shortLabel": "Prop. VII.25",
|
| 515 |
+
"short": "Square relatively prime",
|
| 516 |
+
"book": 7,
|
| 517 |
+
"number": 25,
|
| 518 |
+
"colorClass": "proposition"
|
| 519 |
+
},
|
| 520 |
+
{
|
| 521 |
+
"id": "Prop26",
|
| 522 |
+
"type": "proposition",
|
| 523 |
+
"label": "If a,c and b,d relatively prime, a×b, c×d relatively prime",
|
| 524 |
+
"shortLabel": "Prop. VII.26",
|
| 525 |
+
"short": "Products relatively prime",
|
| 526 |
+
"book": 7,
|
| 527 |
+
"number": 26,
|
| 528 |
+
"colorClass": "proposition"
|
| 529 |
+
},
|
| 530 |
+
{
|
| 531 |
+
"id": "Prop27",
|
| 532 |
+
"type": "proposition",
|
| 533 |
+
"label": "If a,b relatively prime, a²,b² relatively prime; a×a², b×b²",
|
| 534 |
+
"shortLabel": "Prop. VII.27",
|
| 535 |
+
"short": "Squares relatively prime",
|
| 536 |
+
"book": 7,
|
| 537 |
+
"number": 27,
|
| 538 |
+
"colorClass": "proposition"
|
| 539 |
+
},
|
| 540 |
+
{
|
| 541 |
+
"id": "Prop28",
|
| 542 |
+
"type": "proposition",
|
| 543 |
+
"label": "If a,b relatively prime, a+b prime to each; converse",
|
| 544 |
+
"shortLabel": "Prop. VII.28",
|
| 545 |
+
"short": "Sum relatively prime",
|
| 546 |
+
"book": 7,
|
| 547 |
+
"number": 28,
|
| 548 |
+
"colorClass": "proposition"
|
| 549 |
+
},
|
| 550 |
+
{
|
| 551 |
+
"id": "Prop29",
|
| 552 |
+
"type": "proposition",
|
| 553 |
+
"label": "Prime relatively prime to any number it does not measure",
|
| 554 |
+
"shortLabel": "Prop. VII.29",
|
| 555 |
+
"short": "Prime to non-multiple",
|
| 556 |
+
"book": 7,
|
| 557 |
+
"number": 29,
|
| 558 |
+
"colorClass": "proposition"
|
| 559 |
+
},
|
| 560 |
+
{
|
| 561 |
+
"id": "Prop30",
|
| 562 |
+
"type": "proposition",
|
| 563 |
+
"label": "If prime measures product, it measures one factor",
|
| 564 |
+
"shortLabel": "Prop. VII.30",
|
| 565 |
+
"short": "Prime divides product",
|
| 566 |
+
"book": 7,
|
| 567 |
+
"number": 30,
|
| 568 |
+
"colorClass": "proposition"
|
| 569 |
+
},
|
| 570 |
+
{
|
| 571 |
+
"id": "Prop31",
|
| 572 |
+
"type": "proposition",
|
| 573 |
+
"label": "Any composite measured by some prime",
|
| 574 |
+
"shortLabel": "Prop. VII.31",
|
| 575 |
+
"short": "Composite has prime factor",
|
| 576 |
+
"book": 7,
|
| 577 |
+
"number": 31,
|
| 578 |
+
"colorClass": "proposition"
|
| 579 |
+
},
|
| 580 |
+
{
|
| 581 |
+
"id": "Prop32",
|
| 582 |
+
"type": "proposition",
|
| 583 |
+
"label": "Any number is prime or measured by some prime",
|
| 584 |
+
"shortLabel": "Prop. VII.32",
|
| 585 |
+
"short": "Prime or has prime factor",
|
| 586 |
+
"book": 7,
|
| 587 |
+
"number": 32,
|
| 588 |
+
"colorClass": "proposition"
|
| 589 |
+
},
|
| 590 |
+
{
|
| 591 |
+
"id": "Prop33",
|
| 592 |
+
"type": "proposition",
|
| 593 |
+
"label": "Given numbers, find least in same ratio",
|
| 594 |
+
"shortLabel": "Prop. VII.33",
|
| 595 |
+
"short": "Least in ratio",
|
| 596 |
+
"book": 7,
|
| 597 |
+
"number": 33,
|
| 598 |
+
"colorClass": "proposition"
|
| 599 |
+
},
|
| 600 |
+
{
|
| 601 |
+
"id": "Prop34",
|
| 602 |
+
"type": "proposition",
|
| 603 |
+
"label": "To find least number that two given numbers measure",
|
| 604 |
+
"shortLabel": "Prop. VII.34",
|
| 605 |
+
"short": "LCM of two",
|
| 606 |
+
"book": 7,
|
| 607 |
+
"number": 34,
|
| 608 |
+
"colorClass": "proposition"
|
| 609 |
+
},
|
| 610 |
+
{
|
| 611 |
+
"id": "Prop35",
|
| 612 |
+
"type": "proposition",
|
| 613 |
+
"label": "If two numbers measure some number, LCM also measures it",
|
| 614 |
+
"shortLabel": "Prop. VII.35",
|
| 615 |
+
"short": "LCM divides common multiple",
|
| 616 |
+
"book": 7,
|
| 617 |
+
"number": 35,
|
| 618 |
+
"colorClass": "proposition"
|
| 619 |
+
},
|
| 620 |
+
{
|
| 621 |
+
"id": "Prop36",
|
| 622 |
+
"type": "proposition",
|
| 623 |
+
"label": "To find least number that three given numbers measure",
|
| 624 |
+
"shortLabel": "Prop. VII.36",
|
| 625 |
+
"short": "LCM of three",
|
| 626 |
+
"book": 7,
|
| 627 |
+
"number": 36,
|
| 628 |
+
"colorClass": "proposition"
|
| 629 |
+
},
|
| 630 |
+
{
|
| 631 |
+
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| 645 |
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| 651 |
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| 653 |
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| 654 |
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| 655 |
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| 657 |
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|
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|
| 761 |
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}
|
data/euclid-elements-book-viii.json
ADDED
|
@@ -0,0 +1,540 @@
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|
|
| 1 |
+
{
|
| 2 |
+
"schemaVersion": "1.0",
|
| 3 |
+
"discourse": {
|
| 4 |
+
"id": "euclid-elements-book-viii",
|
| 5 |
+
"name": "Euclid's Elements, Book VIII",
|
| 6 |
+
"subject": "number_theory",
|
| 7 |
+
"variant": "classical",
|
| 8 |
+
"description": "Continued proportions. 27 propositions. Depends on Book VII. Source: David E. Joyce.",
|
| 9 |
+
"structure": {
|
| 10 |
+
"books": 8,
|
| 11 |
+
"propositions": 27,
|
| 12 |
+
"foundationTypes": [
|
| 13 |
+
"foundation"
|
| 14 |
+
]
|
| 15 |
+
}
|
| 16 |
+
},
|
| 17 |
+
"metadata": {
|
| 18 |
+
"created": "2026-03-18",
|
| 19 |
+
"lastUpdated": "2026-03-18",
|
| 20 |
+
"version": "1.0.0",
|
| 21 |
+
"license": "CC BY 4.0",
|
| 22 |
+
"authors": [
|
| 23 |
+
"Welz, G."
|
| 24 |
+
],
|
| 25 |
+
"methodology": "Programming Framework",
|
| 26 |
+
"citation": "Welz, G. (2026). Euclid's Elements Book VIII Dependency Graph. Programming Framework.",
|
| 27 |
+
"keywords": [
|
| 28 |
+
"Euclid",
|
| 29 |
+
"Elements",
|
| 30 |
+
"Book VIII",
|
| 31 |
+
"continued proportion",
|
| 32 |
+
"plane",
|
| 33 |
+
"solid"
|
| 34 |
+
]
|
| 35 |
+
},
|
| 36 |
+
"sources": [
|
| 37 |
+
{
|
| 38 |
+
"id": "joyce",
|
| 39 |
+
"type": "digital",
|
| 40 |
+
"authors": "Joyce, David E.",
|
| 41 |
+
"title": "Euclid's Elements, Book VIII",
|
| 42 |
+
"year": "1996",
|
| 43 |
+
"url": "https://mathcs.clarku.edu/~djoyce/java/elements/bookVIII/bookVIII.html",
|
| 44 |
+
"notes": "Clark University"
|
| 45 |
+
}
|
| 46 |
+
],
|
| 47 |
+
"nodes": [
|
| 48 |
+
{
|
| 49 |
+
"id": "BookVII",
|
| 50 |
+
"type": "foundation",
|
| 51 |
+
"label": "Book VII — Number theory",
|
| 52 |
+
"shortLabel": "Book VII",
|
| 53 |
+
"short": "Foundation",
|
| 54 |
+
"book": 7,
|
| 55 |
+
"colorClass": "foundation"
|
| 56 |
+
},
|
| 57 |
+
{
|
| 58 |
+
"id": "Prop1",
|
| 59 |
+
"type": "proposition",
|
| 60 |
+
"label": "Continued proportion, extremes relatively prime: least in ratio",
|
| 61 |
+
"shortLabel": "Prop. VIII.1",
|
| 62 |
+
"short": "Continued proportion, extremes prime",
|
| 63 |
+
"book": 8,
|
| 64 |
+
"number": 1,
|
| 65 |
+
"colorClass": "proposition"
|
| 66 |
+
},
|
| 67 |
+
{
|
| 68 |
+
"id": "Prop2",
|
| 69 |
+
"type": "proposition",
|
| 70 |
+
"label": "To find numbers in continued proportion, least in given ratio",
|
| 71 |
+
"shortLabel": "Prop. VIII.2",
|
| 72 |
+
"short": "Find numbers in continued proportion",
|
| 73 |
+
"book": 8,
|
| 74 |
+
"number": 2,
|
| 75 |
+
"colorClass": "proposition"
|
| 76 |
+
},
|
| 77 |
+
{
|
| 78 |
+
"id": "Prop3",
|
| 79 |
+
"type": "proposition",
|
| 80 |
+
"label": "Least in continued proportion: extremes relatively prime",
|
| 81 |
+
"shortLabel": "Prop. VIII.3",
|
| 82 |
+
"short": "Least: extremes prime",
|
| 83 |
+
"book": 8,
|
| 84 |
+
"number": 3,
|
| 85 |
+
"colorClass": "proposition"
|
| 86 |
+
},
|
| 87 |
+
{
|
| 88 |
+
"id": "Prop4",
|
| 89 |
+
"type": "proposition",
|
| 90 |
+
"label": "Given ratios in least numbers, find least in continued proportion",
|
| 91 |
+
"shortLabel": "Prop. VIII.4",
|
| 92 |
+
"short": "Find continued proportion from ratios",
|
| 93 |
+
"book": 8,
|
| 94 |
+
"number": 4,
|
| 95 |
+
"colorClass": "proposition"
|
| 96 |
+
},
|
| 97 |
+
{
|
| 98 |
+
"id": "Prop5",
|
| 99 |
+
"type": "proposition",
|
| 100 |
+
"label": "Plane numbers have ratio compounded of ratios of sides",
|
| 101 |
+
"shortLabel": "Prop. VIII.5",
|
| 102 |
+
"short": "Plane numbers: compound ratio",
|
| 103 |
+
"book": 8,
|
| 104 |
+
"number": 5,
|
| 105 |
+
"colorClass": "proposition"
|
| 106 |
+
},
|
| 107 |
+
{
|
| 108 |
+
"id": "Prop6",
|
| 109 |
+
"type": "proposition",
|
| 110 |
+
"label": "Continued proportion: if first does not measure second, none measures another",
|
| 111 |
+
"shortLabel": "Prop. VIII.6",
|
| 112 |
+
"short": "First does not measure second",
|
| 113 |
+
"book": 8,
|
| 114 |
+
"number": 6,
|
| 115 |
+
"colorClass": "proposition"
|
| 116 |
+
},
|
| 117 |
+
{
|
| 118 |
+
"id": "Prop7",
|
| 119 |
+
"type": "proposition",
|
| 120 |
+
"label": "Continued proportion: if first measures last, it measures second",
|
| 121 |
+
"shortLabel": "Prop. VIII.7",
|
| 122 |
+
"short": "First measures last",
|
| 123 |
+
"book": 8,
|
| 124 |
+
"number": 7,
|
| 125 |
+
"colorClass": "proposition"
|
| 126 |
+
},
|
| 127 |
+
{
|
| 128 |
+
"id": "Prop8",
|
| 129 |
+
"type": "proposition",
|
| 130 |
+
"label": "Numbers between two in continued proportion correspond to ratios",
|
| 131 |
+
"shortLabel": "Prop. VIII.8",
|
| 132 |
+
"short": "Numbers between in proportion",
|
| 133 |
+
"book": 8,
|
| 134 |
+
"number": 8,
|
| 135 |
+
"colorClass": "proposition"
|
| 136 |
+
},
|
| 137 |
+
{
|
| 138 |
+
"id": "Prop9",
|
| 139 |
+
"type": "proposition",
|
| 140 |
+
"label": "Two relatively prime: numbers between them as between each and unit",
|
| 141 |
+
"shortLabel": "Prop. VIII.9",
|
| 142 |
+
"short": "Relatively prime: numbers to unit",
|
| 143 |
+
"book": 8,
|
| 144 |
+
"number": 9,
|
| 145 |
+
"colorClass": "proposition"
|
| 146 |
+
},
|
| 147 |
+
{
|
| 148 |
+
"id": "Prop10",
|
| 149 |
+
"type": "proposition",
|
| 150 |
+
"label": "Numbers between number and unit correspond to between two numbers",
|
| 151 |
+
"shortLabel": "Prop. VIII.10",
|
| 152 |
+
"short": "Numbers from unit",
|
| 153 |
+
"book": 8,
|
| 154 |
+
"number": 10,
|
| 155 |
+
"colorClass": "proposition"
|
| 156 |
+
},
|
| 157 |
+
{
|
| 158 |
+
"id": "Prop11",
|
| 159 |
+
"type": "proposition",
|
| 160 |
+
"label": "Between two squares one mean proportional; duplicate ratio",
|
| 161 |
+
"shortLabel": "Prop. VIII.11",
|
| 162 |
+
"short": "Mean proportional of squares",
|
| 163 |
+
"book": 8,
|
| 164 |
+
"number": 11,
|
| 165 |
+
"colorClass": "proposition"
|
| 166 |
+
},
|
| 167 |
+
{
|
| 168 |
+
"id": "Prop12",
|
| 169 |
+
"type": "proposition",
|
| 170 |
+
"label": "Between two cubes two mean proportionals; triplicate ratio",
|
| 171 |
+
"shortLabel": "Prop. VIII.12",
|
| 172 |
+
"short": "Two means between cubes",
|
| 173 |
+
"book": 8,
|
| 174 |
+
"number": 12,
|
| 175 |
+
"colorClass": "proposition"
|
| 176 |
+
},
|
| 177 |
+
{
|
| 178 |
+
"id": "Prop13",
|
| 179 |
+
"type": "proposition",
|
| 180 |
+
"label": "Continued proportion: products proportional; products of products",
|
| 181 |
+
"shortLabel": "Prop. VIII.13",
|
| 182 |
+
"short": "Products proportional",
|
| 183 |
+
"book": 8,
|
| 184 |
+
"number": 13,
|
| 185 |
+
"colorClass": "proposition"
|
| 186 |
+
},
|
| 187 |
+
{
|
| 188 |
+
"id": "Prop14",
|
| 189 |
+
"type": "proposition",
|
| 190 |
+
"label": "Square measures square iff side measures side",
|
| 191 |
+
"shortLabel": "Prop. VIII.14",
|
| 192 |
+
"short": "Square measures square",
|
| 193 |
+
"book": 8,
|
| 194 |
+
"number": 14,
|
| 195 |
+
"colorClass": "proposition"
|
| 196 |
+
},
|
| 197 |
+
{
|
| 198 |
+
"id": "Prop15",
|
| 199 |
+
"type": "proposition",
|
| 200 |
+
"label": "Cube measures cube iff side measures side",
|
| 201 |
+
"shortLabel": "Prop. VIII.15",
|
| 202 |
+
"short": "Cube measures cube",
|
| 203 |
+
"book": 8,
|
| 204 |
+
"number": 15,
|
| 205 |
+
"colorClass": "proposition"
|
| 206 |
+
},
|
| 207 |
+
{
|
| 208 |
+
"id": "Prop16",
|
| 209 |
+
"type": "proposition",
|
| 210 |
+
"label": "Square does not measure square iff side does not measure side",
|
| 211 |
+
"shortLabel": "Prop. VIII.16",
|
| 212 |
+
"short": "Square does not measure square",
|
| 213 |
+
"book": 8,
|
| 214 |
+
"number": 16,
|
| 215 |
+
"colorClass": "proposition"
|
| 216 |
+
},
|
| 217 |
+
{
|
| 218 |
+
"id": "Prop17",
|
| 219 |
+
"type": "proposition",
|
| 220 |
+
"label": "Cube does not measure cube iff side does not measure side",
|
| 221 |
+
"shortLabel": "Prop. VIII.17",
|
| 222 |
+
"short": "Cube does not measure cube",
|
| 223 |
+
"book": 8,
|
| 224 |
+
"number": 17,
|
| 225 |
+
"colorClass": "proposition"
|
| 226 |
+
},
|
| 227 |
+
{
|
| 228 |
+
"id": "Prop18",
|
| 229 |
+
"type": "proposition",
|
| 230 |
+
"label": "Between similar plane numbers one mean proportional; duplicate ratio",
|
| 231 |
+
"shortLabel": "Prop. VIII.18",
|
| 232 |
+
"short": "Similar plane: mean proportional",
|
| 233 |
+
"book": 8,
|
| 234 |
+
"number": 18,
|
| 235 |
+
"colorClass": "proposition"
|
| 236 |
+
},
|
| 237 |
+
{
|
| 238 |
+
"id": "Prop19",
|
| 239 |
+
"type": "proposition",
|
| 240 |
+
"label": "Between similar solid numbers two mean proportionals; triplicate ratio",
|
| 241 |
+
"shortLabel": "Prop. VIII.19",
|
| 242 |
+
"short": "Similar solid: two means",
|
| 243 |
+
"book": 8,
|
| 244 |
+
"number": 19,
|
| 245 |
+
"colorClass": "proposition"
|
| 246 |
+
},
|
| 247 |
+
{
|
| 248 |
+
"id": "Prop20",
|
| 249 |
+
"type": "proposition",
|
| 250 |
+
"label": "If one mean between two numbers, they are similar plane",
|
| 251 |
+
"shortLabel": "Prop. VIII.20",
|
| 252 |
+
"short": "One mean: similar plane",
|
| 253 |
+
"book": 8,
|
| 254 |
+
"number": 20,
|
| 255 |
+
"colorClass": "proposition"
|
| 256 |
+
},
|
| 257 |
+
{
|
| 258 |
+
"id": "Prop21",
|
| 259 |
+
"type": "proposition",
|
| 260 |
+
"label": "If two means between two numbers, they are similar solid",
|
| 261 |
+
"shortLabel": "Prop. VIII.21",
|
| 262 |
+
"short": "Two means: similar solid",
|
| 263 |
+
"book": 8,
|
| 264 |
+
"number": 21,
|
| 265 |
+
"colorClass": "proposition"
|
| 266 |
+
},
|
| 267 |
+
{
|
| 268 |
+
"id": "Prop22",
|
| 269 |
+
"type": "proposition",
|
| 270 |
+
"label": "Three in continued proportion, first square: third square",
|
| 271 |
+
"shortLabel": "Prop. VIII.22",
|
| 272 |
+
"short": "Three in proportion: first square",
|
| 273 |
+
"book": 8,
|
| 274 |
+
"number": 22,
|
| 275 |
+
"colorClass": "proposition"
|
| 276 |
+
},
|
| 277 |
+
{
|
| 278 |
+
"id": "Prop23",
|
| 279 |
+
"type": "proposition",
|
| 280 |
+
"label": "Four in continued proportion, first cube: fourth cube",
|
| 281 |
+
"shortLabel": "Prop. VIII.23",
|
| 282 |
+
"short": "Four in proportion: first cube",
|
| 283 |
+
"book": 8,
|
| 284 |
+
"number": 23,
|
| 285 |
+
"colorClass": "proposition"
|
| 286 |
+
},
|
| 287 |
+
{
|
| 288 |
+
"id": "Prop24",
|
| 289 |
+
"type": "proposition",
|
| 290 |
+
"label": "If ratio as square to square and first square, second square",
|
| 291 |
+
"shortLabel": "Prop. VIII.24",
|
| 292 |
+
"short": "Ratio as square to square",
|
| 293 |
+
"book": 8,
|
| 294 |
+
"number": 24,
|
| 295 |
+
"colorClass": "proposition"
|
| 296 |
+
},
|
| 297 |
+
{
|
| 298 |
+
"id": "Prop25",
|
| 299 |
+
"type": "proposition",
|
| 300 |
+
"label": "If ratio as cube to cube and first cube, second cube",
|
| 301 |
+
"shortLabel": "Prop. VIII.25",
|
| 302 |
+
"short": "Ratio as cube to cube",
|
| 303 |
+
"book": 8,
|
| 304 |
+
"number": 25,
|
| 305 |
+
"colorClass": "proposition"
|
| 306 |
+
},
|
| 307 |
+
{
|
| 308 |
+
"id": "Prop26",
|
| 309 |
+
"type": "proposition",
|
| 310 |
+
"label": "Similar plane numbers have ratio of square to square",
|
| 311 |
+
"shortLabel": "Prop. VIII.26",
|
| 312 |
+
"short": "Similar plane: square ratio",
|
| 313 |
+
"book": 8,
|
| 314 |
+
"number": 26,
|
| 315 |
+
"colorClass": "proposition"
|
| 316 |
+
},
|
| 317 |
+
{
|
| 318 |
+
"id": "Prop27",
|
| 319 |
+
"type": "proposition",
|
| 320 |
+
"label": "Similar solid numbers have ratio of cube to cube",
|
| 321 |
+
"shortLabel": "Prop. VIII.27",
|
| 322 |
+
"short": "Similar solid: cube ratio",
|
| 323 |
+
"book": 8,
|
| 324 |
+
"number": 27,
|
| 325 |
+
"colorClass": "proposition"
|
| 326 |
+
}
|
| 327 |
+
],
|
| 328 |
+
"edges": [
|
| 329 |
+
{
|
| 330 |
+
"from": "BookVII",
|
| 331 |
+
"to": "Prop1"
|
| 332 |
+
},
|
| 333 |
+
{
|
| 334 |
+
"from": "BookVII",
|
| 335 |
+
"to": "Prop2"
|
| 336 |
+
},
|
| 337 |
+
{
|
| 338 |
+
"from": "Prop1",
|
| 339 |
+
"to": "Prop2"
|
| 340 |
+
},
|
| 341 |
+
{
|
| 342 |
+
"from": "BookVII",
|
| 343 |
+
"to": "Prop3"
|
| 344 |
+
},
|
| 345 |
+
{
|
| 346 |
+
"from": "Prop2",
|
| 347 |
+
"to": "Prop3"
|
| 348 |
+
},
|
| 349 |
+
{
|
| 350 |
+
"from": "BookVII",
|
| 351 |
+
"to": "Prop4"
|
| 352 |
+
},
|
| 353 |
+
{
|
| 354 |
+
"from": "Prop2",
|
| 355 |
+
"to": "Prop4"
|
| 356 |
+
},
|
| 357 |
+
{
|
| 358 |
+
"from": "BookVII",
|
| 359 |
+
"to": "Prop5"
|
| 360 |
+
},
|
| 361 |
+
{
|
| 362 |
+
"from": "BookVII",
|
| 363 |
+
"to": "Prop6"
|
| 364 |
+
},
|
| 365 |
+
{
|
| 366 |
+
"from": "Prop1",
|
| 367 |
+
"to": "Prop6"
|
| 368 |
+
},
|
| 369 |
+
{
|
| 370 |
+
"from": "BookVII",
|
| 371 |
+
"to": "Prop7"
|
| 372 |
+
},
|
| 373 |
+
{
|
| 374 |
+
"from": "Prop1",
|
| 375 |
+
"to": "Prop7"
|
| 376 |
+
},
|
| 377 |
+
{
|
| 378 |
+
"from": "BookVII",
|
| 379 |
+
"to": "Prop8"
|
| 380 |
+
},
|
| 381 |
+
{
|
| 382 |
+
"from": "BookVII",
|
| 383 |
+
"to": "Prop9"
|
| 384 |
+
},
|
| 385 |
+
{
|
| 386 |
+
"from": "Prop8",
|
| 387 |
+
"to": "Prop9"
|
| 388 |
+
},
|
| 389 |
+
{
|
| 390 |
+
"from": "BookVII",
|
| 391 |
+
"to": "Prop10"
|
| 392 |
+
},
|
| 393 |
+
{
|
| 394 |
+
"from": "Prop9",
|
| 395 |
+
"to": "Prop10"
|
| 396 |
+
},
|
| 397 |
+
{
|
| 398 |
+
"from": "BookVII",
|
| 399 |
+
"to": "Prop11"
|
| 400 |
+
},
|
| 401 |
+
{
|
| 402 |
+
"from": "Prop8",
|
| 403 |
+
"to": "Prop11"
|
| 404 |
+
},
|
| 405 |
+
{
|
| 406 |
+
"from": "BookVII",
|
| 407 |
+
"to": "Prop12"
|
| 408 |
+
},
|
| 409 |
+
{
|
| 410 |
+
"from": "Prop8",
|
| 411 |
+
"to": "Prop12"
|
| 412 |
+
},
|
| 413 |
+
{
|
| 414 |
+
"from": "BookVII",
|
| 415 |
+
"to": "Prop13"
|
| 416 |
+
},
|
| 417 |
+
{
|
| 418 |
+
"from": "BookVII",
|
| 419 |
+
"to": "Prop14"
|
| 420 |
+
},
|
| 421 |
+
{
|
| 422 |
+
"from": "Prop11",
|
| 423 |
+
"to": "Prop14"
|
| 424 |
+
},
|
| 425 |
+
{
|
| 426 |
+
"from": "BookVII",
|
| 427 |
+
"to": "Prop15"
|
| 428 |
+
},
|
| 429 |
+
{
|
| 430 |
+
"from": "Prop12",
|
| 431 |
+
"to": "Prop15"
|
| 432 |
+
},
|
| 433 |
+
{
|
| 434 |
+
"from": "BookVII",
|
| 435 |
+
"to": "Prop16"
|
| 436 |
+
},
|
| 437 |
+
{
|
| 438 |
+
"from": "Prop14",
|
| 439 |
+
"to": "Prop16"
|
| 440 |
+
},
|
| 441 |
+
{
|
| 442 |
+
"from": "BookVII",
|
| 443 |
+
"to": "Prop17"
|
| 444 |
+
},
|
| 445 |
+
{
|
| 446 |
+
"from": "Prop15",
|
| 447 |
+
"to": "Prop17"
|
| 448 |
+
},
|
| 449 |
+
{
|
| 450 |
+
"from": "BookVII",
|
| 451 |
+
"to": "Prop18"
|
| 452 |
+
},
|
| 453 |
+
{
|
| 454 |
+
"from": "Prop8",
|
| 455 |
+
"to": "Prop18"
|
| 456 |
+
},
|
| 457 |
+
{
|
| 458 |
+
"from": "BookVII",
|
| 459 |
+
"to": "Prop19"
|
| 460 |
+
},
|
| 461 |
+
{
|
| 462 |
+
"from": "Prop8",
|
| 463 |
+
"to": "Prop19"
|
| 464 |
+
},
|
| 465 |
+
{
|
| 466 |
+
"from": "BookVII",
|
| 467 |
+
"to": "Prop20"
|
| 468 |
+
},
|
| 469 |
+
{
|
| 470 |
+
"from": "Prop18",
|
| 471 |
+
"to": "Prop20"
|
| 472 |
+
},
|
| 473 |
+
{
|
| 474 |
+
"from": "BookVII",
|
| 475 |
+
"to": "Prop21"
|
| 476 |
+
},
|
| 477 |
+
{
|
| 478 |
+
"from": "Prop19",
|
| 479 |
+
"to": "Prop21"
|
| 480 |
+
},
|
| 481 |
+
{
|
| 482 |
+
"from": "BookVII",
|
| 483 |
+
"to": "Prop22"
|
| 484 |
+
},
|
| 485 |
+
{
|
| 486 |
+
"from": "Prop1",
|
| 487 |
+
"to": "Prop22"
|
| 488 |
+
},
|
| 489 |
+
{
|
| 490 |
+
"from": "BookVII",
|
| 491 |
+
"to": "Prop23"
|
| 492 |
+
},
|
| 493 |
+
{
|
| 494 |
+
"from": "Prop1",
|
| 495 |
+
"to": "Prop23"
|
| 496 |
+
},
|
| 497 |
+
{
|
| 498 |
+
"from": "BookVII",
|
| 499 |
+
"to": "Prop24"
|
| 500 |
+
},
|
| 501 |
+
{
|
| 502 |
+
"from": "Prop22",
|
| 503 |
+
"to": "Prop24"
|
| 504 |
+
},
|
| 505 |
+
{
|
| 506 |
+
"from": "BookVII",
|
| 507 |
+
"to": "Prop25"
|
| 508 |
+
},
|
| 509 |
+
{
|
| 510 |
+
"from": "Prop23",
|
| 511 |
+
"to": "Prop25"
|
| 512 |
+
},
|
| 513 |
+
{
|
| 514 |
+
"from": "BookVII",
|
| 515 |
+
"to": "Prop26"
|
| 516 |
+
},
|
| 517 |
+
{
|
| 518 |
+
"from": "Prop18",
|
| 519 |
+
"to": "Prop26"
|
| 520 |
+
},
|
| 521 |
+
{
|
| 522 |
+
"from": "BookVII",
|
| 523 |
+
"to": "Prop27"
|
| 524 |
+
},
|
| 525 |
+
{
|
| 526 |
+
"from": "Prop19",
|
| 527 |
+
"to": "Prop27"
|
| 528 |
+
}
|
| 529 |
+
],
|
| 530 |
+
"colorScheme": {
|
| 531 |
+
"foundation": {
|
| 532 |
+
"fill": "#95a5a6",
|
| 533 |
+
"stroke": "#7f8c8d"
|
| 534 |
+
},
|
| 535 |
+
"proposition": {
|
| 536 |
+
"fill": "#1abc9c",
|
| 537 |
+
"stroke": "#16a085"
|
| 538 |
+
}
|
| 539 |
+
}
|
| 540 |
+
}
|
data/euclid-elements-book-x.json
ADDED
|
@@ -0,0 +1,2620 @@
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| 1 |
+
{
|
| 2 |
+
"schemaVersion": "1.0",
|
| 3 |
+
"discourse": {
|
| 4 |
+
"id": "euclid-elements-book-x",
|
| 5 |
+
"name": "Euclid's Elements, Book X",
|
| 6 |
+
"subject": "incommensurables",
|
| 7 |
+
"variant": "classical",
|
| 8 |
+
"description": "Incommensurables, binomials, apotomes. 16 definitions, 115 propositions. Depends on Books I, V, VI. Source: David E. Joyce.",
|
| 9 |
+
"structure": {
|
| 10 |
+
"books": 10,
|
| 11 |
+
"definitions": 16,
|
| 12 |
+
"propositions": 115,
|
| 13 |
+
"foundationTypes": [
|
| 14 |
+
"foundation"
|
| 15 |
+
]
|
| 16 |
+
}
|
| 17 |
+
},
|
| 18 |
+
"metadata": {
|
| 19 |
+
"created": "2026-03-18",
|
| 20 |
+
"lastUpdated": "2026-03-18",
|
| 21 |
+
"version": "1.0.0",
|
| 22 |
+
"license": "CC BY 4.0",
|
| 23 |
+
"authors": [
|
| 24 |
+
"Welz, G."
