OpenLLM-France/wikimedia huggingface dataset:
# Illustrated Companion to the Latin Dictionary/Gradus

This article