|
| 25 |
+
],
|
| 26 |
+
"methodology": "Programming Framework",
|
| 27 |
+
"citation": "Welz, G. (2026). Euclid's Elements Book X Dependency Graph. Programming Framework.",
|
| 28 |
+
"keywords": [
|
| 29 |
+
"Euclid",
|
| 30 |
+
"Elements",
|
| 31 |
+
"Book X",
|
| 32 |
+
"incommensurable",
|
| 33 |
+
"binomial",
|
| 34 |
+
"apotome",
|
| 35 |
+
"medial"
|
| 36 |
+
]
|
| 37 |
+
},
|
| 38 |
+
"sources": [
|
| 39 |
+
{
|
| 40 |
+
"id": "joyce",
|
| 41 |
+
"type": "digital",
|
| 42 |
+
"authors": "Joyce, David E.",
|
| 43 |
+
"title": "Euclid's Elements, Book X",
|
| 44 |
+
"year": "1996",
|
| 45 |
+
"url": "https://mathcs.clarku.edu/~djoyce/java/elements/bookX/bookX.html",
|
| 46 |
+
"notes": "Clark University"
|
| 47 |
+
}
|
| 48 |
+
],
|
| 49 |
+
"nodes": [
|
| 50 |
+
{
|
| 51 |
+
"id": "BookI",
|
| 52 |
+
"type": "foundation",
|
| 53 |
+
"label": "Book I — Plane geometry",
|
| 54 |
+
"shortLabel": "Book I",
|
| 55 |
+
"short": "Foundation",
|
| 56 |
+
"book": 1,
|
| 57 |
+
"colorClass": "foundation"
|
| 58 |
+
},
|
| 59 |
+
{
|
| 60 |
+
"id": "BookV",
|
| 61 |
+
"type": "foundation",
|
| 62 |
+
"label": "Book V — Proportions",
|
| 63 |
+
"shortLabel": "Book V",
|
| 64 |
+
"short": "Foundation",
|
| 65 |
+
"book": 5,
|
| 66 |
+
"colorClass": "foundation"
|
| 67 |
+
},
|
| 68 |
+
{
|
| 69 |
+
"id": "BookVI",
|
| 70 |
+
"type": "foundation",
|
| 71 |
+
"label": "Book VI — Similar figures",
|
| 72 |
+
"shortLabel": "Book VI",
|
| 73 |
+
"short": "Foundation",
|
| 74 |
+
"book": 6,
|
| 75 |
+
"colorClass": "foundation"
|
| 76 |
+
},
|
| 77 |
+
{
|
| 78 |
+
"id": "Prop1",
|
| 79 |
+
"type": "proposition",
|
| 80 |
+
"label": "Two unequal magnitudes: subtract more than half repeatedly; remainder less than lesser",
|
| 81 |
+
"shortLabel": "Prop. X.1",
|
| 82 |
+
"short": "Antenaresis for magnitudes",
|
| 83 |
+
"book": 10,
|
| 84 |
+
"number": 1,
|
| 85 |
+
"colorClass": "proposition"
|
| 86 |
+
},
|
| 87 |
+
{
|
| 88 |
+
"id": "Prop2",
|
| 89 |
+
"type": "proposition",
|
| 90 |
+
"label": "If less subtracted from greater repeatedly and remainder never measures prior: incommensurable",
|
| 91 |
+
"shortLabel": "Prop. X.2",
|
| 92 |
+
"short": "Incommensurable criterion",
|
| 93 |
+
"book": 10,
|
| 94 |
+
"number": 2,
|
| 95 |
+
"colorClass": "proposition"
|
| 96 |
+
},
|
| 97 |
+
{
|
| 98 |
+
"id": "Prop3",
|
| 99 |
+
"type": "proposition",
|
| 100 |
+
"label": "To find greatest common measure of two commensurable magnitudes",
|
| 101 |
+
"shortLabel": "Prop. X.3",
|
| 102 |
+
"short": "GCM of two commensurable",
|
| 103 |
+
"book": 10,
|
| 104 |
+
"number": 3,
|
| 105 |
+
"colorClass": "proposition"
|
| 106 |
+
},
|
| 107 |
+
{
|
| 108 |
+
"id": "Prop4",
|
| 109 |
+
"type": "proposition",
|
| 110 |
+
"label": "To find greatest common measure of three commensurable magnitudes",
|
| 111 |
+
"shortLabel": "Prop. X.4",
|
| 112 |
+
"short": "GCM of three commensurable",
|
| 113 |
+
"book": 10,
|
| 114 |
+
"number": 4,
|
| 115 |
+
"colorClass": "proposition"
|
| 116 |
+
},
|
| 117 |
+
{
|
| 118 |
+
"id": "Prop5",
|
| 119 |
+
"type": "proposition",
|
| 120 |
+
"label": "Commensurable magnitudes have ratio which a number has to a number",
|
| 121 |
+
"shortLabel": "Prop. X.5",
|
| 122 |
+
"short": "Commensurable: number ratio",
|
| 123 |
+
"book": 10,
|
| 124 |
+
"number": 5,
|
| 125 |
+
"colorClass": "proposition"
|
| 126 |
+
},
|
| 127 |
+
{
|
| 128 |
+
"id": "Prop6",
|
| 129 |
+
"type": "proposition",
|
| 130 |
+
"label": "If two magnitudes have number-to-number ratio, they are commensurable",
|
| 131 |
+
"shortLabel": "Prop. X.6",
|
| 132 |
+
"short": "Number ratio: commensurable",
|
| 133 |
+
"book": 10,
|
| 134 |
+
"number": 6,
|
| 135 |
+
"colorClass": "proposition"
|
| 136 |
+
},
|
| 137 |
+
{
|
| 138 |
+
"id": "Prop7",
|
| 139 |
+
"type": "proposition",
|
| 140 |
+
"label": "Incommensurable magnitudes do not have number-to-number ratio",
|
| 141 |
+
"shortLabel": "Prop. X.7",
|
| 142 |
+
"short": "Incommensurable: no number ratio",
|
| 143 |
+
"book": 10,
|
| 144 |
+
"number": 7,
|
| 145 |
+
"colorClass": "proposition"
|
| 146 |
+
},
|
| 147 |
+
{
|
| 148 |
+
"id": "Prop8",
|
| 149 |
+
"type": "proposition",
|
| 150 |
+
"label": "If magnitudes lack number-to-number ratio, they are incommensurable",
|
| 151 |
+
"shortLabel": "Prop. X.8",
|
| 152 |
+
"short": "No number ratio: incommensurable",
|
| 153 |
+
"book": 10,
|
| 154 |
+
"number": 8,
|
| 155 |
+
"colorClass": "proposition"
|
| 156 |
+
},
|
| 157 |
+
{
|
| 158 |
+
"id": "Prop9",
|
| 159 |
+
"type": "proposition",
|
| 160 |
+
"label": "Squares on commensurable lines have square-to-square ratio; converse",
|
| 161 |
+
"shortLabel": "Prop. X.9",
|
| 162 |
+
"short": "Squares: commensurable iff square ratio",
|
| 163 |
+
"book": 10,
|
| 164 |
+
"number": 9,
|
| 165 |
+
"colorClass": "proposition"
|
| 166 |
+
},
|
| 167 |
+
{
|
| 168 |
+
"id": "Prop10",
|
| 169 |
+
"type": "proposition",
|
| 170 |
+
"label": "To find two lines incommensurable with assigned: one in length, one in square",
|
| 171 |
+
"shortLabel": "Prop. X.10",
|
| 172 |
+
"short": "Find incommensurable lines",
|
| 173 |
+
"book": 10,
|
| 174 |
+
"number": 10,
|
| 175 |
+
"colorClass": "proposition"
|
| 176 |
+
},
|
| 177 |
+
{
|
| 178 |
+
"id": "Prop11",
|
| 179 |
+
"type": "proposition",
|
| 180 |
+
"label": "Four proportional: first commensurable with second iff third with fourth",
|
| 181 |
+
"shortLabel": "Prop. X.11",
|
| 182 |
+
"short": "Proportion preserves commensurability",
|
| 183 |
+
"book": 10,
|
| 184 |
+
"number": 11,
|
| 185 |
+
"colorClass": "proposition"
|
| 186 |
+
},
|
| 187 |
+
{
|
| 188 |
+
"id": "Prop12",
|
| 189 |
+
"type": "proposition",
|
| 190 |
+
"label": "Magnitudes commensurable with same magnitude are commensurable",
|
| 191 |
+
"shortLabel": "Prop. X.12",
|
| 192 |
+
"short": "Commensurable with same",
|
| 193 |
+
"book": 10,
|
| 194 |
+
"number": 12,
|
| 195 |
+
"colorClass": "proposition"
|
| 196 |
+
},
|
| 197 |
+
{
|
| 198 |
+
"id": "Prop13",
|
| 199 |
+
"type": "proposition",
|
| 200 |
+
"label": "If two commensurable, one incommensurable with third, so is the other",
|
| 201 |
+
"shortLabel": "Prop. X.13",
|
| 202 |
+
"short": "Commensurable: incommensurable partner",
|
| 203 |
+
"book": 10,
|
| 204 |
+
"number": 13,
|
| 205 |
+
"colorClass": "proposition"
|
| 206 |
+
},
|
| 207 |
+
{
|
| 208 |
+
"id": "Prop14",
|
| 209 |
+
"type": "proposition",
|
| 210 |
+
"label": "Given two lines: find square by which greater square exceeds less; find line whose square equals sum",
|
| 211 |
+
"shortLabel": "Prop. X.14",
|
| 212 |
+
"short": "Square difference, sum of squares",
|
| 213 |
+
"book": 10,
|
| 214 |
+
"number": 14,
|
| 215 |
+
"colorClass": "proposition"
|
| 216 |
+
},
|
| 217 |
+
{
|
| 218 |
+
"id": "Prop15",
|
| 219 |
+
"type": "proposition",
|
| 220 |
+
"label": "Two commensurable added: whole commensurable with each",
|
| 221 |
+
"shortLabel": "Prop. X.15",
|
| 222 |
+
"short": "Commensurable sum",
|
| 223 |
+
"book": 10,
|
| 224 |
+
"number": 15,
|
| 225 |
+
"colorClass": "proposition"
|
| 226 |
+
},
|
| 227 |
+
{
|
| 228 |
+
"id": "Prop16",
|
| 229 |
+
"type": "proposition",
|
| 230 |
+
"label": "Two incommensurable added: sum incommensurable with each",
|
| 231 |
+
"shortLabel": "Prop. X.16",
|
| 232 |
+
"short": "Incommensurable sum",
|
| 233 |
+
"book": 10,
|
| 234 |
+
"number": 16,
|
| 235 |
+
"colorClass": "proposition"
|
| 236 |
+
},
|
| 237 |
+
{
|
| 238 |
+
"id": "Prop17",
|
| 239 |
+
"type": "proposition",
|
| 240 |
+
"label": "Applied parallelogram falling short by square: parts commensurable iff square difference commensurable",
|
| 241 |
+
"shortLabel": "Prop. X.17",
|
| 242 |
+
"short": "Parallelogram falling short",
|
| 243 |
+
"book": 10,
|
| 244 |
+
"number": 17,
|
| 245 |
+
"colorClass": "proposition"
|
| 246 |
+
},
|
| 247 |
+
{
|
| 248 |
+
"id": "Prop18",
|
| 249 |
+
"type": "proposition",
|
| 250 |
+
"label": "Applied parallelogram: parts incommensurable iff square difference incommensurable",
|
| 251 |
+
"shortLabel": "Prop. X.18",
|
| 252 |
+
"short": "Parallelogram: incommensurable parts",
|
| 253 |
+
"book": 10,
|
| 254 |
+
"number": 18,
|
| 255 |
+
"colorClass": "proposition"
|
| 256 |
+
},
|
| 257 |
+
{
|
| 258 |
+
"id": "Prop19",
|
| 259 |
+
"type": "proposition",
|
| 260 |
+
"label": "Rectangle by rational lines commensurable in length is rational",
|
| 261 |
+
"shortLabel": "Prop. X.19",
|
| 262 |
+
"short": "Rational rectangle from rational",
|
| 263 |
+
"book": 10,
|
| 264 |
+
"number": 19,
|
| 265 |
+
"colorClass": "proposition"
|
| 266 |
+
},
|
| 267 |
+
{
|
| 268 |
+
"id": "Prop20",
|
| 269 |
+
"type": "proposition",
|
| 270 |
+
"label": "Rational area applied to rational line: breadth rational and commensurable",
|
| 271 |
+
"shortLabel": "Prop. X.20",
|
| 272 |
+
"short": "Rational area on rational",
|
| 273 |
+
"book": 10,
|
| 274 |
+
"number": 20,
|
| 275 |
+
"colorClass": "proposition"
|
| 276 |
+
},
|
| 277 |
+
{
|
| 278 |
+
"id": "Prop21",
|
| 279 |
+
"type": "proposition",
|
| 280 |
+
"label": "Rectangle by rational in square only is irrational; side called medial",
|
| 281 |
+
"shortLabel": "Prop. X.21",
|
| 282 |
+
"short": "Medial: rational in square only",
|
| 283 |
+
"book": 10,
|
| 284 |
+
"number": 21,
|
| 285 |
+
"colorClass": "proposition"
|
| 286 |
+
},
|
| 287 |
+
{
|
| 288 |
+
"id": "Prop22",
|
| 289 |
+
"type": "proposition",
|
| 290 |
+
"label": "Square on medial applied to rational: breadth rational, incommensurable in length",
|
| 291 |
+
"shortLabel": "Prop. X.22",
|
| 292 |
+
"short": "Medial applied to rational",
|
| 293 |
+
"book": 10,
|
| 294 |
+
"number": 22,
|
| 295 |
+
"colorClass": "proposition"
|
| 296 |
+
},
|
| 297 |
+
{
|
| 298 |
+
"id": "Prop23",
|
| 299 |
+
"type": "proposition",
|
| 300 |
+
"label": "Line commensurable with medial is medial",
|
| 301 |
+
"shortLabel": "Prop. X.23",
|
| 302 |
+
"short": "Commensurable with medial",
|
| 303 |
+
"book": 10,
|
| 304 |
+
"number": 23,
|
| 305 |
+
"colorClass": "proposition"
|
| 306 |
+
},
|
| 307 |
+
{
|
| 308 |
+
"id": "Prop24",
|
| 309 |
+
"type": "proposition",
|
| 310 |
+
"label": "Rectangle by medial lines commensurable in length is medial",
|
| 311 |
+
"shortLabel": "Prop. X.24",
|
| 312 |
+
"short": "Medial rectangle: commensurable length",
|
| 313 |
+
"book": 10,
|
| 314 |
+
"number": 24,
|
| 315 |
+
"colorClass": "proposition"
|
| 316 |
+
},
|
| 317 |
+
{
|
| 318 |
+
"id": "Prop25",
|
| 319 |
+
"type": "proposition",
|
| 320 |
+
"label": "Rectangle by medial in square only: rational or medial",
|
| 321 |
+
"shortLabel": "Prop. X.25",
|
| 322 |
+
"short": "Medial: square only",
|
| 323 |
+
"book": 10,
|
| 324 |
+
"number": 25,
|
| 325 |
+
"colorClass": "proposition"
|
| 326 |
+
},
|
| 327 |
+
{
|
| 328 |
+
"id": "Prop26",
|
| 329 |
+
"type": "proposition",
|
| 330 |
+
"label": "Medial area does not exceed medial by rational area",
|
| 331 |
+
"shortLabel": "Prop. X.26",
|
| 332 |
+
"short": "Medial minus medial",
|
| 333 |
+
"book": 10,
|
| 334 |
+
"number": 26,
|
| 335 |
+
"colorClass": "proposition"
|
| 336 |
+
},
|
| 337 |
+
{
|
| 338 |
+
"id": "Prop27",
|
| 339 |
+
"type": "proposition",
|
| 340 |
+
"label": "To find medial lines commensurable in square only containing rational rectangle",
|
| 341 |
+
"shortLabel": "Prop. X.27",
|
| 342 |
+
"short": "Find medial in square only, rational rect",
|
| 343 |
+
"book": 10,
|
| 344 |
+
"number": 27,
|
| 345 |
+
"colorClass": "proposition"
|
| 346 |
+
},
|
| 347 |
+
{
|
| 348 |
+
"id": "Prop28",
|
| 349 |
+
"type": "proposition",
|
| 350 |
+
"label": "To find medial lines commensurable in square only containing medial rectangle",
|
| 351 |
+
"shortLabel": "Prop. X.28",
|
| 352 |
+
"short": "Find medial in square only, medial rect",
|
| 353 |
+
"book": 10,
|
| 354 |
+
"number": 28,
|
| 355 |
+
"colorClass": "proposition"
|
| 356 |
+
},
|
| 357 |
+
{
|
| 358 |
+
"id": "Prop29",
|
| 359 |
+
"type": "proposition",
|
| 360 |
+
"label": "To find two rational in square only: square diff commensurable with greater",
|
| 361 |
+
"shortLabel": "Prop. X.29",
|
| 362 |
+
"short": "Find rational in square only, commensurable diff",
|
| 363 |
+
"book": 10,
|
| 364 |
+
"number": 29,
|
| 365 |
+
"colorClass": "proposition"
|
| 366 |
+
},
|
| 367 |
+
{
|
| 368 |
+
"id": "Prop30",
|
| 369 |
+
"type": "proposition",
|
| 370 |
+
"label": "To find two rational in square only: square diff incommensurable with greater",
|
| 371 |
+
"shortLabel": "Prop. X.30",
|
| 372 |
+
"short": "Find rational in square only, incommensurable diff",
|
| 373 |
+
"book": 10,
|
| 374 |
+
"number": 30,
|
| 375 |
+
"colorClass": "proposition"
|
| 376 |
+
},
|
| 377 |
+
{
|
| 378 |
+
"id": "Prop31",
|
| 379 |
+
"type": "proposition",
|
| 380 |
+
"label": "To find two medial in square only, rational rect: diff commensurable with greater",
|
| 381 |
+
"shortLabel": "Prop. X.31",
|
| 382 |
+
"short": "Find medial, rational rect, commensurable diff",
|
| 383 |
+
"book": 10,
|
| 384 |
+
"number": 31,
|
| 385 |
+
"colorClass": "proposition"
|
| 386 |
+
},
|
| 387 |
+
{
|
| 388 |
+
"id": "Prop32",
|
| 389 |
+
"type": "proposition",
|
| 390 |
+
"label": "To find two medial in square only, medial rect: diff commensurable with greater",
|
| 391 |
+
"shortLabel": "Prop. X.32",
|
| 392 |
+
"short": "Find medial, medial rect, commensurable diff",
|
| 393 |
+
"book": 10,
|
| 394 |
+
"number": 32,
|
| 395 |
+
"colorClass": "proposition"
|
| 396 |
+
},
|
| 397 |
+
{
|
| 398 |
+
"id": "Prop33",
|
| 399 |
+
"type": "proposition",
|
| 400 |
+
"label": "To find two incommensurable in square: sum of squares rational, rectangle medial",
|
| 401 |
+
"shortLabel": "Prop. X.33",
|
| 402 |
+
"short": "Find incommensurable: rational sum, medial rect",
|
| 403 |
+
"book": 10,
|
| 404 |
+
"number": 33,
|
| 405 |
+
"colorClass": "proposition"
|
| 406 |
+
},
|
| 407 |
+
{
|
| 408 |
+
"id": "Prop34",
|
| 409 |
+
"type": "proposition",
|
| 410 |
+
"label": "To find two incommensurable in square: sum medial, rectangle rational",
|
| 411 |
+
"shortLabel": "Prop. X.34",
|
| 412 |
+
"short": "Find incommensurable: medial sum, rational rect",
|
| 413 |
+
"book": 10,
|
| 414 |
+
"number": 34,
|
| 415 |
+
"colorClass": "proposition"
|
| 416 |
+
},
|
| 417 |
+
{
|
| 418 |
+
"id": "Prop35",
|
| 419 |
+
"type": "proposition",
|
| 420 |
+
"label": "To find two incommensurable in square: sum and rect medial, incommensurable",
|
| 421 |
+
"shortLabel": "Prop. X.35",
|
| 422 |
+
"short": "Find incommensurable: both medial",
|
| 423 |
+
"book": 10,
|
| 424 |
+
"number": 35,
|
| 425 |
+
"colorClass": "proposition"
|
| 426 |
+
},
|
| 427 |
+
{
|
| 428 |
+
"id": "Prop36",
|
| 429 |
+
"type": "proposition",
|
| 430 |
+
"label": "Two rational in square only added: whole irrational, called binomial",
|
| 431 |
+
"shortLabel": "Prop. X.36",
|
| 432 |
+
"short": "Binomial defined",
|
| 433 |
+
"book": 10,
|
| 434 |
+
"number": 36,
|
| 435 |
+
"colorClass": "proposition"
|
| 436 |
+
},
|
| 437 |
+
{
|
| 438 |
+
"id": "Prop37",
|
| 439 |
+
"type": "proposition",
|
| 440 |
+
"label": "Two medial in square only, rational rect added: first bimedial",
|
| 441 |
+
"shortLabel": "Prop. X.37",
|
| 442 |
+
"short": "First bimedial defined",
|
| 443 |
+
"book": 10,
|
| 444 |
+
"number": 37,
|
| 445 |
+
"colorClass": "proposition"
|
| 446 |
+
},
|
| 447 |
+
{
|
| 448 |
+
"id": "Prop38",
|
| 449 |
+
"type": "proposition",
|
| 450 |
+
"label": "Two medial in square only, medial rect added: second bimedial",
|
| 451 |
+
"shortLabel": "Prop. X.38",
|
| 452 |
+
"short": "Second bimedial defined",
|
| 453 |
+
"book": 10,
|
| 454 |
+
"number": 38,
|
| 455 |
+
"colorClass": "proposition"
|
| 456 |
+
},
|
| 457 |
+
{
|
| 458 |
+
"id": "Prop39",
|
| 459 |
+
"type": "proposition",
|
| 460 |
+
"label": "Two incommensurable in square, rational sum, medial rect added: major",
|
| 461 |
+
"shortLabel": "Prop. X.39",
|
| 462 |
+
"short": "Major defined",
|
| 463 |
+
"book": 10,
|
| 464 |
+
"number": 39,
|
| 465 |
+
"colorClass": "proposition"
|
| 466 |
+
},
|
| 467 |
+
{
|
| 468 |
+
"id": "Prop40",
|
| 469 |
+
"type": "proposition",
|
| 470 |
+
"label": "Two incommensurable in square, medial sum, rational rect added: side of rational plus medial",
|
| 471 |
+
"shortLabel": "Prop. X.40",
|
| 472 |
+
"short": "Side of rational plus medial",
|
| 473 |
+
"book": 10,
|
| 474 |
+
"number": 40,
|
| 475 |
+
"colorClass": "proposition"
|
| 476 |
+
},
|
| 477 |
+
{
|
| 478 |
+
"id": "Prop41",
|
| 479 |
+
"type": "proposition",
|
| 480 |
+
"label": "Two incommensurable in square, both medial added: side of sum of two medial",
|
| 481 |
+
"shortLabel": "Prop. X.41",
|
| 482 |
+
"short": "Side of sum of two medial",
|
| 483 |
+
"book": 10,
|
| 484 |
+
"number": 41,
|
| 485 |
+
"colorClass": "proposition"
|
| 486 |
+
},
|
| 487 |
+
{
|
| 488 |
+
"id": "Prop42",
|
| 489 |
+
"type": "proposition",
|
| 490 |
+
"label": "Binomial divided into terms at one point only",
|
| 491 |
+
"shortLabel": "Prop. X.42",
|
| 492 |
+
"short": "Binomial: unique division",
|
| 493 |
+
"book": 10,
|
| 494 |
+
"number": 42,
|
| 495 |
+
"colorClass": "proposition"
|
| 496 |
+
},
|
| 497 |
+
{
|
| 498 |
+
"id": "Prop43",
|
| 499 |
+
"type": "proposition",
|
| 500 |
+
"label": "First bimedial divided at one point only",
|
| 501 |
+
"shortLabel": "Prop. X.43",
|
| 502 |
+
"short": "First bimedial: unique division",
|
| 503 |
+
"book": 10,
|
| 504 |
+
"number": 43,
|
| 505 |
+
"colorClass": "proposition"
|
| 506 |
+
},
|
| 507 |
+
{
|
| 508 |
+
"id": "Prop44",
|
| 509 |
+
"type": "proposition",
|
| 510 |
+
"label": "Second bimedial divided at one point only",
|
| 511 |
+
"shortLabel": "Prop. X.44",
|
| 512 |
+
"short": "Second bimedial: unique division",
|
| 513 |
+
"book": 10,
|
| 514 |
+
"number": 44,
|
| 515 |
+
"colorClass": "proposition"
|
| 516 |
+
},
|
| 517 |
+
{
|
| 518 |
+
"id": "Prop45",
|
| 519 |
+
"type": "proposition",
|
| 520 |
+
"label": "Major divided at one point only",
|
| 521 |
+
"shortLabel": "Prop. X.45",
|
| 522 |
+
"short": "Major: unique division",
|
| 523 |
+
"book": 10,
|
| 524 |
+
"number": 45,
|
| 525 |
+
"colorClass": "proposition"
|
| 526 |
+
},
|
| 527 |
+
{
|
| 528 |
+
"id": "Prop46",
|
| 529 |
+
"type": "proposition",
|
| 530 |
+
"label": "Side of rational plus medial divided at one point only",
|
| 531 |
+
"shortLabel": "Prop. X.46",
|
| 532 |
+
"short": "Side rational+medial: unique division",
|
| 533 |
+
"book": 10,
|
| 534 |
+
"number": 46,
|
| 535 |
+
"colorClass": "proposition"
|
| 536 |
+
},
|
| 537 |
+
{
|
| 538 |
+
"id": "Prop47",
|
| 539 |
+
"type": "proposition",
|
| 540 |
+
"label": "Side of sum of two medial divided at one point only",
|
| 541 |
+
"shortLabel": "Prop. X.47",
|
| 542 |
+
"short": "Side two medial: unique division",
|
| 543 |
+
"book": 10,
|
| 544 |
+
"number": 47,
|
| 545 |
+
"colorClass": "proposition"
|
| 546 |
+
},
|
| 547 |
+
{
|
| 548 |
+
"id": "Prop48",
|
| 549 |
+
"type": "proposition",
|
| 550 |
+
"label": "To find the first binomial line",
|
| 551 |
+
"shortLabel": "Prop. X.48",
|
| 552 |
+
"short": "Find first binomial",
|
| 553 |
+
"book": 10,
|
| 554 |
+
"number": 48,
|
| 555 |
+
"colorClass": "proposition"
|
| 556 |
+
},
|
| 557 |
+
{
|
| 558 |
+
"id": "Prop49",
|
| 559 |
+
"type": "proposition",
|
| 560 |
+
"label": "To find the second binomial line",
|
| 561 |
+
"shortLabel": "Prop. X.49",
|
| 562 |
+
"short": "Find second binomial",
|
| 563 |
+
"book": 10,
|
| 564 |
+
"number": 49,
|
| 565 |
+
"colorClass": "proposition"
|
| 566 |
+
},
|
| 567 |
+
{
|
| 568 |
+
"id": "Prop50",
|
| 569 |
+
"type": "proposition",
|
| 570 |
+
"label": "To find the third binomial line",
|
| 571 |
+
"shortLabel": "Prop. X.50",
|
| 572 |
+
"short": "Find third binomial",
|
| 573 |
+
"book": 10,
|
| 574 |
+
"number": 50,
|
| 575 |
+
"colorClass": "proposition"
|
| 576 |
+
},
|
| 577 |
+
{
|
| 578 |
+
"id": "Prop51",
|
| 579 |
+
"type": "proposition",
|
| 580 |
+
"label": "To find the fourth binomial line",
|
| 581 |
+
"shortLabel": "Prop. X.51",
|
| 582 |
+
"short": "Find fourth binomial",
|
| 583 |
+
"book": 10,
|
| 584 |
+
"number": 51,
|
| 585 |
+
"colorClass": "proposition"
|
| 586 |
+
},
|
| 587 |
+
{
|
| 588 |
+
"id": "Prop52",
|
| 589 |
+
"type": "proposition",
|
| 590 |
+
"label": "To find the fifth binomial line",
|
| 591 |
+
"shortLabel": "Prop. X.52",
|
| 592 |
+
"short": "Find fifth binomial",
|
| 593 |
+
"book": 10,
|
| 594 |
+
"number": 52,
|
| 595 |
+
"colorClass": "proposition"
|
| 596 |
+
},
|
| 597 |
+
{
|
| 598 |
+
"id": "Prop53",
|
| 599 |
+
"type": "proposition",
|
| 600 |
+
"label": "To find the sixth binomial line",
|
| 601 |
+
"shortLabel": "Prop. X.53",
|
| 602 |
+
"short": "Find sixth binomial",
|
| 603 |
+
"book": 10,
|
| 604 |
+
"number": 53,
|
| 605 |
+
"colorClass": "proposition"
|
| 606 |
+
},
|
| 607 |
+
{
|
| 608 |
+
"id": "Prop54",
|
| 609 |
+
"type": "proposition",
|
| 610 |
+
"label": "Area by rational and first binomial: side is binomial",
|
| 611 |
+
"shortLabel": "Prop. X.54",
|
| 612 |
+
"short": "Rational × first binomial",
|
| 613 |
+
"book": 10,
|
| 614 |
+
"number": 54,
|
| 615 |
+
"colorClass": "proposition"
|
| 616 |
+
},
|
| 617 |
+
{
|
| 618 |
+
"id": "Prop55",
|
| 619 |
+
"type": "proposition",
|
| 620 |
+
"label": "Area by rational and second binomial: side is first bimedial",
|
| 621 |
+
"shortLabel": "Prop. X.55",
|
| 622 |
+
"short": "Rational × second binomial",
|
| 623 |
+
"book": 10,
|
| 624 |
+
"number": 55,
|
| 625 |
+
"colorClass": "proposition"
|
| 626 |
+
},
|
| 627 |
+
{
|
| 628 |
+
"id": "Prop56",
|
| 629 |
+
"type": "proposition",
|
| 630 |
+
"label": "Area by rational and third binomial: side is second bimedial",
|
| 631 |
+
"shortLabel": "Prop. X.56",
|
| 632 |
+
"short": "Rational × third binomial",
|
| 633 |
+
"book": 10,
|
| 634 |
+
"number": 56,
|
| 635 |
+
"colorClass": "proposition"
|
| 636 |
+
},
|
| 637 |
+
{
|
| 638 |
+
"id": "Prop57",
|
| 639 |
+
"type": "proposition",
|
| 640 |
+
"label": "Area by rational and fourth binomial: side is major",
|
| 641 |
+
"shortLabel": "Prop. X.57",
|
| 642 |
+
"short": "Rational × fourth binomial",
|
| 643 |
+
"book": 10,
|
| 644 |
+
"number": 57,
|
| 645 |
+
"colorClass": "proposition"
|
| 646 |
+
},
|
| 647 |
+
{
|
| 648 |
+
"id": "Prop58",
|
| 649 |
+
"type": "proposition",
|
| 650 |
+
"label": "Area by rational and fifth binomial: side is rational plus medial",
|
| 651 |
+
"shortLabel": "Prop. X.58",
|
| 652 |
+
"short": "Rational × fifth binomial",
|
| 653 |
+
"book": 10,
|
| 654 |
+
"number": 58,
|
| 655 |
+
"colorClass": "proposition"
|
| 656 |
+
},
|
| 657 |
+
{
|
| 658 |
+
"id": "Prop59",
|
| 659 |
+
"type": "proposition",
|
| 660 |
+
"label": "Area by rational and sixth binomial: side is sum of two medial",
|
| 661 |
+
"shortLabel": "Prop. X.59",
|
| 662 |
+
"short": "Rational × sixth binomial",
|
| 663 |
+
"book": 10,
|
| 664 |
+
"number": 59,
|
| 665 |
+
"colorClass": "proposition"
|
| 666 |
+
},
|
| 667 |
+
{
|
| 668 |
+
"id": "Prop60",
|
| 669 |
+
"type": "proposition",
|
| 670 |
+
"label": "Square on binomial applied to rational: breadth first binomial",
|
| 671 |
+
"shortLabel": "Prop. X.60",
|
| 672 |
+
"short": "Square on binomial",
|
| 673 |
+
"book": 10,
|
| 674 |
+
"number": 60,
|
| 675 |
+
"colorClass": "proposition"
|
| 676 |
+
},
|
| 677 |
+
{
|
| 678 |
+
"id": "Prop61",
|
| 679 |
+
"type": "proposition",
|
| 680 |
+
"label": "Square on first bimedial applied to rational: breadth second binomial",
|
| 681 |
+
"shortLabel": "Prop. X.61",
|
| 682 |
+
"short": "Square on first bimedial",
|
| 683 |
+
"book": 10,
|
| 684 |
+
"number": 61,
|
| 685 |
+
"colorClass": "proposition"
|
| 686 |
+
},
|
| 687 |
+
{
|
| 688 |
+
"id": "Prop62",
|
| 689 |
+
"type": "proposition",
|
| 690 |
+
"label": "Square on second bimedial applied to rational: breadth third binomial",
|
| 691 |
+
"shortLabel": "Prop. X.62",
|
| 692 |
+
"short": "Square on second bimedial",
|
| 693 |
+
"book": 10,
|
| 694 |
+
"number": 62,
|
| 695 |
+
"colorClass": "proposition"
|
| 696 |
+
},
|
| 697 |
+
{
|
| 698 |
+
"id": "Prop63",
|
| 699 |
+
"type": "proposition",
|
| 700 |
+
"label": "Square on major applied to rational: breadth fourth binomial",
|
| 701 |
+
"shortLabel": "Prop. X.63",
|
| 702 |
+
"short": "Square on major",
|
| 703 |
+
"book": 10,
|
| 704 |
+
"number": 63,
|
| 705 |
+
"colorClass": "proposition"
|
| 706 |
+
},
|
| 707 |
+
{
|
| 708 |
+
"id": "Prop64",
|
| 709 |
+
"type": "proposition",
|
| 710 |
+
"label": "Square on rational+medial applied to rational: breadth fifth binomial",
|
| 711 |
+
"shortLabel": "Prop. X.64",
|
| 712 |
+
"short": "Square on rational+medial",
|
| 713 |
+
"book": 10,
|
| 714 |
+
"number": 64,
|
| 715 |
+
"colorClass": "proposition"
|
| 716 |
+
},
|
| 717 |
+
{
|
| 718 |
+
"id": "Prop65",
|
| 719 |
+
"type": "proposition",
|
| 720 |
+
"label": "Square on sum of two medial applied to rational: breadth sixth binomial",
|
| 721 |
+
"shortLabel": "Prop. X.65",
|
| 722 |
+
"short": "Square on two medial",
|
| 723 |
+
"book": 10,
|
| 724 |
+
"number": 65,
|
| 725 |
+
"colorClass": "proposition"
|
| 726 |
+
},
|
| 727 |
+
{
|
| 728 |
+
"id": "Prop66",
|
| 729 |
+
"type": "proposition",
|
| 730 |
+
"label": "Line commensurable with binomial is binomial, same order",
|
| 731 |
+
"shortLabel": "Prop. X.66",
|
| 732 |
+
"short": "Commensurable with binomial",
|
| 733 |
+
"book": 10,
|
| 734 |
+
"number": 66,
|
| 735 |
+
"colorClass": "proposition"
|
| 736 |
+
},
|
| 737 |
+
{
|
| 738 |
+
"id": "Prop67",
|
| 739 |
+
"type": "proposition",
|
| 740 |
+
"label": "Line commensurable with bimedial is bimedial, same order",
|
| 741 |
+
"shortLabel": "Prop. X.67",
|
| 742 |
+
"short": "Commensurable with bimedial",
|
| 743 |
+
"book": 10,
|
| 744 |
+
"number": 67,
|
| 745 |
+
"colorClass": "proposition"
|
| 746 |
+
},
|
| 747 |
+
{
|
| 748 |
+
"id": "Prop68",
|
| 749 |
+
"type": "proposition",
|
| 750 |
+
"label": "Line commensurable with major is major",
|
| 751 |
+
"shortLabel": "Prop. X.68",
|
| 752 |
+
"short": "Commensurable with major",
|
| 753 |
+
"book": 10,
|
| 754 |
+
"number": 68,
|
| 755 |
+
"colorClass": "proposition"
|
| 756 |
+
},
|
| 757 |
+
{
|
| 758 |
+
"id": "Prop69",
|
| 759 |
+
"type": "proposition",
|
| 760 |
+
"label": "Line commensurable with rational+medial is rational+medial",
|
| 761 |
+
"shortLabel": "Prop. X.69",
|
| 762 |
+
"short": "Commensurable with rational+medial",
|
| 763 |
+
"book": 10,
|
| 764 |
+
"number": 69,
|
| 765 |
+
"colorClass": "proposition"
|
| 766 |
+
},
|
| 767 |
+
{
|
| 768 |
+
"id": "Prop70",
|
| 769 |
+
"type": "proposition",
|
| 770 |
+
"label": "Line commensurable with sum of two medial is sum of two medial",
|
| 771 |
+
"shortLabel": "Prop. X.70",
|
| 772 |
+
"short": "Commensurable with two medial",
|
| 773 |
+
"book": 10,
|
| 774 |
+
"number": 70,
|
| 775 |
+
"colorClass": "proposition"
|
| 776 |
+
},
|
| 777 |
+
{
|
| 778 |
+
"id": "Prop71",
|
| 779 |
+
"type": "proposition",
|
| 780 |
+
"label": "Rational and medial added: four irrationals arise",
|
| 781 |
+
"shortLabel": "Prop. X.71",
|
| 782 |
+
"short": "Rational + medial: four irrationals",
|
| 783 |
+
"book": 10,
|
| 784 |
+
"number": 71,
|
| 785 |
+
"colorClass": "proposition"
|
| 786 |
+
},
|
| 787 |
+
{
|
| 788 |
+
"id": "Prop72",
|
| 789 |
+
"type": "proposition",
|
| 790 |
+
"label": "Two medial incommensurable added: two irrationals arise",
|
| 791 |
+
"shortLabel": "Prop. X.72",
|
| 792 |
+
"short": "Two medial: two irrationals",
|
| 793 |
+
"book": 10,
|
| 794 |
+
"number": 72,
|
| 795 |
+
"colorClass": "proposition"
|
| 796 |
+
},
|
| 797 |
+
{
|
| 798 |
+
"id": "Prop73",
|
| 799 |
+
"type": "proposition",
|
| 800 |
+
"label": "Rational minus rational in square only: remainder irrational, apotome",
|
| 801 |
+
"shortLabel": "Prop. X.73",
|
| 802 |
+
"short": "Apotome defined",
|
| 803 |
+
"book": 10,
|
| 804 |
+
"number": 73,
|
| 805 |
+
"colorClass": "proposition"
|
| 806 |
+
},
|
| 807 |
+
{
|
| 808 |
+
"id": "Prop74",
|
| 809 |
+
"type": "proposition",
|
| 810 |
+
"label": "Medial minus medial, rational rect: first apotome of medial",
|
| 811 |
+
"shortLabel": "Prop. X.74",
|
| 812 |
+
"short": "First apotome of medial",
|
| 813 |
+
"book": 10,
|
| 814 |
+
"number": 74,
|
| 815 |
+
"colorClass": "proposition"
|
| 816 |
+
},
|
| 817 |
+
{
|
| 818 |
+
"id": "Prop75",
|
| 819 |
+
"type": "proposition",
|
| 820 |
+
"label": "Medial minus medial, medial rect: second apotome of medial",
|
| 821 |
+
"shortLabel": "Prop. X.75",
|
| 822 |
+
"short": "Second apotome of medial",
|
| 823 |
+
"book": 10,
|
| 824 |
+
"number": 75,
|
| 825 |
+
"colorClass": "proposition"
|
| 826 |
+
},
|
| 827 |
+
{
|
| 828 |
+
"id": "Prop76",
|
| 829 |
+
"type": "proposition",
|
| 830 |
+
"label": "Line minus incommensurable: sum rational, rect medial: remainder minor",
|
| 831 |
+
"shortLabel": "Prop. X.76",
|
| 832 |
+
"short": "Minor defined",
|
| 833 |
+
"book": 10,
|
| 834 |
+
"number": 76,
|
| 835 |
+
"colorClass": "proposition"
|
| 836 |
+
},
|
| 837 |
+
{
|
| 838 |
+
"id": "Prop77",
|
| 839 |
+
"type": "proposition",
|
| 840 |
+
"label": "Line minus incommensurable: sum medial, rect rational: produces rational+medial",
|
| 841 |
+
"shortLabel": "Prop. X.77",
|
| 842 |
+
"short": "Produces rational+medial",
|
| 843 |
+
"book": 10,
|
| 844 |
+
"number": 77,
|
| 845 |
+
"colorClass": "proposition"
|
| 846 |
+
},
|
| 847 |
+
{
|
| 848 |
+
"id": "Prop78",
|
| 849 |
+
"type": "proposition",
|
| 850 |
+
"label": "Line minus incommensurable: both medial, incommensurable: produces medial+medial",
|
| 851 |
+
"shortLabel": "Prop. X.78",
|
| 852 |
+
"short": "Produces medial+medial",
|
| 853 |
+
"book": 10,
|
| 854 |
+
"number": 78,
|
| 855 |
+
"colorClass": "proposition"
|
| 856 |
+
},
|
| 857 |
+
{
|
| 858 |
+
"id": "Prop79",
|
| 859 |
+
"type": "proposition",
|
| 860 |
+
"label": "To apotome only one rational can be annexed in square only",
|
| 861 |
+
"shortLabel": "Prop. X.79",
|
| 862 |
+
"short": "Apotome: unique annex",
|
| 863 |
+
"book": 10,
|
| 864 |
+
"number": 79,
|
| 865 |
+
"colorClass": "proposition"
|
| 866 |
+
},
|
| 867 |
+
{
|
| 868 |
+
"id": "Prop80",
|
| 869 |
+
"type": "proposition",
|
| 870 |
+
"label": "To first apotome of medial: unique medial annex, rational rect",
|
| 871 |
+
"shortLabel": "Prop. X.80",
|
| 872 |
+
"short": "First apotome medial: unique annex",
|
| 873 |
+
"book": 10,
|
| 874 |
+
"number": 80,
|
| 875 |
+
"colorClass": "proposition"
|
| 876 |
+
},
|
| 877 |
+
{
|
| 878 |
+
"id": "Prop81",
|
| 879 |
+
"type": "proposition",
|
| 880 |
+
"label": "To second apotome of medial: unique medial annex, medial rect",
|
| 881 |
+
"shortLabel": "Prop. X.81",
|
| 882 |
+
"short": "Second apotome medial: unique annex",
|
| 883 |
+
"book": 10,
|
| 884 |
+
"number": 81,
|
| 885 |
+
"colorClass": "proposition"
|
| 886 |
+
},
|
| 887 |
+
{
|
| 888 |
+
"id": "Prop82",
|
| 889 |
+
"type": "proposition",
|
| 890 |
+
"label": "To minor: unique annex incommensurable in square",
|
| 891 |
+
"shortLabel": "Prop. X.82",
|
| 892 |
+
"short": "Minor: unique annex",
|
| 893 |
+
"book": 10,
|
| 894 |
+
"number": 82,
|
| 895 |
+
"colorClass": "proposition"
|
| 896 |
+
},
|
| 897 |
+
{
|
| 898 |
+
"id": "Prop83",
|
| 899 |
+
"type": "proposition",
|
| 900 |
+
"label": "To produces rational+medial: unique annex",
|
| 901 |
+
"shortLabel": "Prop. X.83",
|
| 902 |
+
"short": "Rational+medial: unique annex",
|
| 903 |
+
"book": 10,
|
| 904 |
+
"number": 83,
|
| 905 |
+
"colorClass": "proposition"
|
| 906 |
+
},
|
| 907 |
+
{
|
| 908 |
+
"id": "Prop84",
|
| 909 |
+
"type": "proposition",
|
| 910 |
+
"label": "To produces medial+medial: unique annex",
|
| 911 |
+
"shortLabel": "Prop. X.84",
|
| 912 |
+
"short": "Medial+medial: unique annex",
|
| 913 |
+
"book": 10,
|
| 914 |
+
"number": 84,
|
| 915 |
+
"colorClass": "proposition"
|
| 916 |
+
},
|
| 917 |
+
{
|
| 918 |
+
"id": "Prop85",
|
| 919 |
+
"type": "proposition",
|
| 920 |
+
"label": "To find the first apotome",
|
| 921 |
+
"shortLabel": "Prop. X.85",
|
| 922 |
+
"short": "Find first apotome",
|
| 923 |
+
"book": 10,
|
| 924 |
+
"number": 85,
|
| 925 |
+
"colorClass": "proposition"
|
| 926 |
+
},
|
| 927 |
+
{
|
| 928 |
+
"id": "Prop86",
|
| 929 |
+
"type": "proposition",
|
| 930 |
+
"label": "To find the second apotome",
|
| 931 |
+
"shortLabel": "Prop. X.86",
|
| 932 |
+
"short": "Find second apotome",
|
| 933 |
+
"book": 10,
|
| 934 |
+
"number": 86,
|
| 935 |
+
"colorClass": "proposition"
|
| 936 |
+
},
|
| 937 |
+
{
|
| 938 |
+
"id": "Prop87",
|
| 939 |
+
"type": "proposition",
|
| 940 |
+
"label": "To find the third apotome",
|
| 941 |
+
"shortLabel": "Prop. X.87",
|
| 942 |
+
"short": "Find third apotome",
|
| 943 |
+
"book": 10,
|
| 944 |
+
"number": 87,
|
| 945 |
+
"colorClass": "proposition"
|
| 946 |
+
},
|
| 947 |
+
{
|
| 948 |
+
"id": "Prop88",
|
| 949 |
+
"type": "proposition",
|
| 950 |
+
"label": "To find the fourth apotome",
|
| 951 |
+
"shortLabel": "Prop. X.88",
|
| 952 |
+
"short": "Find fourth apotome",
|
| 953 |
+
"book": 10,
|
| 954 |
+
"number": 88,
|
| 955 |
+
"colorClass": "proposition"
|
| 956 |
+
},
|
| 957 |
+
{
|
| 958 |
+
"id": "Prop89",
|
| 959 |
+
"type": "proposition",
|
| 960 |
+
"label": "To find the fifth apotome",
|
| 961 |
+
"shortLabel": "Prop. X.89",
|
| 962 |
+
"short": "Find fifth apotome",
|
| 963 |
+
"book": 10,
|
| 964 |
+
"number": 89,
|
| 965 |
+
"colorClass": "proposition"
|
| 966 |
+
},
|
| 967 |
+
{
|
| 968 |
+
"id": "Prop90",
|
| 969 |
+
"type": "proposition",
|
| 970 |
+
"label": "To find the sixth apotome",
|
| 971 |
+
"shortLabel": "Prop. X.90",
|
| 972 |
+
"short": "Find sixth apotome",
|
| 973 |
+
"book": 10,
|
| 974 |
+
"number": 90,
|
| 975 |
+
"colorClass": "proposition"
|
| 976 |
+
},
|
| 977 |
+
{
|
| 978 |
+
"id": "Prop91",
|
| 979 |
+
"type": "proposition",
|
| 980 |
+
"label": "Area by rational and first apotome: side is apotome",
|
| 981 |
+
"shortLabel": "Prop. X.91",
|
| 982 |
+
"short": "Rational × first apotome",
|
| 983 |
+
"book": 10,
|
| 984 |
+
"number": 91,
|
| 985 |
+
"colorClass": "proposition"
|
| 986 |
+
},
|
| 987 |
+
{
|
| 988 |
+
"id": "Prop92",
|
| 989 |
+
"type": "proposition",
|
| 990 |
+
"label": "Area by rational and second apotome: side is first apotome of medial",
|
| 991 |
+
"shortLabel": "Prop. X.92",
|
| 992 |
+
"short": "Rational × second apotome",
|
| 993 |
+
"book": 10,
|
| 994 |
+
"number": 92,
|
| 995 |
+
"colorClass": "proposition"
|
| 996 |
+
},
|
| 997 |
+
{
|
| 998 |
+
"id": "Prop93",
|
| 999 |
+
"type": "proposition",
|
| 1000 |
+
"label": "Area by rational and third apotome: side is second apotome of medial",
|
| 1001 |
+
"shortLabel": "Prop. X.93",
|
| 1002 |
+
"short": "Rational × third apotome",
|
| 1003 |
+
"book": 10,
|
| 1004 |
+
"number": 93,
|
| 1005 |
+
"colorClass": "proposition"
|
| 1006 |
+
},
|
| 1007 |
+
{
|
| 1008 |
+
"id": "Prop94",
|
| 1009 |
+
"type": "proposition",
|
| 1010 |
+
"label": "Area by rational and fourth apotome: side is minor",
|
| 1011 |
+
"shortLabel": "Prop. X.94",
|
| 1012 |
+
"short": "Rational × fourth apotome",
|
| 1013 |
+
"book": 10,
|
| 1014 |
+
"number": 94,
|
| 1015 |
+
"colorClass": "proposition"
|
| 1016 |
+
},
|
| 1017 |
+
{
|
| 1018 |
+
"id": "Prop95",
|
| 1019 |
+
"type": "proposition",
|
| 1020 |
+
"label": "Area by rational and fifth apotome: side produces rational+medial",
|
| 1021 |
+
"shortLabel": "Prop. X.95",
|
| 1022 |
+
"short": "Rational × fifth apotome",
|
| 1023 |
+
"book": 10,
|
| 1024 |
+
"number": 95,
|
| 1025 |
+
"colorClass": "proposition"
|
| 1026 |
+
},
|
| 1027 |
+
{
|
| 1028 |
+
"id": "Prop96",
|
| 1029 |
+
"type": "proposition",
|
| 1030 |
+
"label": "Area by rational and sixth apotome: side produces medial+medial",
|
| 1031 |
+
"shortLabel": "Prop. X.96",
|
| 1032 |
+
"short": "Rational × sixth apotome",
|
| 1033 |
+
"book": 10,
|
| 1034 |
+
"number": 96,
|
| 1035 |
+
"colorClass": "proposition"
|
| 1036 |
+
},
|
| 1037 |
+
{
|
| 1038 |
+
"id": "Prop97",
|
| 1039 |
+
"type": "proposition",
|
| 1040 |
+
"label": "Square on apotome of medial applied to rational: breadth first apotome",
|
| 1041 |
+
"shortLabel": "Prop. X.97",
|
| 1042 |
+
"short": "Square on apotome medial",
|
| 1043 |
+
"book": 10,
|
| 1044 |
+
"number": 97,
|
| 1045 |
+
"colorClass": "proposition"
|
| 1046 |
+
},
|
| 1047 |
+
{
|
| 1048 |
+
"id": "Prop98",
|
| 1049 |
+
"type": "proposition",
|
| 1050 |
+
"label": "Square on first apotome of medial: breadth second apotome",
|
| 1051 |
+
"shortLabel": "Prop. X.98",
|
| 1052 |
+
"short": "Square on first apotome medial",
|
| 1053 |
+
"book": 10,
|
| 1054 |
+
"number": 98,
|
| 1055 |
+
"colorClass": "proposition"
|
| 1056 |
+
},
|
| 1057 |
+
{
|
| 1058 |
+
"id": "Prop99",
|
| 1059 |
+
"type": "proposition",
|
| 1060 |
+
"label": "Square on second apotome of medial: breadth third apotome",
|
| 1061 |
+
"shortLabel": "Prop. X.99",
|
| 1062 |
+
"short": "Square on second apotome medial",
|
| 1063 |
+
"book": 10,
|
| 1064 |
+
"number": 99,
|
| 1065 |
+
"colorClass": "proposition"
|
| 1066 |
+
},
|
| 1067 |
+
{
|
| 1068 |
+
"id": "Prop100",
|
| 1069 |
+
"type": "proposition",
|
| 1070 |
+
"label": "Square on minor applied to rational: breadth fourth apotome",
|
| 1071 |
+
"shortLabel": "Prop. X.100",
|
| 1072 |
+
"short": "Square on minor",
|
| 1073 |
+
"book": 10,
|
| 1074 |
+
"number": 100,
|
| 1075 |
+
"colorClass": "proposition"
|
| 1076 |
+
},
|
| 1077 |
+
{
|
| 1078 |
+
"id": "Prop101",
|
| 1079 |
+
"type": "proposition",
|
| 1080 |
+
"label": "Square on produces rational+medial: breadth fifth apotome",
|
| 1081 |
+
"shortLabel": "Prop. X.101",
|
| 1082 |
+
"short": "Square on rational+medial",
|
| 1083 |
+
"book": 10,
|
| 1084 |
+
"number": 101,
|
| 1085 |
+
"colorClass": "proposition"
|
| 1086 |
+
},
|
| 1087 |
+
{
|
| 1088 |
+
"id": "Prop102",
|
| 1089 |
+
"type": "proposition",
|
| 1090 |
+
"label": "Square on produces medial+medial: breadth sixth apotome",
|
| 1091 |
+
"shortLabel": "Prop. X.102",
|
| 1092 |
+
"short": "Square on medial+medial",
|
| 1093 |
+
"book": 10,
|
| 1094 |
+
"number": 102,
|
| 1095 |
+
"colorClass": "proposition"
|
| 1096 |
+
},
|
| 1097 |
+
{
|
| 1098 |
+
"id": "Prop103",
|
| 1099 |
+
"type": "proposition",
|
| 1100 |
+
"label": "Line commensurable with apotome is apotome, same order",
|
| 1101 |
+
"shortLabel": "Prop. X.103",
|
| 1102 |
+
"short": "Commensurable with apotome",
|
| 1103 |
+
"book": 10,
|
| 1104 |
+
"number": 103,
|
| 1105 |
+
"colorClass": "proposition"
|
| 1106 |
+
},
|
| 1107 |
+
{
|
| 1108 |
+
"id": "Prop104",
|
| 1109 |
+
"type": "proposition",
|
| 1110 |
+
"label": "Line commensurable with apotome of medial is apotome of medial",
|
| 1111 |
+
"shortLabel": "Prop. X.104",
|
| 1112 |
+
"short": "Commensurable with apotome medial",
|
| 1113 |
+
"book": 10,
|
| 1114 |
+
"number": 104,
|
| 1115 |
+
"colorClass": "proposition"
|
| 1116 |
+
},
|
| 1117 |
+
{
|
| 1118 |
+
"id": "Prop105",
|
| 1119 |
+
"type": "proposition",
|
| 1120 |
+
"label": "Line commensurable with minor is minor",
|
| 1121 |
+
"shortLabel": "Prop. X.105",
|
| 1122 |
+
"short": "Commensurable with minor",
|
| 1123 |
+
"book": 10,
|
| 1124 |
+
"number": 105,
|
| 1125 |
+
"colorClass": "proposition"
|
| 1126 |
+
},
|
| 1127 |
+
{
|
| 1128 |
+
"id": "Prop106",
|
| 1129 |
+
"type": "proposition",
|
| 1130 |
+
"label": "Line commensurable with produces rational+medial is same",
|
| 1131 |
+
"shortLabel": "Prop. X.106",
|
| 1132 |
+
"short": "Commensurable with rational+medial",
|
| 1133 |
+
"book": 10,
|
| 1134 |
+
"number": 106,
|
| 1135 |
+
"colorClass": "proposition"
|
| 1136 |
+
},
|
| 1137 |
+
{
|
| 1138 |
+
"id": "Prop107",
|
| 1139 |
+
"type": "proposition",
|
| 1140 |
+
"label": "Line commensurable with produces medial+medial is same",
|
| 1141 |
+
"shortLabel": "Prop. X.107",
|
| 1142 |
+
"short": "Commensurable with medial+medial",
|
| 1143 |
+
"book": 10,
|
| 1144 |
+
"number": 107,
|
| 1145 |
+
"colorClass": "proposition"
|
| 1146 |
+
},
|
| 1147 |
+
{
|
| 1148 |
+
"id": "Prop108",
|
| 1149 |
+
"type": "proposition",
|
| 1150 |
+
"label": "From rational area subtract medial: side is apotome or minor",
|
| 1151 |
+
"shortLabel": "Prop. X.108",
|
| 1152 |
+
"short": "Rational minus medial",
|
| 1153 |
+
"book": 10,
|
| 1154 |
+
"number": 108,
|
| 1155 |
+
"colorClass": "proposition"
|
| 1156 |
+
},
|
| 1157 |
+
{
|
| 1158 |
+
"id": "Prop109",
|
| 1159 |
+
"type": "proposition",
|
| 1160 |
+
"label": "From medial subtract rational: first apotome of medial or rational+medial",
|
| 1161 |
+
"shortLabel": "Prop. X.109",
|
| 1162 |
+
"short": "Medial minus rational",
|
| 1163 |
+
"book": 10,
|
| 1164 |
+
"number": 109,
|
| 1165 |
+
"colorClass": "proposition"
|
| 1166 |
+
},
|
| 1167 |
+
{
|
| 1168 |
+
"id": "Prop110",
|
| 1169 |
+
"type": "proposition",
|
| 1170 |
+
"label": "From medial subtract medial incommensurable: second apotome or medial+medial",
|
| 1171 |
+
"shortLabel": "Prop. X.110",
|
| 1172 |
+
"short": "Medial minus medial",
|
| 1173 |
+
"book": 10,
|
| 1174 |
+
"number": 110,
|
| 1175 |
+
"colorClass": "proposition"
|
| 1176 |
+
},
|
| 1177 |
+
{
|
| 1178 |
+
"id": "Prop111",
|
| 1179 |
+
"type": "proposition",
|
| 1180 |
+
"label": "Apotome is not the same as binomial",
|
| 1181 |
+
"shortLabel": "Prop. X.111",
|
| 1182 |
+
"short": "Apotome ≠ binomial",
|
| 1183 |
+
"book": 10,
|
| 1184 |
+
"number": 111,
|
| 1185 |
+
"colorClass": "proposition"
|
| 1186 |
+
},
|
| 1187 |
+
{
|
| 1188 |
+
"id": "Prop112",
|
| 1189 |
+
"type": "proposition",
|
| 1190 |
+
"label": "Square on rational applied to binomial: breadth apotome, same order",
|
| 1191 |
+
"shortLabel": "Prop. X.112",
|
| 1192 |
+
"short": "Rational on binomial",
|
| 1193 |
+
"book": 10,
|
| 1194 |
+
"number": 112,
|
| 1195 |
+
"colorClass": "proposition"
|
| 1196 |
+
},
|
| 1197 |
+
{
|
| 1198 |
+
"id": "Prop113",
|
| 1199 |
+
"type": "proposition",
|
| 1200 |
+
"label": "Square on rational applied to apotome: breadth binomial, same order",
|
| 1201 |
+
"shortLabel": "Prop. X.113",
|
| 1202 |
+
"short": "Rational on apotome",
|
| 1203 |
+
"book": 10,
|
| 1204 |
+
"number": 113,
|
| 1205 |
+
"colorClass": "proposition"
|
| 1206 |
+
},
|
| 1207 |
+
{
|
| 1208 |
+
"id": "Prop114",
|
| 1209 |
+
"type": "proposition",
|
| 1210 |
+
"label": "Area by apotome and binomial (commensurable terms): side is rational",
|
| 1211 |
+
"shortLabel": "Prop. X.114",
|
| 1212 |
+
"short": "Apotome × binomial: rational",
|
| 1213 |
+
"book": 10,
|
| 1214 |
+
"number": 114,
|
| 1215 |
+
"colorClass": "proposition"
|
| 1216 |
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},
|
| 1217 |
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{
|
| 1218 |
+
"id": "Prop115",
|
| 1219 |
+
"type": "proposition",
|
| 1220 |
+
"label": "From medial arise irrationals infinite in number, none same as preceding",
|
| 1221 |
+
"shortLabel": "Prop. X.115",
|
| 1222 |
+
"short": "Medial: infinite irrationals",
|
| 1223 |
+
"book": 10,
|
| 1224 |
+
"number": 115,
|
| 1225 |
+
"colorClass": "proposition"
|
| 1226 |
+
}
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| 1227 |
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],
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| 1228 |
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"edges": [
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| 1236 |
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| 1240 |
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| 1242 |
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| 1244 |
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| 1250 |
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| 1256 |
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{
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| 1614 |
+
"from": "BookI",
|
| 1615 |
+
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|
| 1616 |
+
},
|
| 1617 |
+
{
|
| 1618 |
+
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|
| 1619 |
+
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|
| 1620 |
+
},
|
| 1621 |
+
{
|
| 1622 |
+
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|
| 1623 |
+
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|
| 1624 |
+
},
|
| 1625 |
+
{
|
| 1626 |
+
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|
| 1627 |
+
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|
| 1628 |
+
},
|
| 1629 |
+
{
|
| 1630 |
+
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|
| 1631 |
+
"to": "Prop34"
|
| 1632 |
+
},
|
| 1633 |
+
{
|
| 1634 |
+
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|
| 1635 |
+
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|
| 1636 |
+
},
|
| 1637 |
+
{
|
| 1638 |
+
"from": "BookI",
|
| 1639 |
+
"to": "Prop35"
|
| 1640 |
+
},
|
| 1641 |
+
{
|
| 1642 |
+
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|
| 1643 |
+
"to": "Prop35"
|
| 1644 |
+
},
|
| 1645 |
+
{
|
| 1646 |
+
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|
| 1647 |
+
"to": "Prop35"
|
| 1648 |
+
},
|
| 1649 |
+
{
|
| 1650 |
+
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|
| 1651 |
+
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|
| 1652 |
+
},
|
| 1653 |
+
{
|
| 1654 |
+
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|
| 1655 |
+
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|
| 1656 |
+
},
|
| 1657 |
+
{
|
| 1658 |
+
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|
| 1659 |
+
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|
| 1660 |
+
},
|
| 1661 |
+
{
|
| 1662 |
+
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|
| 1663 |
+
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|
| 1664 |
+
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|
| 1665 |
+
{
|
| 1666 |
+
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|
| 1667 |
+
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|
| 1668 |
+
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|
| 1669 |
+
{
|
| 1670 |
+
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|
| 1671 |
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|
| 1672 |
+
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|
| 1673 |
+
{
|
| 1674 |
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|
| 1675 |
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|
| 1676 |
+
},
|
| 1677 |
+
{
|
| 1678 |
+
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|
| 1679 |
+
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|
| 1680 |
+
},
|
| 1681 |
+
{
|
| 1682 |
+
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|
| 1683 |
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|
| 1684 |
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},
|
| 1685 |
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{
|
| 1686 |
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|
| 1687 |
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|
| 1688 |
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},
|
| 1689 |
+
{
|
| 1690 |
+
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|
| 1691 |
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|
| 1692 |
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},
|
| 1693 |
+
{
|
| 1694 |
+
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|
| 1695 |
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"to": "Prop39"
|
| 1696 |
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},
|
| 1697 |
+
{
|
| 1698 |
+
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|
| 1699 |
+
"to": "Prop40"
|
| 1700 |
+
},
|
| 1701 |
+
{
|
| 1702 |
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|
| 1703 |
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|
| 1704 |
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},
|
| 1705 |
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{
|
| 1706 |
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|
| 1707 |
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|
| 1708 |
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},
|
| 1709 |
+
{
|
| 1710 |
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|
| 1711 |
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|
| 1712 |
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},
|
| 1713 |
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{
|
| 1714 |
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|
| 1715 |
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|
| 1716 |
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},
|
| 1717 |
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{
|
| 1718 |
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|
| 1719 |
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|
| 1720 |
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},
|
| 1721 |
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{
|
| 1722 |
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|
| 1723 |
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|
| 1724 |
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},
|
| 1725 |
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{
|
| 1726 |
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|
| 1727 |
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"to": "Prop42"
|
| 1728 |
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},
|
| 1729 |
+
{
|
| 1730 |
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|
| 1731 |
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"to": "Prop42"
|
| 1732 |
+
},
|
| 1733 |
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{
|
| 1734 |
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|
| 1735 |
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|
| 1736 |
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},
|
| 1737 |
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{
|
| 1738 |
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|
| 1739 |
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"to": "Prop43"
|
| 1740 |
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},
|
| 1741 |
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{
|
| 1742 |
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|
| 1743 |
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"to": "Prop43"
|
| 1744 |
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},
|
| 1745 |
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{
|
| 1746 |
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|
| 1747 |
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"to": "Prop44"
|
| 1748 |
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},
|
| 1749 |
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{
|
| 1750 |
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|
| 1751 |
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|
| 1752 |
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},
|
| 1753 |
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{
|
| 1754 |
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|
| 1755 |
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"to": "Prop44"
|
| 1756 |
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},
|
| 1757 |
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{
|
| 1758 |
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|
| 1759 |
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|
| 1760 |
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},
|
| 1761 |
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{
|
| 1762 |
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|
| 1763 |
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|
| 1764 |
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},
|
| 1765 |
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{
|
| 1766 |
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|
| 1767 |
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"to": "Prop45"
|
| 1768 |
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},
|
| 1769 |
+
{
|
| 1770 |
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|
| 1771 |
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"to": "Prop46"
|
| 1772 |
+
},
|
| 1773 |
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{
|
| 1774 |
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|
| 1775 |
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"to": "Prop46"
|
| 1776 |
+
},
|
| 1777 |
+
{
|
| 1778 |
+
"from": "BookVI",
|
| 1779 |
+
"to": "Prop46"
|
| 1780 |
+
},
|
| 1781 |
+
{
|
| 1782 |
+
"from": "BookI",
|
| 1783 |
+
"to": "Prop47"
|
| 1784 |
+
},
|
| 1785 |
+
{
|
| 1786 |
+
"from": "BookV",
|
| 1787 |
+
"to": "Prop47"
|
| 1788 |
+
},
|
| 1789 |
+
{
|
| 1790 |
+
"from": "BookVI",
|
| 1791 |
+
"to": "Prop47"
|
| 1792 |
+
},
|
| 1793 |
+
{
|
| 1794 |
+
"from": "BookI",
|
| 1795 |
+
"to": "Prop48"
|
| 1796 |
+
},
|
| 1797 |
+
{
|
| 1798 |
+
"from": "BookV",
|
| 1799 |
+
"to": "Prop48"
|
| 1800 |
+
},
|
| 1801 |
+
{
|
| 1802 |
+
"from": "BookVI",
|
| 1803 |
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"to": "Prop48"
|
| 1804 |
+
},
|
| 1805 |
+
{
|
| 1806 |
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"from": "BookI",
|
| 1807 |
+
"to": "Prop49"
|
| 1808 |
+
},
|
| 1809 |
+
{
|
| 1810 |
+
"from": "BookV",
|
| 1811 |
+
"to": "Prop49"
|
| 1812 |
+
},
|
| 1813 |
+
{
|
| 1814 |
+
"from": "BookVI",
|
| 1815 |
+
"to": "Prop49"
|
| 1816 |
+
},
|
| 1817 |
+
{
|
| 1818 |
+
"from": "BookI",
|
| 1819 |
+
"to": "Prop50"
|
| 1820 |
+
},
|
| 1821 |
+
{
|
| 1822 |
+
"from": "BookV",
|
| 1823 |
+
"to": "Prop50"
|
| 1824 |
+
},
|
| 1825 |
+
{
|
| 1826 |
+
"from": "BookVI",
|
| 1827 |
+
"to": "Prop50"
|
| 1828 |
+
},
|
| 1829 |
+
{
|
| 1830 |
+
"from": "BookI",
|
| 1831 |
+
"to": "Prop51"
|
| 1832 |
+
},
|
| 1833 |
+
{
|
| 1834 |
+
"from": "BookV",
|
| 1835 |
+
"to": "Prop51"
|
| 1836 |
+
},
|
| 1837 |
+
{
|
| 1838 |
+
"from": "BookVI",
|
| 1839 |
+
"to": "Prop51"
|
| 1840 |
+
},
|
| 1841 |
+
{
|
| 1842 |
+
"from": "BookI",
|
| 1843 |
+
"to": "Prop52"
|
| 1844 |
+
},
|
| 1845 |
+
{
|
| 1846 |
+
"from": "BookV",
|
| 1847 |
+
"to": "Prop52"
|
| 1848 |
+
},
|
| 1849 |
+
{
|
| 1850 |
+
"from": "BookVI",
|
| 1851 |
+
"to": "Prop52"
|
| 1852 |
+
},
|
| 1853 |
+
{
|
| 1854 |
+
"from": "BookI",
|
| 1855 |
+
"to": "Prop53"
|
| 1856 |
+
},
|
| 1857 |
+
{
|
| 1858 |
+
"from": "BookV",
|
| 1859 |
+
"to": "Prop53"
|
| 1860 |
+
},
|
| 1861 |
+
{
|
| 1862 |
+
"from": "BookVI",
|
| 1863 |
+
"to": "Prop53"
|
| 1864 |
+
},
|
| 1865 |
+
{
|
| 1866 |
+
"from": "BookI",
|
| 1867 |
+
"to": "Prop54"
|
| 1868 |
+
},
|
| 1869 |
+
{
|
| 1870 |
+
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|
| 1871 |
+
"to": "Prop54"
|
| 1872 |
+
},
|
| 1873 |
+
{
|
| 1874 |
+
"from": "BookVI",
|
| 1875 |
+
"to": "Prop54"
|
| 1876 |
+
},
|
| 1877 |
+
{
|
| 1878 |
+
"from": "BookI",
|
| 1879 |
+
"to": "Prop55"
|
| 1880 |
+
},
|
| 1881 |
+
{
|
| 1882 |
+
"from": "BookV",
|
| 1883 |
+
"to": "Prop55"
|
| 1884 |
+
},
|
| 1885 |
+
{
|
| 1886 |
+
"from": "BookVI",
|
| 1887 |
+
"to": "Prop55"
|
| 1888 |
+
},
|
| 1889 |
+
{
|
| 1890 |
+
"from": "BookI",
|
| 1891 |
+
"to": "Prop56"
|
| 1892 |
+
},
|
| 1893 |
+
{
|
| 1894 |
+
"from": "BookV",
|
| 1895 |
+
"to": "Prop56"
|
| 1896 |
+
},
|
| 1897 |
+
{
|
| 1898 |
+
"from": "BookVI",
|
| 1899 |
+
"to": "Prop56"
|
| 1900 |
+
},
|
| 1901 |
+
{
|
| 1902 |
+
"from": "BookI",
|
| 1903 |
+
"to": "Prop57"
|
| 1904 |
+
},
|
| 1905 |
+
{
|
| 1906 |
+
"from": "BookV",
|
| 1907 |
+
"to": "Prop57"
|
| 1908 |
+
},
|
| 1909 |
+
{
|
| 1910 |
+
"from": "BookVI",
|
| 1911 |
+
"to": "Prop57"
|
| 1912 |
+
},
|
| 1913 |
+
{
|
| 1914 |
+
"from": "BookI",
|
| 1915 |
+
"to": "Prop58"
|
| 1916 |
+
},
|
| 1917 |
+
{
|
| 1918 |
+
"from": "BookV",
|
| 1919 |
+
"to": "Prop58"
|
| 1920 |
+
},
|
| 1921 |
+
{
|
| 1922 |
+
"from": "BookVI",
|
| 1923 |
+
"to": "Prop58"
|
| 1924 |
+
},
|
| 1925 |
+
{
|
| 1926 |
+
"from": "BookI",
|
| 1927 |
+
"to": "Prop59"
|
| 1928 |
+
},
|
| 1929 |
+
{
|
| 1930 |
+
"from": "BookV",
|
| 1931 |
+
"to": "Prop59"
|
| 1932 |
+
},
|
| 1933 |
+
{
|
| 1934 |
+
"from": "BookVI",
|
| 1935 |
+
"to": "Prop59"
|
| 1936 |
+
},
|
| 1937 |
+
{
|
| 1938 |
+
"from": "BookI",
|
| 1939 |
+
"to": "Prop60"
|
| 1940 |
+
},
|
| 1941 |
+
{
|
| 1942 |
+
"from": "BookV",
|
| 1943 |
+
"to": "Prop60"
|
| 1944 |
+
},
|
| 1945 |
+
{
|
| 1946 |
+
"from": "BookVI",
|
| 1947 |
+
"to": "Prop60"
|
| 1948 |
+
},
|
| 1949 |
+
{
|
| 1950 |
+
"from": "BookI",
|
| 1951 |
+
"to": "Prop61"
|
| 1952 |
+
},
|
| 1953 |
+
{
|
| 1954 |
+
"from": "BookV",
|
| 1955 |
+
"to": "Prop61"
|
| 1956 |
+
},
|
| 1957 |
+
{
|
| 1958 |
+
"from": "BookVI",
|
| 1959 |
+
"to": "Prop61"
|
| 1960 |
+
},
|
| 1961 |
+
{
|
| 1962 |
+
"from": "BookI",
|
| 1963 |
+
"to": "Prop62"
|
| 1964 |
+
},
|
| 1965 |
+
{
|
| 1966 |
+
"from": "BookV",
|
| 1967 |
+
"to": "Prop62"
|
| 1968 |
+
},
|
| 1969 |
+
{
|
| 1970 |
+
"from": "BookVI",
|
| 1971 |
+
"to": "Prop62"
|
| 1972 |
+
},
|
| 1973 |
+
{
|
| 1974 |
+
"from": "BookI",
|
| 1975 |
+
"to": "Prop63"
|
| 1976 |
+
},
|
| 1977 |
+
{
|
| 1978 |
+
"from": "BookV",
|
| 1979 |
+
"to": "Prop63"
|
| 1980 |
+
},
|
| 1981 |
+
{
|
| 1982 |
+
"from": "BookVI",
|
| 1983 |
+
"to": "Prop63"
|
| 1984 |
+
},
|
| 1985 |
+
{
|
| 1986 |
+
"from": "BookI",
|
| 1987 |
+
"to": "Prop64"
|
| 1988 |
+
},
|
| 1989 |
+
{
|
| 1990 |
+
"from": "BookV",
|
| 1991 |
+
"to": "Prop64"
|
| 1992 |
+
},
|
| 1993 |
+
{
|
| 1994 |
+
"from": "BookVI",
|
| 1995 |
+
"to": "Prop64"
|
| 1996 |
+
},
|
| 1997 |
+
{
|
| 1998 |
+
"from": "BookI",
|
| 1999 |
+
"to": "Prop65"
|
| 2000 |
+
},
|
| 2001 |
+
{
|
| 2002 |
+
"from": "BookV",
|
| 2003 |
+
"to": "Prop65"
|
| 2004 |
+
},
|
| 2005 |
+
{
|
| 2006 |
+
"from": "BookVI",
|
| 2007 |
+
"to": "Prop65"
|
| 2008 |
+
},
|
| 2009 |
+
{
|
| 2010 |
+
"from": "BookI",
|
| 2011 |
+
"to": "Prop66"
|
| 2012 |
+
},
|
| 2013 |
+
{
|
| 2014 |
+
"from": "BookV",
|
| 2015 |
+
"to": "Prop66"
|
| 2016 |
+
},
|
| 2017 |
+
{
|
| 2018 |
+
"from": "BookVI",
|
| 2019 |
+
"to": "Prop66"
|
| 2020 |
+
},
|
| 2021 |
+
{
|
| 2022 |
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"from": "BookI",
|
| 2023 |
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"to": "Prop67"
|
| 2024 |
+
},
|
| 2025 |
+
{
|
| 2026 |
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"from": "BookV",
|
| 2027 |
+
"to": "Prop67"
|
| 2028 |
+
},
|
| 2029 |
+
{
|
| 2030 |
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|
| 2031 |
+
"to": "Prop67"
|
| 2032 |
+
},
|
| 2033 |
+
{
|
| 2034 |
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"from": "BookI",
|
| 2035 |
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"to": "Prop68"
|
| 2036 |
+
},
|
| 2037 |
+
{
|
| 2038 |
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"from": "BookV",
|
| 2039 |
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"to": "Prop68"
|
| 2040 |
+
},
|
| 2041 |
+
{
|
| 2042 |
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"from": "BookVI",
|
| 2043 |
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"to": "Prop68"
|
| 2044 |
+
},
|
| 2045 |
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{
|
| 2046 |
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"from": "BookI",
|
| 2047 |
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"to": "Prop69"
|
| 2048 |
+
},
|
| 2049 |
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{
|
| 2050 |
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|
| 2051 |
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|
| 2052 |
+
},
|
| 2053 |
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{
|
| 2054 |
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|
| 2055 |
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|
| 2056 |
+
},
|
| 2057 |
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{
|
| 2058 |
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|
| 2059 |
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|
| 2060 |
+
},
|
| 2061 |
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{
|
| 2062 |
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|
| 2063 |
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|
| 2064 |
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},
|
| 2065 |
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{
|
| 2066 |
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|
| 2067 |
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|
| 2068 |
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},
|
| 2069 |
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{
|
| 2070 |
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|
| 2071 |
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|
| 2072 |
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},
|
| 2073 |
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{
|
| 2074 |
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|
| 2075 |
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|
| 2076 |
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|
| 2077 |
+
{
|
| 2078 |
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|
| 2079 |
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|
| 2080 |
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|
| 2081 |
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{
|
| 2082 |
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|
| 2083 |
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|
| 2084 |
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|
| 2085 |
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{
|
| 2086 |
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|
| 2087 |
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|
| 2088 |
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|
| 2089 |
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{
|
| 2090 |
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|
| 2091 |
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|
| 2092 |
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|
| 2093 |
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{
|
| 2094 |
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|
| 2095 |
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|
| 2096 |
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|
| 2097 |
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{
|
| 2098 |
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|
| 2099 |
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|
| 2100 |
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|
| 2101 |
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{
|
| 2102 |
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|
| 2103 |
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|
| 2104 |
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|
| 2105 |
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{
|
| 2106 |
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|
| 2107 |
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|
| 2108 |
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|
| 2109 |
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{
|
| 2110 |
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|
| 2111 |
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|
| 2112 |
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|
| 2113 |
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{
|
| 2114 |
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|
| 2115 |
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|
| 2116 |
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|
| 2117 |
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{
|
| 2118 |
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|
| 2119 |
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|
| 2120 |
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|
| 2121 |
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{
|
| 2122 |
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|
| 2123 |
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|
| 2124 |
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|
| 2125 |
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{
|
| 2126 |
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|
| 2127 |
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|
| 2128 |
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|
| 2129 |
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{
|
| 2130 |
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|
| 2131 |
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|
| 2132 |
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|
| 2133 |
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{
|
| 2134 |
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|
| 2135 |
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|
| 2136 |
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|
| 2137 |
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{
|
| 2138 |
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|
| 2139 |
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|
| 2140 |
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|
| 2141 |
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{
|
| 2142 |
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|
| 2143 |
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|
| 2144 |
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|
| 2145 |
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{
|
| 2146 |
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|
| 2147 |
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|
| 2148 |
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|
| 2149 |
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{
|
| 2150 |
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|
| 2151 |
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|
| 2152 |
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|
| 2153 |
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{
|
| 2154 |
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|
| 2155 |
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|
| 2156 |
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|
| 2157 |
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{
|
| 2158 |
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|
| 2159 |
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|
| 2160 |
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|
| 2161 |
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{
|
| 2162 |
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|
| 2163 |
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|
| 2164 |
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|
| 2165 |
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{
|
| 2166 |
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|
| 2167 |
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|
| 2168 |
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|
| 2169 |
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{
|
| 2170 |
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|
| 2171 |
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|
| 2172 |
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|
| 2173 |
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{
|
| 2174 |
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|
| 2175 |
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|
| 2176 |
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|
| 2177 |
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{
|
| 2178 |
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|
| 2179 |
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|
| 2180 |
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|
| 2181 |
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{
|
| 2182 |
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|
| 2183 |
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|
| 2184 |
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|
| 2185 |
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{
|
| 2186 |
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|
| 2187 |
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|
| 2188 |
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|
| 2189 |
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{
|
| 2190 |
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|
| 2191 |
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|
| 2192 |
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|
| 2193 |
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{
|
| 2194 |
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|
| 2195 |
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|
| 2196 |
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|
| 2197 |
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{
|
| 2198 |
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|
| 2199 |
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|
| 2200 |
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|
| 2201 |
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{
|
| 2202 |
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|
| 2203 |
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|
| 2204 |
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|
| 2205 |
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{
|
| 2206 |
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|
| 2207 |
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|
| 2208 |
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|
| 2209 |
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{
|
| 2210 |
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|
| 2211 |
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|
| 2212 |
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|
| 2213 |
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{
|
| 2214 |
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|
| 2215 |
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|
| 2216 |
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|
| 2217 |
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{
|
| 2218 |
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|
| 2219 |
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|
| 2220 |
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|
| 2221 |
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{
|
| 2222 |
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|
| 2223 |
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|
| 2224 |
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|
| 2225 |
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{
|
| 2226 |
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|
| 2227 |
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|
| 2228 |
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|
| 2229 |
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{
|
| 2230 |
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|
| 2231 |
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|
| 2232 |
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|
| 2233 |
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{
|
| 2234 |
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|
| 2235 |
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|
| 2236 |
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|
| 2237 |
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{
|
| 2238 |
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|
| 2239 |
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|
| 2240 |
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|
| 2241 |
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{
|
| 2242 |
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|
| 2243 |
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|
| 2244 |
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},
|
| 2245 |
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{
|
| 2246 |
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|
| 2247 |
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|
| 2248 |
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},
|
| 2249 |
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{
|
| 2250 |
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|
| 2251 |
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|
| 2252 |
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},
|
| 2253 |
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{
|
| 2254 |
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|
| 2255 |
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|
| 2256 |
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|
| 2257 |
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{
|
| 2258 |
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|
| 2259 |
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|
| 2260 |
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|
| 2261 |
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{
|
| 2262 |
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|
| 2263 |
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|
| 2264 |
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|
| 2265 |
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{
|
| 2266 |
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|
| 2267 |
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|
| 2268 |
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|
| 2269 |
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{
|
| 2270 |
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|
| 2271 |
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|
| 2272 |
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|
| 2273 |
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{
|
| 2274 |
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|
| 2275 |
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|
| 2276 |
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},
|
| 2277 |
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{
|
| 2278 |
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|
| 2279 |
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|
| 2280 |
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},
|
| 2281 |
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{
|
| 2282 |
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|
| 2283 |
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|
| 2284 |
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},
|
| 2285 |
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{
|
| 2286 |
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|
| 2287 |
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|
| 2288 |
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},
|
| 2289 |
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{
|
| 2290 |
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|
| 2291 |
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|
| 2292 |
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},
|
| 2293 |
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{
|
| 2294 |
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|
| 2295 |
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|
| 2296 |
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},
|
| 2297 |
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{
|
| 2298 |
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|
| 2299 |
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|
| 2300 |
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},
|
| 2301 |
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{
|
| 2302 |
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|
| 2303 |
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"to": "Prop90"
|
| 2304 |
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},
|
| 2305 |
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{
|
| 2306 |
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|
| 2307 |
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|
| 2308 |
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},
|
| 2309 |
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{
|
| 2310 |
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|
| 2311 |
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|
| 2312 |
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},
|
| 2313 |
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{
|
| 2314 |
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|
| 2315 |
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|
| 2316 |
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},
|
| 2317 |
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{
|
| 2318 |
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|
| 2319 |
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|
| 2320 |
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|
| 2321 |
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{
|
| 2322 |
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|
| 2323 |
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|
| 2324 |
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|
| 2325 |
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{
|
| 2326 |
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|
| 2327 |
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|
| 2328 |
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|
| 2329 |
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{
|
| 2330 |
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|
| 2331 |
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|
| 2332 |
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|
| 2333 |
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{
|
| 2334 |
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|
| 2335 |
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|
| 2336 |
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|
| 2337 |
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{
|
| 2338 |
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|
| 2339 |
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|
| 2340 |
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|
| 2341 |
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{
|
| 2342 |
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|
| 2343 |
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|
| 2344 |
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},
|
| 2345 |
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{
|
| 2346 |
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|
| 2347 |
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|
| 2348 |
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|
| 2349 |
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{
|
| 2350 |
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|
| 2351 |
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|
| 2352 |
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},
|
| 2353 |
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{
|
| 2354 |
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|
| 2355 |
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|
| 2356 |
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|
| 2357 |
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{
|
| 2358 |
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|
| 2359 |
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|
| 2360 |
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|
| 2361 |
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{
|
| 2362 |
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|
| 2363 |
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|
| 2364 |
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|
| 2365 |
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{
|
| 2366 |
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|
| 2367 |
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|
| 2368 |
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|
| 2369 |
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{
|
| 2370 |
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|
| 2371 |
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|
| 2372 |
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|
| 2373 |
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{
|
| 2374 |
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|
| 2375 |
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|
| 2376 |
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|
| 2377 |
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{
|
| 2378 |
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|
| 2379 |
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|
| 2380 |
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|
| 2381 |
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{
|
| 2382 |
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|
| 2383 |
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|
| 2384 |
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|
| 2385 |
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{
|
| 2386 |
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|
| 2387 |
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|
| 2388 |
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|
| 2389 |
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{
|
| 2390 |
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|
| 2391 |
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|
| 2392 |
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|
| 2393 |
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{
|
| 2394 |
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|
| 2395 |
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|
| 2396 |
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|
| 2397 |
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{
|
| 2398 |
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|
| 2399 |
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|
| 2400 |
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},
|
| 2401 |
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{
|
| 2402 |
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|
| 2403 |
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|
| 2404 |
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},
|
| 2405 |
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{
|
| 2406 |
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|
| 2407 |
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|
| 2408 |
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},
|
| 2409 |
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{
|
| 2410 |
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|
| 2411 |
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|
| 2412 |
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},
|
| 2413 |
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{
|
| 2414 |
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|
| 2415 |
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|
| 2416 |
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|
| 2417 |
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{
|
| 2418 |
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|
| 2419 |
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|
| 2420 |
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|
| 2421 |
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{
|
| 2422 |
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|
| 2423 |
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|
| 2424 |
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},
|
| 2425 |
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{
|
| 2426 |
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|
| 2427 |
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|
| 2428 |
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},
|
| 2429 |
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{
|
| 2430 |
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|
| 2431 |
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|
| 2432 |
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},
|
| 2433 |
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{
|
| 2434 |
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|
| 2435 |
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|
| 2436 |
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},
|
| 2437 |
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{
|
| 2438 |
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|
| 2439 |
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|
| 2440 |
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|
| 2441 |
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{
|
| 2442 |
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|
| 2443 |
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|
| 2444 |
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},
|
| 2445 |
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{
|
| 2446 |
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|
| 2447 |
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|
| 2448 |
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},
|
| 2449 |
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{
|
| 2450 |
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|
| 2451 |
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|
| 2452 |
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},
|
| 2453 |
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{
|
| 2454 |
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|
| 2455 |
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|
| 2456 |
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},
|
| 2457 |
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{
|
| 2458 |
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|
| 2459 |
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|
| 2460 |
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|
| 2461 |
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{
|
| 2462 |
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|
| 2463 |
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|
| 2464 |
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|
| 2465 |
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{
|
| 2466 |
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|
| 2467 |
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|
| 2468 |
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| 2469 |
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{
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| 2470 |
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|
| 2471 |
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|
| 2472 |
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| 2473 |
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{
|
| 2474 |
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|
| 2475 |
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|
| 2476 |
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|
| 2477 |
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{
|
| 2478 |
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|
| 2479 |
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|
| 2480 |
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|
| 2481 |
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{
|
| 2482 |
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|
| 2483 |
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|
| 2484 |
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|
| 2485 |
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{
|
| 2486 |
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|
| 2487 |
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|
| 2488 |
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|
| 2489 |
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{
|
| 2490 |
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|
| 2491 |
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|
| 2492 |
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|
| 2493 |
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{
|
| 2494 |
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|
| 2495 |
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|
| 2496 |
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},
|
| 2497 |
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{
|
| 2498 |
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|
| 2499 |
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"to": "Prop106"
|
| 2500 |
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|
| 2501 |
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{
|
| 2502 |
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|
| 2503 |
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|
| 2504 |
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|
| 2505 |
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{
|
| 2506 |
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|
| 2507 |
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"to": "Prop107"
|
| 2508 |
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},
|
| 2509 |
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{
|
| 2510 |
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|
| 2511 |
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|
| 2512 |
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},
|
| 2513 |
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{
|
| 2514 |
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|
| 2515 |
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|
| 2516 |
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|
| 2517 |
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{
|
| 2518 |
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|
| 2519 |
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"to": "Prop108"
|
| 2520 |
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},
|
| 2521 |
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{
|
| 2522 |
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|
| 2523 |
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|
| 2524 |
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|
| 2525 |
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{
|
| 2526 |
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|
| 2527 |
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|
| 2528 |
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|
| 2529 |
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{
|
| 2530 |
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|
| 2531 |
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"to": "Prop109"
|
| 2532 |
+
},
|
| 2533 |
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{
|
| 2534 |
+
"from": "BookVI",
|
| 2535 |
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"to": "Prop109"
|
| 2536 |
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},
|
| 2537 |
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{
|
| 2538 |
+
"from": "BookI",
|
| 2539 |
+
"to": "Prop110"
|
| 2540 |
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},
|
| 2541 |
+
{
|
| 2542 |
+
"from": "BookV",
|
| 2543 |
+
"to": "Prop110"
|
| 2544 |
+
},
|
| 2545 |
+
{
|
| 2546 |
+
"from": "BookVI",
|
| 2547 |
+
"to": "Prop110"
|
| 2548 |
+
},
|
| 2549 |
+
{
|
| 2550 |
+
"from": "BookI",
|
| 2551 |
+
"to": "Prop111"
|
| 2552 |
+
},
|
| 2553 |
+
{
|
| 2554 |
+
"from": "BookV",
|
| 2555 |
+
"to": "Prop111"
|
| 2556 |
+
},
|
| 2557 |
+
{
|
| 2558 |
+
"from": "BookVI",
|
| 2559 |
+
"to": "Prop111"
|
| 2560 |
+
},
|
| 2561 |
+
{
|
| 2562 |
+
"from": "BookI",
|
| 2563 |
+
"to": "Prop112"
|
| 2564 |
+
},
|
| 2565 |
+
{
|
| 2566 |
+
"from": "BookV",
|
| 2567 |
+
"to": "Prop112"
|
| 2568 |
+
},
|
| 2569 |
+
{
|
| 2570 |
+
"from": "BookVI",
|
| 2571 |
+
"to": "Prop112"
|
| 2572 |
+
},
|
| 2573 |
+
{
|
| 2574 |
+
"from": "BookI",
|
| 2575 |
+
"to": "Prop113"
|
| 2576 |
+
},
|
| 2577 |
+
{
|
| 2578 |
+
"from": "BookV",
|
| 2579 |
+
"to": "Prop113"
|
| 2580 |
+
},
|
| 2581 |
+
{
|
| 2582 |
+
"from": "BookVI",
|
| 2583 |
+
"to": "Prop113"
|
| 2584 |
+
},
|
| 2585 |
+
{
|
| 2586 |
+
"from": "BookI",
|
| 2587 |
+
"to": "Prop114"
|
| 2588 |
+
},
|
| 2589 |
+
{
|
| 2590 |
+
"from": "BookV",
|
| 2591 |
+
"to": "Prop114"
|
| 2592 |
+
},
|
| 2593 |
+
{
|
| 2594 |
+
"from": "BookVI",
|
| 2595 |
+
"to": "Prop114"
|
| 2596 |
+
},
|
| 2597 |
+
{
|
| 2598 |
+
"from": "BookI",
|
| 2599 |
+
"to": "Prop115"
|
| 2600 |
+
},
|
| 2601 |
+
{
|
| 2602 |
+
"from": "BookV",
|
| 2603 |
+
"to": "Prop115"
|
| 2604 |
+
},
|
| 2605 |
+
{
|
| 2606 |
+
"from": "BookVI",
|
| 2607 |
+
"to": "Prop115"
|
| 2608 |
+
}
|
| 2609 |
+
],
|
| 2610 |
+
"colorScheme": {
|
| 2611 |
+
"foundation": {
|
| 2612 |
+
"fill": "#95a5a6",
|
| 2613 |
+
"stroke": "#7f8c8d"
|
| 2614 |
+
},
|
| 2615 |
+
"proposition": {
|
| 2616 |
+
"fill": "#1abc9c",
|
| 2617 |
+
"stroke": "#16a085"
|
| 2618 |
+
}
|
| 2619 |
+
}
|
| 2620 |
+
}
|
data/euclid-elements-book-xi.json
ADDED
|
@@ -0,0 +1,783 @@
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|
| 1 |
+
{
|
| 2 |
+
"schemaVersion": "1.0",
|
| 3 |
+
"discourse": {
|
| 4 |
+
"id": "euclid-elements-book-xi",
|
| 5 |
+
"name": "Euclid's Elements, Book XI",
|
| 6 |
+
"subject": "solid_geometry",
|
| 7 |
+
"variant": "classical",
|
| 8 |
+
"description": "Solid geometry: planes, perpendiculars, parallelepipeds, prisms. 28 definitions, 39 propositions. Depends on Books I and VI. Source: David E. Joyce.",
|
| 9 |
+
"structure": {
|
| 10 |
+
"books": 11,
|
| 11 |
+
"definitions": 28,
|
| 12 |
+
"propositions": 39,
|
| 13 |
+
"foundationTypes": [
|
| 14 |
+
"foundation"
|
| 15 |
+
]
|
| 16 |
+
}
|
| 17 |
+
},
|
| 18 |
+
"metadata": {
|
| 19 |
+
"created": "2026-03-18",
|
| 20 |
+
"lastUpdated": "2026-03-18",
|
| 21 |
+
"version": "1.0.0",
|
| 22 |
+
"license": "CC BY 4.0",
|
| 23 |
+
"authors": [
|
| 24 |
+
"Welz, G."
|
| 25 |
+
],
|
| 26 |
+
"methodology": "Programming Framework",
|
| 27 |
+
"citation": "Welz, G. (2026). Euclid's Elements Book XI Dependency Graph. Programming Framework.",
|
| 28 |
+
"keywords": [
|
| 29 |
+
"Euclid",
|
| 30 |
+
"Elements",
|
| 31 |
+
"Book XI",
|
| 32 |
+
"solid geometry",
|
| 33 |
+
"plane",
|
| 34 |
+
"parallelepiped",
|
| 35 |
+
"prism"
|
| 36 |
+
]
|
| 37 |
+
},
|
| 38 |
+
"sources": [
|
| 39 |
+
{
|
| 40 |
+
"id": "joyce",
|
| 41 |
+
"type": "digital",
|
| 42 |
+
"authors": "Joyce, David E.",
|
| 43 |
+
"title": "Euclid's Elements, Book XI",
|
| 44 |
+
"year": "1996",
|
| 45 |
+
"url": "https://mathcs.clarku.edu/~djoyce/java/elements/bookXI/bookXI.html",
|
| 46 |
+
"notes": "Clark University"
|
| 47 |
+
}
|
| 48 |
+
],
|
| 49 |
+
"nodes": [
|
| 50 |
+
{
|
| 51 |
+
"id": "BookI",
|
| 52 |
+
"type": "foundation",
|
| 53 |
+
"label": "Book I — Plane geometry",
|
| 54 |
+
"shortLabel": "Book I",
|
| 55 |
+
"short": "Foundation",
|
| 56 |
+
"book": 1,
|
| 57 |
+
"colorClass": "foundation"
|
| 58 |
+
},
|
| 59 |
+
{
|
| 60 |
+
"id": "BookVI",
|
| 61 |
+
"type": "foundation",
|
| 62 |
+
"label": "Book VI — Similar figures",
|
| 63 |
+
"shortLabel": "Book VI",
|
| 64 |
+
"short": "Foundation",
|
| 65 |
+
"book": 6,
|
| 66 |
+
"colorClass": "foundation"
|
| 67 |
+
},
|
| 68 |
+
{
|
| 69 |
+
"id": "Prop1",
|
| 70 |
+
"type": "proposition",
|
| 71 |
+
"label": "A part of a straight line cannot be in one plane and part in another elevated",
|
| 72 |
+
"shortLabel": "Prop. XI.1",
|
| 73 |
+
"short": "Line part in plane",
|
| 74 |
+
"book": 11,
|
| 75 |
+
"number": 1,
|
| 76 |
+
"colorClass": "proposition"
|
| 77 |
+
},
|
| 78 |
+
{
|
| 79 |
+
"id": "Prop2",
|
| 80 |
+
"type": "proposition",
|
| 81 |
+
"label": "If two straight lines cut one another, they lie in one plane; every triangle in one plane",
|
| 82 |
+
"shortLabel": "Prop. XI.2",
|
| 83 |
+
"short": "Two lines cut: one plane",
|
| 84 |
+
"book": 11,
|
| 85 |
+
"number": 2,
|
| 86 |
+
"colorClass": "proposition"
|
| 87 |
+
},
|
| 88 |
+
{
|
| 89 |
+
"id": "Prop3",
|
| 90 |
+
"type": "proposition",
|
| 91 |
+
"label": "If two planes cut one another, their intersection is a straight line",
|
| 92 |
+
"shortLabel": "Prop. XI.3",
|
| 93 |
+
"short": "Planes cut: line",
|
| 94 |
+
"book": 11,
|
| 95 |
+
"number": 3,
|
| 96 |
+
"colorClass": "proposition"
|
| 97 |
+
},
|
| 98 |
+
{
|
| 99 |
+
"id": "Prop4",
|
| 100 |
+
"type": "proposition",
|
| 101 |
+
"label": "If line at right angles to two lines cutting at point, also perpendicular to plane through them",
|
| 102 |
+
"shortLabel": "Prop. XI.4",
|
| 103 |
+
"short": "Line perpendicular to plane",
|
| 104 |
+
"book": 11,
|
| 105 |
+
"number": 4,
|
| 106 |
+
"colorClass": "proposition"
|
| 107 |
+
},
|
| 108 |
+
{
|
| 109 |
+
"id": "Prop5",
|
| 110 |
+
"type": "proposition",
|
| 111 |
+
"label": "If line at right angles to three lines meeting at point, the three lie in one plane",
|
| 112 |
+
"shortLabel": "Prop. XI.5",
|
| 113 |
+
"short": "Three lines from point",
|
| 114 |
+
"book": 11,
|
| 115 |
+
"number": 5,
|
| 116 |
+
"colorClass": "proposition"
|
| 117 |
+
},
|
| 118 |
+
{
|
| 119 |
+
"id": "Prop6",
|
| 120 |
+
"type": "proposition",
|
| 121 |
+
"label": "If two lines at right angles to same plane, they are parallel",
|
| 122 |
+
"shortLabel": "Prop. XI.6",
|
| 123 |
+
"short": "Perpendicular to same plane: parallel",
|
| 124 |
+
"book": 11,
|
| 125 |
+
"number": 6,
|
| 126 |
+
"colorClass": "proposition"
|
| 127 |
+
},
|
| 128 |
+
{
|
| 129 |
+
"id": "Prop7",
|
| 130 |
+
"type": "proposition",
|
| 131 |
+
"label": "If two lines parallel, line joining points on each is in same plane",
|
| 132 |
+
"shortLabel": "Prop. XI.7",
|
| 133 |
+
"short": "Parallel lines: join in plane",
|
| 134 |
+
"book": 11,
|
| 135 |
+
"number": 7,
|
| 136 |
+
"colorClass": "proposition"
|
| 137 |
+
},
|
| 138 |
+
{
|
| 139 |
+
"id": "Prop8",
|
| 140 |
+
"type": "proposition",
|
| 141 |
+
"label": "If two lines parallel, one perpendicular to plane, so is the other",
|
| 142 |
+
"shortLabel": "Prop. XI.8",
|
| 143 |
+
"short": "Parallel: one perpendicular",
|
| 144 |
+
"book": 11,
|
| 145 |
+
"number": 8,
|
| 146 |
+
"colorClass": "proposition"
|
| 147 |
+
},
|
| 148 |
+
{
|
| 149 |
+
"id": "Prop9",
|
| 150 |
+
"type": "proposition",
|
| 151 |
+
"label": "Lines parallel to same line but not in same plane are parallel to each other",
|
| 152 |
+
"shortLabel": "Prop. XI.9",
|
| 153 |
+
"short": "Parallel to same: parallel",
|
| 154 |
+
"book": 11,
|
| 155 |
+
"number": 9,
|
| 156 |
+
"colorClass": "proposition"
|
| 157 |
+
},
|
| 158 |
+
{
|
| 159 |
+
"id": "Prop10",
|
| 160 |
+
"type": "proposition",
|
| 161 |
+
"label": "Two lines meeting parallel to two meeting not in same plane: contain equal angles",
|
| 162 |
+
"shortLabel": "Prop. XI.10",
|
| 163 |
+
"short": "Skew lines: equal angles",
|
| 164 |
+
"book": 11,
|
| 165 |
+
"number": 10,
|
| 166 |
+
"colorClass": "proposition"
|
| 167 |
+
},
|
| 168 |
+
{
|
| 169 |
+
"id": "Prop11",
|
| 170 |
+
"type": "proposition",
|
| 171 |
+
"label": "To draw line perpendicular to given plane from given elevated point",
|
| 172 |
+
"shortLabel": "Prop. XI.11",
|
| 173 |
+
"short": "Perpendicular from point to plane",
|
| 174 |
+
"book": 11,
|
| 175 |
+
"number": 11,
|
| 176 |
+
"colorClass": "proposition"
|
| 177 |
+
},
|
| 178 |
+
{
|
| 179 |
+
"id": "Prop12",
|
| 180 |
+
"type": "proposition",
|
| 181 |
+
"label": "To set up line at right angles to plane from given point in it",
|
| 182 |
+
"shortLabel": "Prop. XI.12",
|
| 183 |
+
"short": "Perpendicular from point in plane",
|
| 184 |
+
"book": 11,
|
| 185 |
+
"number": 12,
|
| 186 |
+
"colorClass": "proposition"
|
| 187 |
+
},
|
| 188 |
+
{
|
| 189 |
+
"id": "Prop13",
|
| 190 |
+
"type": "proposition",
|
| 191 |
+
"label": "From same point two lines cannot be perpendicular to same plane on same side",
|
| 192 |
+
"shortLabel": "Prop. XI.13",
|
| 193 |
+
"short": "One perpendicular only",
|
| 194 |
+
"book": 11,
|
| 195 |
+
"number": 13,
|
| 196 |
+
"colorClass": "proposition"
|
| 197 |
+
},
|
| 198 |
+
{
|
| 199 |
+
"id": "Prop14",
|
| 200 |
+
"type": "proposition",
|
| 201 |
+
"label": "Planes to which same line is perpendicular are parallel",
|
| 202 |
+
"shortLabel": "Prop. XI.14",
|
| 203 |
+
"short": "Planes perpendicular to line: parallel",
|
| 204 |
+
"book": 11,
|
| 205 |
+
"number": 14,
|
| 206 |
+
"colorClass": "proposition"
|
| 207 |
+
},
|
| 208 |
+
{
|
| 209 |
+
"id": "Prop15",
|
| 210 |
+
"type": "proposition",
|
| 211 |
+
"label": "Two lines meeting parallel to two meeting not in same plane: planes through them parallel",
|
| 212 |
+
"shortLabel": "Prop. XI.15",
|
| 213 |
+
"short": "Skew lines: planes parallel",
|
| 214 |
+
"book": 11,
|
| 215 |
+
"number": 15,
|
| 216 |
+
"colorClass": "proposition"
|
| 217 |
+
},
|
| 218 |
+
{
|
| 219 |
+
"id": "Prop16",
|
| 220 |
+
"type": "proposition",
|
| 221 |
+
"label": "If two parallel planes cut by any plane, intersections are parallel",
|
| 222 |
+
"shortLabel": "Prop. XI.16",
|
| 223 |
+
"short": "Parallel planes cut: parallel",
|
| 224 |
+
"book": 11,
|
| 225 |
+
"number": 16,
|
| 226 |
+
"colorClass": "proposition"
|
| 227 |
+
},
|
| 228 |
+
{
|
| 229 |
+
"id": "Prop17",
|
| 230 |
+
"type": "proposition",
|
| 231 |
+
"label": "If two lines cut by parallel planes, they are cut in same ratios",
|
| 232 |
+
"shortLabel": "Prop. XI.17",
|
| 233 |
+
"short": "Parallel planes: same ratio",
|
| 234 |
+
"book": 11,
|
| 235 |
+
"number": 17,
|
| 236 |
+
"colorClass": "proposition"
|
| 237 |
+
},
|
| 238 |
+
{
|
| 239 |
+
"id": "Prop18",
|
| 240 |
+
"type": "proposition",
|
| 241 |
+
"label": "If line perpendicular to plane, all planes through it perpendicular to that plane",
|
| 242 |
+
"shortLabel": "Prop. XI.18",
|
| 243 |
+
"short": "Line perpendicular: planes through it",
|
| 244 |
+
"book": 11,
|
| 245 |
+
"number": 18,
|
| 246 |
+
"colorClass": "proposition"
|
| 247 |
+
},
|
| 248 |
+
{
|
| 249 |
+
"id": "Prop19",
|
| 250 |
+
"type": "proposition",
|
| 251 |
+
"label": "If two planes cutting one another perpendicular to plane, intersection perpendicular",
|
| 252 |
+
"shortLabel": "Prop. XI.19",
|
| 253 |
+
"short": "Planes perpendicular: intersection",
|
| 254 |
+
"book": 11,
|
| 255 |
+
"number": 19,
|
| 256 |
+
"colorClass": "proposition"
|
| 257 |
+
},
|
| 258 |
+
{
|
| 259 |
+
"id": "Prop20",
|
| 260 |
+
"type": "proposition",
|
| 261 |
+
"label": "Solid angle by three plane angles: sum of any two greater than third",
|
| 262 |
+
"shortLabel": "Prop. XI.20",
|
| 263 |
+
"short": "Solid angle: plane angles",
|
| 264 |
+
"book": 11,
|
| 265 |
+
"number": 20,
|
| 266 |
+
"colorClass": "proposition"
|
| 267 |
+
},
|
| 268 |
+
{
|
| 269 |
+
"id": "Prop21",
|
| 270 |
+
"type": "proposition",
|
| 271 |
+
"label": "Any solid angle contained by plane angles summing to less than four right angles",
|
| 272 |
+
"shortLabel": "Prop. XI.21",
|
| 273 |
+
"short": "Solid angle: less than four right",
|
| 274 |
+
"book": 11,
|
| 275 |
+
"number": 21,
|
| 276 |
+
"colorClass": "proposition"
|
| 277 |
+
},
|
| 278 |
+
{
|
| 279 |
+
"id": "Prop22",
|
| 280 |
+
"type": "proposition",
|
| 281 |
+
"label": "Three plane angles with sum of any two greater than third, equal sides: construct triangle",
|
| 282 |
+
"shortLabel": "Prop. XI.22",
|
| 283 |
+
"short": "Three plane angles: construct triangle",
|
| 284 |
+
"book": 11,
|
| 285 |
+
"number": 22,
|
| 286 |
+
"colorClass": "proposition"
|
| 287 |
+
},
|
| 288 |
+
{
|
| 289 |
+
"id": "Prop23",
|
| 290 |
+
"type": "proposition",
|
| 291 |
+
"label": "To construct solid angle from three plane angles (sum of any two greater than third)",
|
| 292 |
+
"shortLabel": "Prop. XI.23",
|
| 293 |
+
"short": "Construct solid angle",
|
| 294 |
+
"book": 11,
|
| 295 |
+
"number": 23,
|
| 296 |
+
"colorClass": "proposition"
|
| 297 |
+
},
|
| 298 |
+
{
|
| 299 |
+
"id": "Prop24",
|
| 300 |
+
"type": "proposition",
|
| 301 |
+
"label": "If solid contained by parallel planes, opposite planes equal and parallelogrammic",
|
| 302 |
+
"shortLabel": "Prop. XI.24",
|
| 303 |
+
"short": "Solid by parallel planes",
|
| 304 |
+
"book": 11,
|
| 305 |
+
"number": 24,
|
| 306 |
+
"colorClass": "proposition"
|
| 307 |
+
},
|
| 308 |
+
{
|
| 309 |
+
"id": "Prop25",
|
| 310 |
+
"type": "proposition",
|
| 311 |
+
"label": "Parallelepiped cut by plane parallel to opposite: base to base as solid to solid",
|
| 312 |
+
"shortLabel": "Prop. XI.25",
|
| 313 |
+
"short": "Parallelepiped cut: base ratio",
|
| 314 |
+
"book": 11,
|
| 315 |
+
"number": 25,
|
| 316 |
+
"colorClass": "proposition"
|
| 317 |
+
},
|
| 318 |
+
{
|
| 319 |
+
"id": "Prop26",
|
| 320 |
+
"type": "proposition",
|
| 321 |
+
"label": "To construct solid angle equal to given on given line at given point",
|
| 322 |
+
"shortLabel": "Prop. XI.26",
|
| 323 |
+
"short": "Construct equal solid angle",
|
| 324 |
+
"book": 11,
|
| 325 |
+
"number": 26,
|
| 326 |
+
"colorClass": "proposition"
|
| 327 |
+
},
|
| 328 |
+
{
|
| 329 |
+
"id": "Prop27",
|
| 330 |
+
"type": "proposition",
|
| 331 |
+
"label": "To describe parallelepiped similar to given on given straight line",
|
| 332 |
+
"shortLabel": "Prop. XI.27",
|
| 333 |
+
"short": "Similar parallelepiped on line",
|
| 334 |
+
"book": 11,
|
| 335 |
+
"number": 27,
|
| 336 |
+
"colorClass": "proposition"
|
| 337 |
+
},
|
| 338 |
+
{
|
| 339 |
+
"id": "Prop28",
|
| 340 |
+
"type": "proposition",
|
| 341 |
+
"label": "Parallelepiped cut by plane through diagonals of opposite planes: bisected",
|
| 342 |
+
"shortLabel": "Prop. XI.28",
|
| 343 |
+
"short": "Parallelepiped: diagonal plane bisects",
|
| 344 |
+
"book": 11,
|
| 345 |
+
"number": 28,
|
| 346 |
+
"colorClass": "proposition"
|
| 347 |
+
},
|
| 348 |
+
{
|
| 349 |
+
"id": "Prop29",
|
| 350 |
+
"type": "proposition",
|
| 351 |
+
"label": "Parallelepipeds same base, height, ends on same lines: equal",
|
| 352 |
+
"shortLabel": "Prop. XI.29",
|
| 353 |
+
"short": "Same base, height, same lines: equal",
|
| 354 |
+
"book": 11,
|
| 355 |
+
"number": 29,
|
| 356 |
+
"colorClass": "proposition"
|
| 357 |
+
},
|
| 358 |
+
{
|
| 359 |
+
"id": "Prop30",
|
| 360 |
+
"type": "proposition",
|
| 361 |
+
"label": "Parallelepipeds same base, height, ends not on same lines: equal",
|
| 362 |
+
"shortLabel": "Prop. XI.30",
|
| 363 |
+
"short": "Same base, height, different lines: equal",
|
| 364 |
+
"book": 11,
|
| 365 |
+
"number": 30,
|
| 366 |
+
"colorClass": "proposition"
|
| 367 |
+
},
|
| 368 |
+
{
|
| 369 |
+
"id": "Prop31",
|
| 370 |
+
"type": "proposition",
|
| 371 |
+
"label": "Parallelepipeds on equal bases, same height: equal",
|
| 372 |
+
"shortLabel": "Prop. XI.31",
|
| 373 |
+
"short": "Equal bases, same height: equal",
|
| 374 |
+
"book": 11,
|
| 375 |
+
"number": 31,
|
| 376 |
+
"colorClass": "proposition"
|
| 377 |
+
},
|
| 378 |
+
{
|
| 379 |
+
"id": "Prop32",
|
| 380 |
+
"type": "proposition",
|
| 381 |
+
"label": "Parallelepipeds same height: to one another as bases",
|
| 382 |
+
"shortLabel": "Prop. XI.32",
|
| 383 |
+
"short": "Same height: as bases",
|
| 384 |
+
"book": 11,
|
| 385 |
+
"number": 32,
|
| 386 |
+
"colorClass": "proposition"
|
| 387 |
+
},
|
| 388 |
+
{
|
| 389 |
+
"id": "Prop33",
|
| 390 |
+
"type": "proposition",
|
| 391 |
+
"label": "Similar parallelepipeds: to one another in triplicate ratio of corresponding sides",
|
| 392 |
+
"shortLabel": "Prop. XI.33",
|
| 393 |
+
"short": "Similar: triplicate ratio",
|
| 394 |
+
"book": 11,
|
| 395 |
+
"number": 33,
|
| 396 |
+
"colorClass": "proposition"
|
| 397 |
+
},
|
| 398 |
+
{
|
| 399 |
+
"id": "Prop34",
|
| 400 |
+
"type": "proposition",
|
| 401 |
+
"label": "Equal parallelepipeds: bases reciprocally proportional to heights",
|
| 402 |
+
"shortLabel": "Prop. XI.34",
|
| 403 |
+
"short": "Equal: bases reciprocally proportional",
|
| 404 |
+
"book": 11,
|
| 405 |
+
"number": 34,
|
| 406 |
+
"colorClass": "proposition"
|
| 407 |
+
},
|
| 408 |
+
{
|
| 409 |
+
"id": "Prop35",
|
| 410 |
+
"type": "proposition",
|
| 411 |
+
"label": "Equal plane angles, elevated lines with equal angles: perpendiculars, joins",
|
| 412 |
+
"shortLabel": "Prop. XI.35",
|
| 413 |
+
"short": "Equal plane angles: elevated lines",
|
| 414 |
+
"book": 11,
|
| 415 |
+
"number": 35,
|
| 416 |
+
"colorClass": "proposition"
|
| 417 |
+
},
|
| 418 |
+
{
|
| 419 |
+
"id": "Prop36",
|
| 420 |
+
"type": "proposition",
|
| 421 |
+
"label": "Three proportional lines: parallelepiped from three equals that on mean equilateral",
|
| 422 |
+
"shortLabel": "Prop. XI.36",
|
| 423 |
+
"short": "Three proportional: parallelepiped",
|
| 424 |
+
"book": 11,
|
| 425 |
+
"number": 36,
|
| 426 |
+
"colorClass": "proposition"
|
| 427 |
+
},
|
| 428 |
+
{
|
| 429 |
+
"id": "Prop37",
|
| 430 |
+
"type": "proposition",
|
| 431 |
+
"label": "Four proportional: similar parallelepipeds proportional; converse",
|
| 432 |
+
"shortLabel": "Prop. XI.37",
|
| 433 |
+
"short": "Four proportional: parallelepipeds",
|
| 434 |
+
"book": 11,
|
| 435 |
+
"number": 37,
|
| 436 |
+
"colorClass": "proposition"
|
| 437 |
+
},
|
| 438 |
+
{
|
| 439 |
+
"id": "Prop38",
|
| 440 |
+
"type": "proposition",
|
| 441 |
+
"label": "Cube opposite sides bisected, planes through: intersection and diameter bisect each other",
|
| 442 |
+
"shortLabel": "Prop. XI.38",
|
| 443 |
+
"short": "Cube: bisected by planes",
|
| 444 |
+
"book": 11,
|
| 445 |
+
"number": 38,
|
| 446 |
+
"colorClass": "proposition"
|
| 447 |
+
},
|
| 448 |
+
{
|
| 449 |
+
"id": "Prop39",
|
| 450 |
+
"type": "proposition",
|
| 451 |
+
"label": "Two prisms equal height, parallelogram and triangle bases, parallelogram double: equal",
|
| 452 |
+
"shortLabel": "Prop. XI.39",
|
| 453 |
+
"short": "Prisms: parallelogram, triangle",
|
| 454 |
+
"book": 11,
|
| 455 |
+
"number": 39,
|
| 456 |
+
"colorClass": "proposition"
|
| 457 |
+
}
|
| 458 |
+
],
|
| 459 |
+
"edges": [
|
| 460 |
+
{
|
| 461 |
+
"from": "BookI",
|
| 462 |
+
"to": "Prop1"
|
| 463 |
+
},
|
| 464 |
+
{
|
| 465 |
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"from": "BookVI",
|
| 466 |
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"to": "Prop1"
|
| 467 |
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},
|
| 468 |
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{
|
| 469 |
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"from": "BookI",
|
| 470 |
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"to": "Prop2"
|
| 471 |
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},
|
| 472 |
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{
|
| 473 |
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"from": "BookVI",
|
| 474 |
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"to": "Prop2"
|
| 475 |
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},
|
| 476 |
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{
|
| 477 |
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|
| 478 |
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"to": "Prop3"
|
| 479 |
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},
|
| 480 |
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{
|
| 481 |
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"from": "BookVI",
|
| 482 |
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"to": "Prop3"
|
| 483 |
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},
|
| 484 |
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{
|
| 485 |
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"from": "BookI",
|
| 486 |
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"to": "Prop4"
|
| 487 |
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},
|
| 488 |
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{
|
| 489 |
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"from": "BookVI",
|
| 490 |
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"to": "Prop4"
|
| 491 |
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},
|
| 492 |
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{
|
| 493 |
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|
| 494 |
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|
| 495 |
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},
|
| 496 |
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{
|
| 497 |
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|
| 498 |
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|
| 499 |
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},
|
| 500 |
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{
|
| 501 |
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"from": "BookI",
|
| 502 |
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"to": "Prop6"
|
| 503 |
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},
|
| 504 |
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{
|
| 505 |
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"from": "BookVI",
|
| 506 |
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"to": "Prop6"
|
| 507 |
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},
|
| 508 |
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{
|
| 509 |
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|
| 510 |
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|
| 511 |
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},
|
| 512 |
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{
|
| 513 |
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|
| 514 |
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"to": "Prop7"
|
| 515 |
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},
|
| 516 |
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{
|
| 517 |
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|
| 518 |
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"to": "Prop8"
|
| 519 |
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},
|
| 520 |
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{
|
| 521 |
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|
| 522 |
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"to": "Prop8"
|
| 523 |
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},
|
| 524 |
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{
|
| 525 |
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"from": "BookI",
|
| 526 |
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"to": "Prop9"
|
| 527 |
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},
|
| 528 |
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{
|
| 529 |
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"from": "BookVI",
|
| 530 |
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"to": "Prop9"
|
| 531 |
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},
|
| 532 |
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{
|
| 533 |
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"from": "BookI",
|
| 534 |
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"to": "Prop10"
|
| 535 |
+
},
|
| 536 |
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{
|
| 537 |
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"from": "BookVI",
|
| 538 |
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"to": "Prop10"
|
| 539 |
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},
|
| 540 |
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{
|
| 541 |
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|
| 542 |
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"to": "Prop11"
|
| 543 |
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},
|
| 544 |
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{
|
| 545 |
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"from": "BookVI",
|
| 546 |
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"to": "Prop11"
|
| 547 |
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},
|
| 548 |
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{
|
| 549 |
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"from": "BookI",
|
| 550 |
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"to": "Prop12"
|
| 551 |
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},
|
| 552 |
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{
|
| 553 |
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"from": "BookVI",
|
| 554 |
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"to": "Prop12"
|
| 555 |
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},
|
| 556 |
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{
|
| 557 |
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"from": "BookI",
|
| 558 |
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"to": "Prop13"
|
| 559 |
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},
|
| 560 |
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{
|
| 561 |
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"from": "BookVI",
|
| 562 |
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|
| 563 |
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},
|
| 564 |
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{
|
| 565 |
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|
| 566 |
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"to": "Prop14"
|
| 567 |
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},
|
| 568 |
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{
|
| 569 |
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"from": "BookVI",
|
| 570 |
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"to": "Prop14"
|
| 571 |
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},
|
| 572 |
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{
|
| 573 |
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"from": "BookI",
|
| 574 |
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"to": "Prop15"
|
| 575 |
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},
|
| 576 |
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{
|
| 577 |
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"from": "BookVI",
|
| 578 |
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"to": "Prop15"
|
| 579 |
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},
|
| 580 |
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{
|
| 581 |
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"from": "BookI",
|
| 582 |
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"to": "Prop16"
|
| 583 |
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},
|
| 584 |
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{
|
| 585 |
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"from": "BookVI",
|
| 586 |
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"to": "Prop16"
|
| 587 |
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},
|
| 588 |
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{
|
| 589 |
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"from": "BookI",
|
| 590 |
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"to": "Prop17"
|
| 591 |
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},
|
| 592 |
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{
|
| 593 |
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"from": "BookVI",
|
| 594 |
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"to": "Prop17"
|
| 595 |
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},
|
| 596 |
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{
|
| 597 |
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"from": "BookI",
|
| 598 |
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"to": "Prop18"
|
| 599 |
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},
|
| 600 |
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{
|
| 601 |
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"from": "BookVI",
|
| 602 |
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"to": "Prop18"
|
| 603 |
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},
|
| 604 |
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{
|
| 605 |
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|
| 606 |
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"to": "Prop19"
|
| 607 |
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},
|
| 608 |
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{
|
| 609 |
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"from": "BookVI",
|
| 610 |
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"to": "Prop19"
|
| 611 |
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},
|
| 612 |
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{
|
| 613 |
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"from": "BookI",
|
| 614 |
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"to": "Prop20"
|
| 615 |
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},
|
| 616 |
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{
|
| 617 |
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"from": "BookVI",
|
| 618 |
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"to": "Prop20"
|
| 619 |
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},
|
| 620 |
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{
|
| 621 |
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"from": "BookI",
|
| 622 |
+
"to": "Prop21"
|
| 623 |
+
},
|
| 624 |
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{
|
| 625 |
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"from": "BookVI",
|
| 626 |
+
"to": "Prop21"
|
| 627 |
+
},
|
| 628 |
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{
|
| 629 |
+
"from": "BookI",
|
| 630 |
+
"to": "Prop22"
|
| 631 |
+
},
|
| 632 |
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{
|
| 633 |
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"from": "BookVI",
|
| 634 |
+
"to": "Prop22"
|
| 635 |
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},
|
| 636 |
+
{
|
| 637 |
+
"from": "BookI",
|
| 638 |
+
"to": "Prop23"
|
| 639 |
+
},
|
| 640 |
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{
|
| 641 |
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"from": "BookVI",
|
| 642 |
+
"to": "Prop23"
|
| 643 |
+
},
|
| 644 |
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{
|
| 645 |
+
"from": "BookI",
|
| 646 |
+
"to": "Prop24"
|
| 647 |
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},
|
| 648 |
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{
|
| 649 |
+
"from": "BookVI",
|
| 650 |
+
"to": "Prop24"
|
| 651 |
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},
|
| 652 |
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{
|
| 653 |
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"from": "BookI",
|
| 654 |
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"to": "Prop25"
|
| 655 |
+
},
|
| 656 |
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{
|
| 657 |
+
"from": "BookVI",
|
| 658 |
+
"to": "Prop25"
|
| 659 |
+
},
|
| 660 |
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{
|
| 661 |
+
"from": "BookI",
|
| 662 |
+
"to": "Prop26"
|
| 663 |
+
},
|
| 664 |
+
{
|
| 665 |
+
"from": "BookVI",
|
| 666 |
+
"to": "Prop26"
|
| 667 |
+
},
|
| 668 |
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{
|
| 669 |
+
"from": "BookI",
|
| 670 |
+
"to": "Prop27"
|
| 671 |
+
},
|
| 672 |
+
{
|
| 673 |
+
"from": "BookVI",
|
| 674 |
+
"to": "Prop27"
|
| 675 |
+
},
|
| 676 |
+
{
|
| 677 |
+
"from": "BookI",
|
| 678 |
+
"to": "Prop28"
|
| 679 |
+
},
|
| 680 |
+
{
|
| 681 |
+
"from": "BookVI",
|
| 682 |
+
"to": "Prop28"
|
| 683 |
+
},
|
| 684 |
+
{
|
| 685 |
+
"from": "BookI",
|
| 686 |
+
"to": "Prop29"
|
| 687 |
+
},
|
| 688 |
+
{
|
| 689 |
+
"from": "BookVI",
|
| 690 |
+
"to": "Prop29"
|
| 691 |
+
},
|
| 692 |
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{
|
| 693 |
+
"from": "BookI",
|
| 694 |
+
"to": "Prop30"
|
| 695 |
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},
|
| 696 |
+
{
|
| 697 |
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"from": "BookVI",
|
| 698 |
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"to": "Prop30"
|
| 699 |
+
},
|
| 700 |
+
{
|
| 701 |
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"from": "BookI",
|
| 702 |
+
"to": "Prop31"
|
| 703 |
+
},
|
| 704 |
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{
|
| 705 |
+
"from": "BookVI",
|
| 706 |
+
"to": "Prop31"
|
| 707 |
+
},
|
| 708 |
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{
|
| 709 |
+
"from": "BookI",
|
| 710 |
+
"to": "Prop32"
|
| 711 |
+
},
|
| 712 |
+
{
|
| 713 |
+
"from": "BookVI",
|
| 714 |
+
"to": "Prop32"
|
| 715 |
+
},
|
| 716 |
+
{
|
| 717 |
+
"from": "BookI",
|
| 718 |
+
"to": "Prop33"
|
| 719 |
+
},
|
| 720 |
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{
|
| 721 |
+
"from": "BookVI",
|
| 722 |
+
"to": "Prop33"
|
| 723 |
+
},
|
| 724 |
+
{
|
| 725 |
+
"from": "BookI",
|
| 726 |
+
"to": "Prop34"
|
| 727 |
+
},
|
| 728 |
+
{
|
| 729 |
+
"from": "BookVI",
|
| 730 |
+
"to": "Prop34"
|
| 731 |
+
},
|
| 732 |
+
{
|
| 733 |
+
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|
| 734 |
+
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|
| 735 |
+
},
|
| 736 |
+
{
|
| 737 |
+
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|
| 738 |
+
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|
| 739 |
+
},
|
| 740 |
+
{
|
| 741 |
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|
| 742 |
+
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|
| 743 |
+
},
|
| 744 |
+
{
|
| 745 |
+
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|
| 746 |
+
"to": "Prop36"
|
| 747 |
+
},
|
| 748 |
+
{
|
| 749 |
+
"from": "BookI",
|
| 750 |
+
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|
| 751 |
+
},
|
| 752 |
+
{
|
| 753 |
+
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|
| 754 |
+
"to": "Prop37"
|
| 755 |
+
},
|
| 756 |
+
{
|
| 757 |
+
"from": "BookI",
|
| 758 |
+
"to": "Prop38"
|
| 759 |
+
},
|
| 760 |
+
{
|
| 761 |
+
"from": "BookVI",
|
| 762 |
+
"to": "Prop38"
|
| 763 |
+
},
|
| 764 |
+
{
|
| 765 |
+
"from": "BookI",
|
| 766 |
+
"to": "Prop39"
|
| 767 |
+
},
|
| 768 |
+
{
|
| 769 |
+
"from": "BookVI",
|
| 770 |
+
"to": "Prop39"
|
| 771 |
+
}
|
| 772 |
+
],
|
| 773 |
+
"colorScheme": {
|
| 774 |
+
"foundation": {
|
| 775 |
+
"fill": "#95a5a6",
|
| 776 |
+
"stroke": "#7f8c8d"
|
| 777 |
+
},
|
| 778 |
+
"proposition": {
|
| 779 |
+
"fill": "#1abc9c",
|
| 780 |
+
"stroke": "#16a085"
|
| 781 |
+
}
|
| 782 |
+
}
|
| 783 |
+
}
|
data/euclid-elements-book-xii.json
ADDED
|
@@ -0,0 +1,567 @@
|
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|
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|
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|
|
|
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|
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|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
| 1 |
+
{
|
| 2 |
+
"schemaVersion": "1.0",
|
| 3 |
+
"discourse": {
|
| 4 |
+
"id": "euclid-elements-book-xii",
|
| 5 |
+
"name": "Euclid's Elements, Book XII",
|
| 6 |
+
"subject": "measurement",
|
| 7 |
+
"variant": "classical",
|
| 8 |
+
"description": "Measurement of figures: circles, pyramids, cones, cylinders, spheres. 18 propositions. Depends on Books I, V, VI, XI. Source: David E. Joyce.",
|
| 9 |
+
"structure": {
|
| 10 |
+
"books": 12,
|
| 11 |
+
"propositions": 18,
|
| 12 |
+
"foundationTypes": [
|
| 13 |
+
"foundation"
|
| 14 |
+
]
|
| 15 |
+
}
|
| 16 |
+
},
|
| 17 |
+
"metadata": {
|
| 18 |
+
"created": "2026-03-18",
|
| 19 |
+
"lastUpdated": "2026-03-18",
|
| 20 |
+
"version": "1.0.0",
|
| 21 |
+
"license": "CC BY 4.0",
|
| 22 |
+
"authors": [
|
| 23 |
+
"Welz, G."
|
| 24 |
+
],
|
| 25 |
+
"methodology": "Programming Framework",
|
| 26 |
+
"citation": "Welz, G. (2026). Euclid's Elements Book XII Dependency Graph. Programming Framework.",
|
| 27 |
+
"keywords": [
|
| 28 |
+
"Euclid",
|
| 29 |
+
"Elements",
|
| 30 |
+
"Book XII",
|
| 31 |
+
"measurement",
|
| 32 |
+
"pyramid",
|
| 33 |
+
"cone",
|
| 34 |
+
"cylinder",
|
| 35 |
+
"sphere"
|
| 36 |
+
]
|
| 37 |
+
},
|
| 38 |
+
"sources": [
|
| 39 |
+
{
|
| 40 |
+
"id": "joyce",
|
| 41 |
+
"type": "digital",
|
| 42 |
+
"authors": "Joyce, David E.",
|
| 43 |
+
"title": "Euclid's Elements, Book XII",
|
| 44 |
+
"year": "1996",
|
| 45 |
+
"url": "https://mathcs.clarku.edu/~djoyce/java/elements/bookXII/bookXII.html",
|
| 46 |
+
"notes": "Clark University"
|
| 47 |
+
}
|
| 48 |
+
],
|
| 49 |
+
"nodes": [
|
| 50 |
+
{
|
| 51 |
+
"id": "BookI",
|
| 52 |
+
"type": "foundation",
|
| 53 |
+
"label": "Book I — Plane geometry",
|
| 54 |
+
"shortLabel": "Book I",
|
| 55 |
+
"short": "Foundation",
|
| 56 |
+
"book": 1,
|
| 57 |
+
"colorClass": "foundation"
|
| 58 |
+
},
|
| 59 |
+
{
|
| 60 |
+
"id": "BookV",
|
| 61 |
+
"type": "foundation",
|
| 62 |
+
"label": "Book V — Proportions",
|
| 63 |
+
"shortLabel": "Book V",
|
| 64 |
+
"short": "Foundation",
|
| 65 |
+
"book": 5,
|
| 66 |
+
"colorClass": "foundation"
|
| 67 |
+
},
|
| 68 |
+
{
|
| 69 |
+
"id": "BookVI",
|
| 70 |
+
"type": "foundation",
|
| 71 |
+
"label": "Book VI — Similar figures",
|
| 72 |
+
"shortLabel": "Book VI",
|
| 73 |
+
"short": "Foundation",
|
| 74 |
+
"book": 6,
|
| 75 |
+
"colorClass": "foundation"
|
| 76 |
+
},
|
| 77 |
+
{
|
| 78 |
+
"id": "BookXI",
|
| 79 |
+
"type": "foundation",
|
| 80 |
+
"label": "Book XI — Solid geometry",
|
| 81 |
+
"shortLabel": "Book XI",
|
| 82 |
+
"short": "Foundation",
|
| 83 |
+
"book": 11,
|
| 84 |
+
"colorClass": "foundation"
|
| 85 |
+
},
|
| 86 |
+
{
|
| 87 |
+
"id": "Prop1",
|
| 88 |
+
"type": "proposition",
|
| 89 |
+
"label": "Similar polygons in circles: to one another as squares on diameters",
|
| 90 |
+
"shortLabel": "Prop. XII.1",
|
| 91 |
+
"short": "Similar polygons: as squares on diameters",
|
| 92 |
+
"book": 12,
|
| 93 |
+
"number": 1,
|
| 94 |
+
"colorClass": "proposition"
|
| 95 |
+
},
|
| 96 |
+
{
|
| 97 |
+
"id": "Prop2",
|
| 98 |
+
"type": "proposition",
|
| 99 |
+
"label": "Circles are to one another as the squares on their diameters",
|
| 100 |
+
"shortLabel": "Prop. XII.2",
|
| 101 |
+
"short": "Circles: as squares on diameters",
|
| 102 |
+
"book": 12,
|
| 103 |
+
"number": 2,
|
| 104 |
+
"colorClass": "proposition"
|
| 105 |
+
},
|
| 106 |
+
{
|
| 107 |
+
"id": "Prop3",
|
| 108 |
+
"type": "proposition",
|
| 109 |
+
"label": "Pyramid with triangular base: divided into two pyramids, two prisms; prisms greater than half",
|
| 110 |
+
"shortLabel": "Prop. XII.3",
|
| 111 |
+
"short": "Pyramid divided",
|
| 112 |
+
"book": 12,
|
| 113 |
+
"number": 3,
|
| 114 |
+
"colorClass": "proposition"
|
| 115 |
+
},
|
| 116 |
+
{
|
| 117 |
+
"id": "Prop4",
|
| 118 |
+
"type": "proposition",
|
| 119 |
+
"label": "Two pyramids same height, triangular bases, divided: base to base as all prisms",
|
| 120 |
+
"shortLabel": "Prop. XII.4",
|
| 121 |
+
"short": "Pyramids: base as prisms",
|
| 122 |
+
"book": 12,
|
| 123 |
+
"number": 4,
|
| 124 |
+
"colorClass": "proposition"
|
| 125 |
+
},
|
| 126 |
+
{
|
| 127 |
+
"id": "Prop5",
|
| 128 |
+
"type": "proposition",
|
| 129 |
+
"label": "Pyramids same height, triangular bases: to one another as bases",
|
| 130 |
+
"shortLabel": "Prop. XII.5",
|
| 131 |
+
"short": "Pyramids: as bases",
|
| 132 |
+
"book": 12,
|
| 133 |
+
"number": 5,
|
| 134 |
+
"colorClass": "proposition"
|
| 135 |
+
},
|
| 136 |
+
{
|
| 137 |
+
"id": "Prop6",
|
| 138 |
+
"type": "proposition",
|
| 139 |
+
"label": "Pyramids same height, polygonal bases: to one another as bases",
|
| 140 |
+
"shortLabel": "Prop. XII.6",
|
| 141 |
+
"short": "Pyramids polygonal: as bases",
|
| 142 |
+
"book": 12,
|
| 143 |
+
"number": 6,
|
| 144 |
+
"colorClass": "proposition"
|
| 145 |
+
},
|
| 146 |
+
{
|
| 147 |
+
"id": "Prop7",
|
| 148 |
+
"type": "proposition",
|
| 149 |
+
"label": "Prism with triangular base: divided into three equal pyramids",
|
| 150 |
+
"shortLabel": "Prop. XII.7",
|
| 151 |
+
"short": "Prism into three pyramids",
|
| 152 |
+
"book": 12,
|
| 153 |
+
"number": 7,
|
| 154 |
+
"colorClass": "proposition"
|
| 155 |
+
},
|
| 156 |
+
{
|
| 157 |
+
"id": "Prop8",
|
| 158 |
+
"type": "proposition",
|
| 159 |
+
"label": "Similar pyramids triangular bases: in triplicate ratio of corresponding sides",
|
| 160 |
+
"shortLabel": "Prop. XII.8",
|
| 161 |
+
"short": "Similar pyramids: triplicate ratio",
|
| 162 |
+
"book": 12,
|
| 163 |
+
"number": 8,
|
| 164 |
+
"colorClass": "proposition"
|
| 165 |
+
},
|
| 166 |
+
{
|
| 167 |
+
"id": "Prop9",
|
| 168 |
+
"type": "proposition",
|
| 169 |
+
"label": "Equal pyramids triangular bases: bases reciprocally proportional to heights",
|
| 170 |
+
"shortLabel": "Prop. XII.9",
|
| 171 |
+
"short": "Equal pyramids: bases reciprocally proportional",
|
| 172 |
+
"book": 12,
|
| 173 |
+
"number": 9,
|
| 174 |
+
"colorClass": "proposition"
|
| 175 |
+
},
|
| 176 |
+
{
|
| 177 |
+
"id": "Prop10",
|
| 178 |
+
"type": "proposition",
|
| 179 |
+
"label": "Any cone is third part of cylinder same base and equal height",
|
| 180 |
+
"shortLabel": "Prop. XII.10",
|
| 181 |
+
"short": "Cone third of cylinder",
|
| 182 |
+
"book": 12,
|
| 183 |
+
"number": 10,
|
| 184 |
+
"colorClass": "proposition"
|
| 185 |
+
},
|
| 186 |
+
{
|
| 187 |
+
"id": "Prop11",
|
| 188 |
+
"type": "proposition",
|
| 189 |
+
"label": "Cones and cylinders same height: to one another as bases",
|
| 190 |
+
"shortLabel": "Prop. XII.11",
|
| 191 |
+
"short": "Cones, cylinders: as bases",
|
| 192 |
+
"book": 12,
|
| 193 |
+
"number": 11,
|
| 194 |
+
"colorClass": "proposition"
|
| 195 |
+
},
|
| 196 |
+
{
|
| 197 |
+
"id": "Prop12",
|
| 198 |
+
"type": "proposition",
|
| 199 |
+
"label": "Similar cones and cylinders: in triplicate ratio of diameters of bases",
|
| 200 |
+
"shortLabel": "Prop. XII.12",
|
| 201 |
+
"short": "Similar cones, cylinders: triplicate",
|
| 202 |
+
"book": 12,
|
| 203 |
+
"number": 12,
|
| 204 |
+
"colorClass": "proposition"
|
| 205 |
+
},
|
| 206 |
+
{
|
| 207 |
+
"id": "Prop13",
|
| 208 |
+
"type": "proposition",
|
| 209 |
+
"label": "Cylinder cut by plane parallel to opposite: cylinder to cylinder as axis to axis",
|
| 210 |
+
"shortLabel": "Prop. XII.13",
|
| 211 |
+
"short": "Cylinder cut: as axes",
|
| 212 |
+
"book": 12,
|
| 213 |
+
"number": 13,
|
| 214 |
+
"colorClass": "proposition"
|
| 215 |
+
},
|
| 216 |
+
{
|
| 217 |
+
"id": "Prop14",
|
| 218 |
+
"type": "proposition",
|
| 219 |
+
"label": "Cones and cylinders on equal bases: to one another as heights",
|
| 220 |
+
"shortLabel": "Prop. XII.14",
|
| 221 |
+
"short": "Cones, cylinders equal bases: as heights",
|
| 222 |
+
"book": 12,
|
| 223 |
+
"number": 14,
|
| 224 |
+
"colorClass": "proposition"
|
| 225 |
+
},
|
| 226 |
+
{
|
| 227 |
+
"id": "Prop15",
|
| 228 |
+
"type": "proposition",
|
| 229 |
+
"label": "Equal cones and cylinders: bases reciprocally proportional to heights",
|
| 230 |
+
"shortLabel": "Prop. XII.15",
|
| 231 |
+
"short": "Equal cones, cylinders: reciprocally proportional",
|
| 232 |
+
"book": 12,
|
| 233 |
+
"number": 15,
|
| 234 |
+
"colorClass": "proposition"
|
| 235 |
+
},
|
| 236 |
+
{
|
| 237 |
+
"id": "Prop16",
|
| 238 |
+
"type": "proposition",
|
| 239 |
+
"label": "Given two circles same center: inscribe in greater equilateral polygon even sides not touching lesser",
|
| 240 |
+
"shortLabel": "Prop. XII.16",
|
| 241 |
+
"short": "Inscribe polygon in greater circle",
|
| 242 |
+
"book": 12,
|
| 243 |
+
"number": 16,
|
| 244 |
+
"colorClass": "proposition"
|
| 245 |
+
},
|
| 246 |
+
{
|
| 247 |
+
"id": "Prop17",
|
| 248 |
+
"type": "proposition",
|
| 249 |
+
"label": "Given two spheres same center: inscribe in greater polyhedral solid not touching lesser",
|
| 250 |
+
"shortLabel": "Prop. XII.17",
|
| 251 |
+
"short": "Inscribe polyhedron in greater sphere",
|
| 252 |
+
"book": 12,
|
| 253 |
+
"number": 17,
|
| 254 |
+
"colorClass": "proposition"
|
| 255 |
+
},
|
| 256 |
+
{
|
| 257 |
+
"id": "Prop18",
|
| 258 |
+
"type": "proposition",
|
| 259 |
+
"label": "Spheres are to one another in triplicate ratio of their diameters",
|
| 260 |
+
"shortLabel": "Prop. XII.18",
|
| 261 |
+
"short": "Spheres: triplicate ratio",
|
| 262 |
+
"book": 12,
|
| 263 |
+
"number": 18,
|
| 264 |
+
"colorClass": "proposition"
|
| 265 |
+
}
|
| 266 |
+
],
|
| 267 |
+
"edges": [
|
| 268 |
+
{
|
| 269 |
+
"from": "BookI",
|
| 270 |
+
"to": "Prop1"
|
| 271 |
+
},
|
| 272 |
+
{
|
| 273 |
+
"from": "BookV",
|
| 274 |
+
"to": "Prop1"
|
| 275 |
+
},
|
| 276 |
+
{
|
| 277 |
+
"from": "BookVI",
|
| 278 |
+
"to": "Prop1"
|
| 279 |
+
},
|
| 280 |
+
{
|
| 281 |
+
"from": "BookXI",
|
| 282 |
+
"to": "Prop1"
|
| 283 |
+
},
|
| 284 |
+
{
|
| 285 |
+
"from": "BookI",
|
| 286 |
+
"to": "Prop2"
|
| 287 |
+
},
|
| 288 |
+
{
|
| 289 |
+
"from": "BookV",
|
| 290 |
+
"to": "Prop2"
|
| 291 |
+
},
|
| 292 |
+
{
|
| 293 |
+
"from": "BookVI",
|
| 294 |
+
"to": "Prop2"
|
| 295 |
+
},
|
| 296 |
+
{
|
| 297 |
+
"from": "BookXI",
|
| 298 |
+
"to": "Prop2"
|
| 299 |
+
},
|
| 300 |
+
{
|
| 301 |
+
"from": "BookI",
|
| 302 |
+
"to": "Prop3"
|
| 303 |
+
},
|
| 304 |
+
{
|
| 305 |
+
"from": "BookV",
|
| 306 |
+
"to": "Prop3"
|
| 307 |
+
},
|
| 308 |
+
{
|
| 309 |
+
"from": "BookVI",
|
| 310 |
+
"to": "Prop3"
|
| 311 |
+
},
|
| 312 |
+
{
|
| 313 |
+
"from": "BookXI",
|
| 314 |
+
"to": "Prop3"
|
| 315 |
+
},
|
| 316 |
+
{
|
| 317 |
+
"from": "BookI",
|
| 318 |
+
"to": "Prop4"
|
| 319 |
+
},
|
| 320 |
+
{
|
| 321 |
+
"from": "BookV",
|
| 322 |
+
"to": "Prop4"
|
| 323 |
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},
|
| 324 |
+
{
|
| 325 |
+
"from": "BookVI",
|
| 326 |
+
"to": "Prop4"
|
| 327 |
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},
|
| 328 |
+
{
|
| 329 |
+
"from": "BookXI",
|
| 330 |
+
"to": "Prop4"
|
| 331 |
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},
|
| 332 |
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{
|
| 333 |
+
"from": "BookI",
|
| 334 |
+
"to": "Prop5"
|
| 335 |
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},
|
| 336 |
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{
|
| 337 |
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"from": "BookV",
|
| 338 |
+
"to": "Prop5"
|
| 339 |
+
},
|
| 340 |
+
{
|
| 341 |
+
"from": "BookVI",
|
| 342 |
+
"to": "Prop5"
|
| 343 |
+
},
|
| 344 |
+
{
|
| 345 |
+
"from": "BookXI",
|
| 346 |
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"to": "Prop5"
|
| 347 |
+
},
|
| 348 |
+
{
|
| 349 |
+
"from": "BookI",
|
| 350 |
+
"to": "Prop6"
|
| 351 |
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},
|
| 352 |
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{
|
| 353 |
+
"from": "BookV",
|
| 354 |
+
"to": "Prop6"
|
| 355 |
+
},
|
| 356 |
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{
|
| 357 |
+
"from": "BookVI",
|
| 358 |
+
"to": "Prop6"
|
| 359 |
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},
|
| 360 |
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{
|
| 361 |
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"from": "BookXI",
|
| 362 |
+
"to": "Prop6"
|
| 363 |
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},
|
| 364 |
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{
|
| 365 |
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"from": "BookI",
|
| 366 |
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"to": "Prop7"
|
| 367 |
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},
|
| 368 |
+
{
|
| 369 |
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"from": "BookV",
|
| 370 |
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"to": "Prop7"
|
| 371 |
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},
|
| 372 |
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{
|
| 373 |
+
"from": "BookVI",
|
| 374 |
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"to": "Prop7"
|
| 375 |
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},
|
| 376 |
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{
|
| 377 |
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"from": "BookXI",
|
| 378 |
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"to": "Prop7"
|
| 379 |
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},
|
| 380 |
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{
|
| 381 |
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"from": "BookI",
|
| 382 |
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"to": "Prop8"
|
| 383 |
+
},
|
| 384 |
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{
|
| 385 |
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"from": "BookV",
|
| 386 |
+
"to": "Prop8"
|
| 387 |
+
},
|
| 388 |
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{
|
| 389 |
+
"from": "BookVI",
|
| 390 |
+
"to": "Prop8"
|
| 391 |
+
},
|
| 392 |
+
{
|
| 393 |
+
"from": "BookXI",
|
| 394 |
+
"to": "Prop8"
|
| 395 |
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},
|
| 396 |
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{
|
| 397 |
+
"from": "BookI",
|
| 398 |
+
"to": "Prop9"
|
| 399 |
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},
|
| 400 |
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{
|
| 401 |
+
"from": "BookV",
|
| 402 |
+
"to": "Prop9"
|
| 403 |
+
},
|
| 404 |
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{
|
| 405 |
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"from": "BookVI",
|
| 406 |
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"to": "Prop9"
|
| 407 |
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},
|
| 408 |
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{
|
| 409 |
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"from": "BookXI",
|
| 410 |
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"to": "Prop9"
|
| 411 |
+
},
|
| 412 |
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{
|
| 413 |
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"from": "BookI",
|
| 414 |
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"to": "Prop10"
|
| 415 |
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},
|
| 416 |
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{
|
| 417 |
+
"from": "BookV",
|
| 418 |
+
"to": "Prop10"
|
| 419 |
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},
|
| 420 |
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{
|
| 421 |
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"from": "BookVI",
|
| 422 |
+
"to": "Prop10"
|
| 423 |
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},
|
| 424 |
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{
|
| 425 |
+
"from": "BookXI",
|
| 426 |
+
"to": "Prop10"
|
| 427 |
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},
|
| 428 |
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{
|
| 429 |
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"from": "BookI",
|
| 430 |
+
"to": "Prop11"
|
| 431 |
+
},
|
| 432 |
+
{
|
| 433 |
+
"from": "BookV",
|
| 434 |
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"to": "Prop11"
|
| 435 |
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},
|
| 436 |
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{
|
| 437 |
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"from": "BookVI",
|
| 438 |
+
"to": "Prop11"
|
| 439 |
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},
|
| 440 |
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{
|
| 441 |
+
"from": "BookXI",
|
| 442 |
+
"to": "Prop11"
|
| 443 |
+
},
|
| 444 |
+
{
|
| 445 |
+
"from": "BookI",
|
| 446 |
+
"to": "Prop12"
|
| 447 |
+
},
|
| 448 |
+
{
|
| 449 |
+
"from": "BookV",
|
| 450 |
+
"to": "Prop12"
|
| 451 |
+
},
|
| 452 |
+
{
|
| 453 |
+
"from": "BookVI",
|
| 454 |
+
"to": "Prop12"
|
| 455 |
+
},
|
| 456 |
+
{
|
| 457 |
+
"from": "BookXI",
|
| 458 |
+
"to": "Prop12"
|
| 459 |
+
},
|
| 460 |
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{
|
| 461 |
+
"from": "BookI",
|
| 462 |
+
"to": "Prop13"
|
| 463 |
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},
|
| 464 |
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{
|
| 465 |
+
"from": "BookV",
|
| 466 |
+
"to": "Prop13"
|
| 467 |
+
},
|
| 468 |
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{
|
| 469 |
+
"from": "BookVI",
|
| 470 |
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"to": "Prop13"
|
| 471 |
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},
|
| 472 |
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{
|
| 473 |
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"from": "BookXI",
|
| 474 |
+
"to": "Prop13"
|
| 475 |
+
},
|
| 476 |
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{
|
| 477 |
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"from": "BookI",
|
| 478 |
+
"to": "Prop14"
|
| 479 |
+
},
|
| 480 |
+
{
|
| 481 |
+
"from": "BookV",
|
| 482 |
+
"to": "Prop14"
|
| 483 |
+
},
|
| 484 |
+
{
|
| 485 |
+
"from": "BookVI",
|
| 486 |
+
"to": "Prop14"
|
| 487 |
+
},
|
| 488 |
+
{
|
| 489 |
+
"from": "BookXI",
|
| 490 |
+
"to": "Prop14"
|
| 491 |
+
},
|
| 492 |
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{
|
| 493 |
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"from": "BookI",
|
| 494 |
+
"to": "Prop15"
|
| 495 |
+
},
|
| 496 |
+
{
|
| 497 |
+
"from": "BookV",
|
| 498 |
+
"to": "Prop15"
|
| 499 |
+
},
|
| 500 |
+
{
|
| 501 |
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"from": "BookVI",
|
| 502 |
+
"to": "Prop15"
|
| 503 |
+
},
|
| 504 |
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{
|
| 505 |
+
"from": "BookXI",
|
| 506 |
+
"to": "Prop15"
|
| 507 |
+
},
|
| 508 |
+
{
|
| 509 |
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"from": "BookI",
|
| 510 |
+
"to": "Prop16"
|
| 511 |
+
},
|
| 512 |
+
{
|
| 513 |
+
"from": "BookV",
|
| 514 |
+
"to": "Prop16"
|
| 515 |
+
},
|
| 516 |
+
{
|
| 517 |
+
"from": "BookVI",
|
| 518 |
+
"to": "Prop16"
|
| 519 |
+
},
|
| 520 |
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{
|
| 521 |
+
"from": "BookXI",
|
| 522 |
+
"to": "Prop16"
|
| 523 |
+
},
|
| 524 |
+
{
|
| 525 |
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"from": "BookI",
|
| 526 |
+
"to": "Prop17"
|
| 527 |
+
},
|
| 528 |
+
{
|
| 529 |
+
"from": "BookV",
|
| 530 |
+
"to": "Prop17"
|
| 531 |
+
},
|
| 532 |
+
{
|
| 533 |
+
"from": "BookVI",
|
| 534 |
+
"to": "Prop17"
|
| 535 |
+
},
|
| 536 |
+
{
|
| 537 |
+
"from": "BookXI",
|
| 538 |
+
"to": "Prop17"
|
| 539 |
+
},
|
| 540 |
+
{
|
| 541 |
+
"from": "BookI",
|
| 542 |
+
"to": "Prop18"
|
| 543 |
+
},
|
| 544 |
+
{
|
| 545 |
+
"from": "BookV",
|
| 546 |
+
"to": "Prop18"
|
| 547 |
+
},
|
| 548 |
+
{
|
| 549 |
+
"from": "BookVI",
|
| 550 |
+
"to": "Prop18"
|
| 551 |
+
},
|
| 552 |
+
{
|
| 553 |
+
"from": "BookXI",
|
| 554 |
+
"to": "Prop18"
|
| 555 |
+
}
|
| 556 |
+
],
|
| 557 |
+
"colorScheme": {
|
| 558 |
+
"foundation": {
|
| 559 |
+
"fill": "#95a5a6",
|
| 560 |
+
"stroke": "#7f8c8d"
|
| 561 |
+
},
|
| 562 |
+
"proposition": {
|
| 563 |
+
"fill": "#1abc9c",
|
| 564 |
+
"stroke": "#16a085"
|
| 565 |
+
}
|
| 566 |
+
}
|
| 567 |
+
}
|
data/euclid-elements-book-xiii.json
ADDED
|
@@ -0,0 +1,650 @@
|
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|
| 1 |
+
{
|
| 2 |
+
"schemaVersion": "1.0",
|
| 3 |
+
"discourse": {
|
| 4 |
+
"id": "euclid-elements-book-xiii",
|
| 5 |
+
"name": "Euclid's Elements, Book XIII",
|
| 6 |
+
"subject": "regular_solids",
|
| 7 |
+
"variant": "classical",
|
| 8 |
+
"description": "Regular solids: tetrahedron, octahedron, cube, icosahedron, dodecahedron. 18 propositions. Depends on Books I, IV, VI, X, XI. Source: David E. Joyce.",
|
| 9 |
+
"structure": {
|
| 10 |
+
"books": 13,
|
| 11 |
+
"propositions": 18,
|
| 12 |
+
"foundationTypes": [
|
| 13 |
+
"foundation"
|
| 14 |
+
]
|
| 15 |
+
}
|
| 16 |
+
},
|
| 17 |
+
"metadata": {
|
| 18 |
+
"created": "2026-03-18",
|
| 19 |
+
"lastUpdated": "2026-03-18",
|
| 20 |
+
"version": "1.0.0",
|
| 21 |
+
"license": "CC BY 4.0",
|
| 22 |
+
"authors": [
|
| 23 |
+
"Welz, G."
|
| 24 |
+
],
|
| 25 |
+
"methodology": "Programming Framework",
|
| 26 |
+
"citation": "Welz, G. (2026). Euclid's Elements Book XIII Dependency Graph. Programming Framework.",
|
| 27 |
+
"keywords": [
|
| 28 |
+
"Euclid",
|
| 29 |
+
"Elements",
|
| 30 |
+
"Book XIII",
|
| 31 |
+
"regular solids",
|
| 32 |
+
"Platonic",
|
| 33 |
+
"tetrahedron",
|
| 34 |
+
"octahedron",
|
| 35 |
+
"cube",
|
| 36 |
+
"icosahedron",
|
| 37 |
+
"dodecahedron"
|
| 38 |
+
]
|
| 39 |
+
},
|
| 40 |
+
"sources": [
|
| 41 |
+
{
|
| 42 |
+
"id": "joyce",
|
| 43 |
+
"type": "digital",
|
| 44 |
+
"authors": "Joyce, David E.",
|
| 45 |
+
"title": "Euclid's Elements, Book XIII",
|
| 46 |
+
"year": "1996",
|
| 47 |
+
"url": "https://mathcs.clarku.edu/~djoyce/java/elements/bookXIII/bookXIII.html",
|
| 48 |
+
"notes": "Clark University"
|
| 49 |
+
}
|
| 50 |
+
],
|
| 51 |
+
"nodes": [
|
| 52 |
+
{
|
| 53 |
+
"id": "BookI",
|
| 54 |
+
"type": "foundation",
|
| 55 |
+
"label": "Book I — Plane geometry",
|
| 56 |
+
"shortLabel": "Book I",
|
| 57 |
+
"short": "Foundation",
|
| 58 |
+
"book": 1,
|
| 59 |
+
"colorClass": "foundation"
|
| 60 |
+
},
|
| 61 |
+
{
|
| 62 |
+
"id": "BookIV",
|
| 63 |
+
"type": "foundation",
|
| 64 |
+
"label": "Book IV — Inscribed figures",
|
| 65 |
+
"shortLabel": "Book IV",
|
| 66 |
+
"short": "Foundation",
|
| 67 |
+
"book": 4,
|
| 68 |
+
"colorClass": "foundation"
|
| 69 |
+
},
|
| 70 |
+
{
|
| 71 |
+
"id": "BookVI",
|
| 72 |
+
"type": "foundation",
|
| 73 |
+
"label": "Book VI — Similar figures",
|
| 74 |
+
"shortLabel": "Book VI",
|
| 75 |
+
"short": "Foundation",
|
| 76 |
+
"book": 6,
|
| 77 |
+
"colorClass": "foundation"
|
| 78 |
+
},
|
| 79 |
+
{
|
| 80 |
+
"id": "BookX",
|
| 81 |
+
"type": "foundation",
|
| 82 |
+
"label": "Book X — Incommensurables",
|
| 83 |
+
"shortLabel": "Book X",
|
| 84 |
+
"short": "Foundation",
|
| 85 |
+
"book": 10,
|
| 86 |
+
"colorClass": "foundation"
|
| 87 |
+
},
|
| 88 |
+
{
|
| 89 |
+
"id": "BookXI",
|
| 90 |
+
"type": "foundation",
|
| 91 |
+
"label": "Book XI — Solid geometry",
|
| 92 |
+
"shortLabel": "Book XI",
|
| 93 |
+
"short": "Foundation",
|
| 94 |
+
"book": 11,
|
| 95 |
+
"colorClass": "foundation"
|
| 96 |
+
},
|
| 97 |
+
{
|
| 98 |
+
"id": "Prop1",
|
| 99 |
+
"type": "proposition",
|
| 100 |
+
"label": "Line cut in extreme and mean ratio: square on greater plus half whole equals five times square on half",
|
| 101 |
+
"shortLabel": "Prop. XIII.1",
|
| 102 |
+
"short": "Extreme and mean: square on greater",
|
| 103 |
+
"book": 13,
|
| 104 |
+
"number": 1,
|
| 105 |
+
"colorClass": "proposition"
|
| 106 |
+
},
|
| 107 |
+
{
|
| 108 |
+
"id": "Prop2",
|
| 109 |
+
"type": "proposition",
|
| 110 |
+
"label": "If square on line five times square on segment: double segment cut in extreme and mean, greater is remainder",
|
| 111 |
+
"shortLabel": "Prop. XIII.2",
|
| 112 |
+
"short": "Square five times: extreme and mean",
|
| 113 |
+
"book": 13,
|
| 114 |
+
"number": 2,
|
| 115 |
+
"colorClass": "proposition"
|
| 116 |
+
},
|
| 117 |
+
{
|
| 118 |
+
"id": "Prop3",
|
| 119 |
+
"type": "proposition",
|
| 120 |
+
"label": "Line cut in extreme and mean: square on lesser + half greater equals five times square on half",
|
| 121 |
+
"shortLabel": "Prop. XIII.3",
|
| 122 |
+
"short": "Extreme and mean: sum of segments",
|
| 123 |
+
"book": 13,
|
| 124 |
+
"number": 3,
|
| 125 |
+
"colorClass": "proposition"
|
| 126 |
+
},
|
| 127 |
+
{
|
| 128 |
+
"id": "Prop4",
|
| 129 |
+
"type": "proposition",
|
| 130 |
+
"label": "Line cut in extreme and mean: sum of squares on whole and lesser triple square on greater",
|
| 131 |
+
"shortLabel": "Prop. XIII.4",
|
| 132 |
+
"short": "Extreme and mean: sum of squares",
|
| 133 |
+
"book": 13,
|
| 134 |
+
"number": 4,
|
| 135 |
+
"colorClass": "proposition"
|
| 136 |
+
},
|
| 137 |
+
{
|
| 138 |
+
"id": "Prop5",
|
| 139 |
+
"type": "proposition",
|
| 140 |
+
"label": "Line cut in extreme and mean, add greater: whole cut in extreme and mean, original is greater",
|
| 141 |
+
"shortLabel": "Prop. XIII.5",
|
| 142 |
+
"short": "Extreme and mean: add greater",
|
| 143 |
+
"book": 13,
|
| 144 |
+
"number": 5,
|
| 145 |
+
"colorClass": "proposition"
|
| 146 |
+
},
|
| 147 |
+
{
|
| 148 |
+
"id": "Prop6",
|
| 149 |
+
"type": "proposition",
|
| 150 |
+
"label": "Rational line cut in extreme and mean ratio: each segment is apotome",
|
| 151 |
+
"shortLabel": "Prop. XIII.6",
|
| 152 |
+
"short": "Rational cut: apotome",
|
| 153 |
+
"book": 13,
|
| 154 |
+
"number": 6,
|
| 155 |
+
"colorClass": "proposition"
|
| 156 |
+
},
|
| 157 |
+
{
|
| 158 |
+
"id": "Prop7",
|
| 159 |
+
"type": "proposition",
|
| 160 |
+
"label": "Equilateral pentagon: if three angles equal (order or not), pentagon equiangular",
|
| 161 |
+
"shortLabel": "Prop. XIII.7",
|
| 162 |
+
"short": "Equilateral pentagon: three angles",
|
| 163 |
+
"book": 13,
|
| 164 |
+
"number": 7,
|
| 165 |
+
"colorClass": "proposition"
|
| 166 |
+
},
|
| 167 |
+
{
|
| 168 |
+
"id": "Prop8",
|
| 169 |
+
"type": "proposition",
|
| 170 |
+
"label": "Equilateral equiangular pentagon: diagonals subtending two angles cut in extreme and mean ratio",
|
| 171 |
+
"shortLabel": "Prop. XIII.8",
|
| 172 |
+
"short": "Pentagon: diagonals in extreme and mean",
|
| 173 |
+
"book": 13,
|
| 174 |
+
"number": 8,
|
| 175 |
+
"colorClass": "proposition"
|
| 176 |
+
},
|
| 177 |
+
{
|
| 178 |
+
"id": "Prop9",
|
| 179 |
+
"type": "proposition",
|
| 180 |
+
"label": "Side of hexagon + decagon in same circle: cut in extreme and mean, greater is hexagon",
|
| 181 |
+
"shortLabel": "Prop. XIII.9",
|
| 182 |
+
"short": "Hexagon + decagon: extreme and mean",
|
| 183 |
+
"book": 13,
|
| 184 |
+
"number": 9,
|
| 185 |
+
"colorClass": "proposition"
|
| 186 |
+
},
|
| 187 |
+
{
|
| 188 |
+
"id": "Prop10",
|
| 189 |
+
"type": "proposition",
|
| 190 |
+
"label": "Equilateral pentagon in circle: square on side equals sum of squares on hexagon and decagon",
|
| 191 |
+
"shortLabel": "Prop. XIII.10",
|
| 192 |
+
"short": "Pentagon: square equals hexagon + decagon",
|
| 193 |
+
"book": 13,
|
| 194 |
+
"number": 10,
|
| 195 |
+
"colorClass": "proposition"
|
| 196 |
+
},
|
| 197 |
+
{
|
| 198 |
+
"id": "Prop11",
|
| 199 |
+
"type": "proposition",
|
| 200 |
+
"label": "Equilateral pentagon in circle with rational diameter: side is minor",
|
| 201 |
+
"shortLabel": "Prop. XIII.11",
|
| 202 |
+
"short": "Pentagon in rational circle: minor",
|
| 203 |
+
"book": 13,
|
| 204 |
+
"number": 11,
|
| 205 |
+
"colorClass": "proposition"
|
| 206 |
+
},
|
| 207 |
+
{
|
| 208 |
+
"id": "Prop12",
|
| 209 |
+
"type": "proposition",
|
| 210 |
+
"label": "Equilateral triangle in circle: square on side triple square on radius",
|
| 211 |
+
"shortLabel": "Prop. XIII.12",
|
| 212 |
+
"short": "Equilateral triangle: side triple radius",
|
| 213 |
+
"book": 13,
|
| 214 |
+
"number": 12,
|
| 215 |
+
"colorClass": "proposition"
|
| 216 |
+
},
|
| 217 |
+
{
|
| 218 |
+
"id": "Prop13",
|
| 219 |
+
"type": "proposition",
|
| 220 |
+
"label": "To construct pyramid (tetrahedron) in given sphere; diameter squared 1.5 times side squared",
|
| 221 |
+
"shortLabel": "Prop. XIII.13",
|
| 222 |
+
"short": "Construct tetrahedron in sphere",
|
| 223 |
+
"book": 13,
|
| 224 |
+
"number": 13,
|
| 225 |
+
"colorClass": "proposition"
|
| 226 |
+
},
|
| 227 |
+
{
|
| 228 |
+
"id": "Prop14",
|
| 229 |
+
"type": "proposition",
|
| 230 |
+
"label": "To construct octahedron in sphere; diameter squared double side squared",
|
| 231 |
+
"shortLabel": "Prop. XIII.14",
|
| 232 |
+
"short": "Construct octahedron in sphere",
|
| 233 |
+
"book": 13,
|
| 234 |
+
"number": 14,
|
| 235 |
+
"colorClass": "proposition"
|
| 236 |
+
},
|
| 237 |
+
{
|
| 238 |
+
"id": "Prop15",
|
| 239 |
+
"type": "proposition",
|
| 240 |
+
"label": "To construct cube in sphere; diameter squared triple side squared",
|
| 241 |
+
"shortLabel": "Prop. XIII.15",
|
| 242 |
+
"short": "Construct cube in sphere",
|
| 243 |
+
"book": 13,
|
| 244 |
+
"number": 15,
|
| 245 |
+
"colorClass": "proposition"
|
| 246 |
+
},
|
| 247 |
+
{
|
| 248 |
+
"id": "Prop16",
|
| 249 |
+
"type": "proposition",
|
| 250 |
+
"label": "To construct icosahedron in sphere; side is minor",
|
| 251 |
+
"shortLabel": "Prop. XIII.16",
|
| 252 |
+
"short": "Construct icosahedron in sphere",
|
| 253 |
+
"book": 13,
|
| 254 |
+
"number": 16,
|
| 255 |
+
"colorClass": "proposition"
|
| 256 |
+
},
|
| 257 |
+
{
|
| 258 |
+
"id": "Prop17",
|
| 259 |
+
"type": "proposition",
|
| 260 |
+
"label": "To construct dodecahedron in sphere; side is apotome",
|
| 261 |
+
"shortLabel": "Prop. XIII.17",
|
| 262 |
+
"short": "Construct dodecahedron in sphere",
|
| 263 |
+
"book": 13,
|
| 264 |
+
"number": 17,
|
| 265 |
+
"colorClass": "proposition"
|
| 266 |
+
},
|
| 267 |
+
{
|
| 268 |
+
"id": "Prop18",
|
| 269 |
+
"type": "proposition",
|
| 270 |
+
"label": "To set out sides of five figures and compare them; no other such figure exists",
|
| 271 |
+
"shortLabel": "Prop. XIII.18",
|
| 272 |
+
"short": "Compare five regular solids",
|
| 273 |
+
"book": 13,
|
| 274 |
+
"number": 18,
|
| 275 |
+
"colorClass": "proposition"
|
| 276 |
+
}
|
| 277 |
+
],
|
| 278 |
+
"edges": [
|
| 279 |
+
{
|
| 280 |
+
"from": "BookI",
|
| 281 |
+
"to": "Prop1"
|
| 282 |
+
},
|
| 283 |
+
{
|
| 284 |
+
"from": "BookIV",
|
| 285 |
+
"to": "Prop1"
|
| 286 |
+
},
|
| 287 |
+
{
|
| 288 |
+
"from": "BookVI",
|
| 289 |
+
"to": "Prop1"
|
| 290 |
+
},
|
| 291 |
+
{
|
| 292 |
+
"from": "BookX",
|
| 293 |
+
"to": "Prop1"
|
| 294 |
+
},
|
| 295 |
+
{
|
| 296 |
+
"from": "BookXI",
|
| 297 |
+
"to": "Prop1"
|
| 298 |
+
},
|
| 299 |
+
{
|
| 300 |
+
"from": "BookI",
|
| 301 |
+
"to": "Prop2"
|
| 302 |
+
},
|
| 303 |
+
{
|
| 304 |
+
"from": "BookIV",
|
| 305 |
+
"to": "Prop2"
|
| 306 |
+
},
|
| 307 |
+
{
|
| 308 |
+
"from": "BookVI",
|
| 309 |
+
"to": "Prop2"
|
| 310 |
+
},
|
| 311 |
+
{
|
| 312 |
+
"from": "BookX",
|
| 313 |
+
"to": "Prop2"
|
| 314 |
+
},
|
| 315 |
+
{
|
| 316 |
+
"from": "BookXI",
|
| 317 |
+
"to": "Prop2"
|
| 318 |
+
},
|
| 319 |
+
{
|
| 320 |
+
"from": "BookI",
|
| 321 |
+
"to": "Prop3"
|
| 322 |
+
},
|
| 323 |
+
{
|
| 324 |
+
"from": "BookIV",
|
| 325 |
+
"to": "Prop3"
|
| 326 |
+
},
|
| 327 |
+
{
|
| 328 |
+
"from": "BookVI",
|
| 329 |
+
"to": "Prop3"
|
| 330 |
+
},
|
| 331 |
+
{
|
| 332 |
+
"from": "BookX",
|
| 333 |
+
"to": "Prop3"
|
| 334 |
+
},
|
| 335 |
+
{
|
| 336 |
+
"from": "BookXI",
|
| 337 |
+
"to": "Prop3"
|
| 338 |
+
},
|
| 339 |
+
{
|
| 340 |
+
"from": "BookI",
|
| 341 |
+
"to": "Prop4"
|
| 342 |
+
},
|
| 343 |
+
{
|
| 344 |
+
"from": "BookIV",
|
| 345 |
+
"to": "Prop4"
|
| 346 |
+
},
|
| 347 |
+
{
|
| 348 |
+
"from": "BookVI",
|
| 349 |
+
"to": "Prop4"
|
| 350 |
+
},
|
| 351 |
+
{
|
| 352 |
+
"from": "BookX",
|
| 353 |
+
"to": "Prop4"
|
| 354 |
+
},
|
| 355 |
+
{
|
| 356 |
+
"from": "BookXI",
|
| 357 |
+
"to": "Prop4"
|
| 358 |
+
},
|
| 359 |
+
{
|
| 360 |
+
"from": "BookI",
|
| 361 |
+
"to": "Prop5"
|
| 362 |
+
},
|
| 363 |
+
{
|
| 364 |
+
"from": "BookIV",
|
| 365 |
+
"to": "Prop5"
|
| 366 |
+
},
|
| 367 |
+
{
|
| 368 |
+
"from": "BookVI",
|
| 369 |
+
"to": "Prop5"
|
| 370 |
+
},
|
| 371 |
+
{
|
| 372 |
+
"from": "BookX",
|
| 373 |
+
"to": "Prop5"
|
| 374 |
+
},
|
| 375 |
+
{
|
| 376 |
+
"from": "BookXI",
|
| 377 |
+
"to": "Prop5"
|
| 378 |
+
},
|
| 379 |
+
{
|
| 380 |
+
"from": "BookI",
|
| 381 |
+
"to": "Prop6"
|
| 382 |
+
},
|
| 383 |
+
{
|
| 384 |
+
"from": "BookIV",
|
| 385 |
+
"to": "Prop6"
|
| 386 |
+
},
|
| 387 |
+
{
|
| 388 |
+
"from": "BookVI",
|
| 389 |
+
"to": "Prop6"
|
| 390 |
+
},
|
| 391 |
+
{
|
| 392 |
+
"from": "BookX",
|
| 393 |
+
"to": "Prop6"
|
| 394 |
+
},
|
| 395 |
+
{
|
| 396 |
+
"from": "BookXI",
|
| 397 |
+
"to": "Prop6"
|
| 398 |
+
},
|
| 399 |
+
{
|
| 400 |
+
"from": "BookI",
|
| 401 |
+
"to": "Prop7"
|
| 402 |
+
},
|
| 403 |
+
{
|
| 404 |
+
"from": "BookIV",
|
| 405 |
+
"to": "Prop7"
|
| 406 |
+
},
|
| 407 |
+
{
|
| 408 |
+
"from": "BookVI",
|
| 409 |
+
"to": "Prop7"
|
| 410 |
+
},
|
| 411 |
+
{
|
| 412 |
+
"from": "BookX",
|
| 413 |
+
"to": "Prop7"
|
| 414 |
+
},
|
| 415 |
+
{
|
| 416 |
+
"from": "BookXI",
|
| 417 |
+
"to": "Prop7"
|
| 418 |
+
},
|
| 419 |
+
{
|
| 420 |
+
"from": "BookI",
|
| 421 |
+
"to": "Prop8"
|
| 422 |
+
},
|
| 423 |
+
{
|
| 424 |
+
"from": "BookIV",
|
| 425 |
+
"to": "Prop8"
|
| 426 |
+
},
|
| 427 |
+
{
|
| 428 |
+
"from": "BookVI",
|
| 429 |
+
"to": "Prop8"
|
| 430 |
+
},
|
| 431 |
+
{
|
| 432 |
+
"from": "BookX",
|
| 433 |
+
"to": "Prop8"
|
| 434 |
+
},
|
| 435 |
+
{
|
| 436 |
+
"from": "BookXI",
|
| 437 |
+
"to": "Prop8"
|
| 438 |
+
},
|
| 439 |
+
{
|
| 440 |
+
"from": "BookI",
|
| 441 |
+
"to": "Prop9"
|
| 442 |
+
},
|
| 443 |
+
{
|
| 444 |
+
"from": "BookIV",
|
| 445 |
+
"to": "Prop9"
|
| 446 |
+
},
|
| 447 |
+
{
|
| 448 |
+
"from": "BookVI",
|
| 449 |
+
"to": "Prop9"
|
| 450 |
+
},
|
| 451 |
+
{
|
| 452 |
+
"from": "BookX",
|
| 453 |
+
"to": "Prop9"
|
| 454 |
+
},
|
| 455 |
+
{
|
| 456 |
+
"from": "BookXI",
|
| 457 |
+
"to": "Prop9"
|
| 458 |
+
},
|
| 459 |
+
{
|
| 460 |
+
"from": "BookI",
|
| 461 |
+
"to": "Prop10"
|
| 462 |
+
},
|
| 463 |
+
{
|
| 464 |
+
"from": "BookIV",
|
| 465 |
+
"to": "Prop10"
|
| 466 |
+
},
|
| 467 |
+
{
|
| 468 |
+
"from": "BookVI",
|
| 469 |
+
"to": "Prop10"
|
| 470 |
+
},
|
| 471 |
+
{
|
| 472 |
+
"from": "BookX",
|
| 473 |
+
"to": "Prop10"
|
| 474 |
+
},
|
| 475 |
+
{
|
| 476 |
+
"from": "BookXI",
|
| 477 |
+
"to": "Prop10"
|
| 478 |
+
},
|
| 479 |
+
{
|
| 480 |
+
"from": "BookI",
|
| 481 |
+
"to": "Prop11"
|
| 482 |
+
},
|
| 483 |
+
{
|
| 484 |
+
"from": "BookIV",
|
| 485 |
+
"to": "Prop11"
|
| 486 |
+
},
|
| 487 |
+
{
|
| 488 |
+
"from": "BookVI",
|
| 489 |
+
"to": "Prop11"
|
| 490 |
+
},
|
| 491 |
+
{
|
| 492 |
+
"from": "BookX",
|
| 493 |
+
"to": "Prop11"
|
| 494 |
+
},
|
| 495 |
+
{
|
| 496 |
+
"from": "BookXI",
|
| 497 |
+
"to": "Prop11"
|
| 498 |
+
},
|
| 499 |
+
{
|
| 500 |
+
"from": "BookI",
|
| 501 |
+
"to": "Prop12"
|
| 502 |
+
},
|
| 503 |
+
{
|
| 504 |
+
"from": "BookIV",
|
| 505 |
+
"to": "Prop12"
|
| 506 |
+
},
|
| 507 |
+
{
|
| 508 |
+
"from": "BookVI",
|
| 509 |
+
"to": "Prop12"
|
| 510 |
+
},
|
| 511 |
+
{
|
| 512 |
+
"from": "BookX",
|
| 513 |
+
"to": "Prop12"
|
| 514 |
+
},
|
| 515 |
+
{
|
| 516 |
+
"from": "BookXI",
|
| 517 |
+
"to": "Prop12"
|
| 518 |
+
},
|
| 519 |
+
{
|
| 520 |
+
"from": "BookI",
|
| 521 |
+
"to": "Prop13"
|
| 522 |
+
},
|
| 523 |
+
{
|
| 524 |
+
"from": "BookIV",
|
| 525 |
+
"to": "Prop13"
|
| 526 |
+
},
|
| 527 |
+
{
|
| 528 |
+
"from": "BookVI",
|
| 529 |
+
"to": "Prop13"
|
| 530 |
+
},
|
| 531 |
+
{
|
| 532 |
+
"from": "BookX",
|
| 533 |
+
"to": "Prop13"
|
| 534 |
+
},
|
| 535 |
+
{
|
| 536 |
+
"from": "BookXI",
|
| 537 |
+
"to": "Prop13"
|
| 538 |
+
},
|
| 539 |
+
{
|
| 540 |
+
"from": "BookI",
|
| 541 |
+
"to": "Prop14"
|
| 542 |
+
},
|
| 543 |
+
{
|
| 544 |
+
"from": "BookIV",
|
| 545 |
+
"to": "Prop14"
|
| 546 |
+
},
|
| 547 |
+
{
|
| 548 |
+
"from": "BookVI",
|
| 549 |
+
"to": "Prop14"
|
| 550 |
+
},
|
| 551 |
+
{
|
| 552 |
+
"from": "BookX",
|
| 553 |
+
"to": "Prop14"
|
| 554 |
+
},
|
| 555 |
+
{
|
| 556 |
+
"from": "BookXI",
|
| 557 |
+
"to": "Prop14"
|
| 558 |
+
},
|
| 559 |
+
{
|
| 560 |
+
"from": "BookI",
|
| 561 |
+
"to": "Prop15"
|
| 562 |
+
},
|
| 563 |
+
{
|
| 564 |
+
"from": "BookIV",
|
| 565 |
+
"to": "Prop15"
|
| 566 |
+
},
|
| 567 |
+
{
|
| 568 |
+
"from": "BookVI",
|
| 569 |
+
"to": "Prop15"
|
| 570 |
+
},
|
| 571 |
+
{
|
| 572 |
+
"from": "BookX",
|
| 573 |
+
"to": "Prop15"
|
| 574 |
+
},
|
| 575 |
+
{
|
| 576 |
+
"from": "BookXI",
|
| 577 |
+
"to": "Prop15"
|
| 578 |
+
},
|
| 579 |
+
{
|
| 580 |
+
"from": "BookI",
|
| 581 |
+
"to": "Prop16"
|
| 582 |
+
},
|
| 583 |
+
{
|
| 584 |
+
"from": "BookIV",
|
| 585 |
+
"to": "Prop16"
|
| 586 |
+
},
|
| 587 |
+
{
|
| 588 |
+
"from": "BookVI",
|
| 589 |
+
"to": "Prop16"
|
| 590 |
+
},
|
| 591 |
+
{
|
| 592 |
+
"from": "BookX",
|
| 593 |
+
"to": "Prop16"
|
| 594 |
+
},
|
| 595 |
+
{
|
| 596 |
+
"from": "BookXI",
|
| 597 |
+
"to": "Prop16"
|
| 598 |
+
},
|
| 599 |
+
{
|
| 600 |
+
"from": "BookI",
|
| 601 |
+
"to": "Prop17"
|
| 602 |
+
},
|
| 603 |
+
{
|
| 604 |
+
"from": "BookIV",
|
| 605 |
+
"to": "Prop17"
|
| 606 |
+
},
|
| 607 |
+
{
|
| 608 |
+
"from": "BookVI",
|
| 609 |
+
"to": "Prop17"
|
| 610 |
+
},
|
| 611 |
+
{
|
| 612 |
+
"from": "BookX",
|
| 613 |
+
"to": "Prop17"
|
| 614 |
+
},
|
| 615 |
+
{
|
| 616 |
+
"from": "BookXI",
|
| 617 |
+
"to": "Prop17"
|
| 618 |
+
},
|
| 619 |
+
{
|
| 620 |
+
"from": "BookI",
|
| 621 |
+
"to": "Prop18"
|
| 622 |
+
},
|
| 623 |
+
{
|
| 624 |
+
"from": "BookIV",
|
| 625 |
+
"to": "Prop18"
|
| 626 |
+
},
|
| 627 |
+
{
|
| 628 |
+
"from": "BookVI",
|
| 629 |
+
"to": "Prop18"
|
| 630 |
+
},
|
| 631 |
+
{
|
| 632 |
+
"from": "BookX",
|
| 633 |
+
"to": "Prop18"
|
| 634 |
+
},
|
| 635 |
+
{
|
| 636 |
+
"from": "BookXI",
|
| 637 |
+
"to": "Prop18"
|
| 638 |
+
}
|
| 639 |
+
],
|
| 640 |
+
"colorScheme": {
|
| 641 |
+
"foundation": {
|
| 642 |
+
"fill": "#95a5a6",
|
| 643 |
+
"stroke": "#7f8c8d"
|
| 644 |
+
},
|
| 645 |
+
"proposition": {
|
| 646 |
+
"fill": "#1abc9c",
|
| 647 |
+
"stroke": "#16a085"
|
| 648 |
+
}
|
| 649 |
+
}
|
| 650 |
+
}
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data/peano-arithmetic-addition-multiplication.mmd
ADDED
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@@ -0,0 +1,65 @@
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| 1 |
+
graph TD
|
| 2 |
+
A5["A5\nInduction"]
|
| 3 |
+
DefAdd["DefAdd\nDefinition of +"]
|
| 4 |
+
T5["T5\nAssociativity of +"]
|
| 5 |
+
T6["T6\nLeft identity"]
|
| 6 |
+
T7["T7\nSuccessor and add"]
|
| 7 |
+
T8["T8\nCommutativity of +"]
|
| 8 |
+
T9["T9\nCancellation for +"]
|
| 9 |
+
DefMul["DefMul\nDefinition of ·"]
|
| 10 |
+
T10["T10\nMul well-defined"]
|
| 11 |
+
T11["T11\nZero times"]
|
| 12 |
+
T12["T12\nZero from left"]
|
| 13 |
+
T13["T13\nSuccessor and mul"]
|
| 14 |
+
T14["T14\nCommutativity of ·"]
|
| 15 |
+
T15["T15\nAssociativity of ·"]
|
| 16 |
+
T16["T16\nDistributivity"]
|
| 17 |
+
T17["T17\nDistributivity (right)"]
|
| 18 |
+
A5 --> DefAdd
|
| 19 |
+
DefAdd --> T5
|
| 20 |
+
A5 --> T5
|
| 21 |
+
DefAdd --> T6
|
| 22 |
+
A5 --> T6
|
| 23 |
+
DefAdd --> T7
|
| 24 |
+
T6 --> T7
|
| 25 |
+
A5 --> T7
|
| 26 |
+
DefAdd --> T8
|
| 27 |
+
T5 --> T8
|
| 28 |
+
T6 --> T8
|
| 29 |
+
T7 --> T8
|
| 30 |
+
A5 --> T8
|
| 31 |
+
DefAdd --> T9
|
| 32 |
+
T8 --> T9
|
| 33 |
+
A5 --> T9
|
| 34 |
+
DefAdd --> DefMul
|
| 35 |
+
A5 --> DefMul
|
| 36 |
+
DefMul --> T10
|
| 37 |
+
A5 --> T10
|
| 38 |
+
DefMul --> T11
|
| 39 |
+
DefMul --> T12
|
| 40 |
+
T6 --> T12
|
| 41 |
+
A5 --> T12
|
| 42 |
+
DefMul --> T13
|
| 43 |
+
T8 --> T13
|
| 44 |
+
A5 --> T13
|
| 45 |
+
DefMul --> T14
|
| 46 |
+
T12 --> T14
|
| 47 |
+
T13 --> T14
|
| 48 |
+
A5 --> T14
|
| 49 |
+
DefMul --> T15
|
| 50 |
+
T5 --> T15
|
| 51 |
+
T8 --> T15
|
| 52 |
+
A5 --> T15
|
| 53 |
+
DefMul --> T16
|
| 54 |
+
T5 --> T16
|
| 55 |
+
T8 --> T16
|
| 56 |
+
T15 --> T16
|
| 57 |
+
A5 --> T16
|
| 58 |
+
T16 --> T17
|
| 59 |
+
T8 --> T17
|
| 60 |
+
classDef axiom fill:#e74c3c,color:#fff,stroke:#c0392b
|
| 61 |
+
classDef definition fill:#3498db,color:#fff,stroke:#2980b9
|
| 62 |
+
classDef theorem fill:#1abc9c,color:#fff,stroke:#16a085
|
| 63 |
+
class A5 axiom
|
| 64 |
+
class DefAdd,DefMul definition
|
| 65 |
+
class T5,T6,T7,T8,T9,T10,T11,T12,T13,T14,T15,T16,T17 theorem
|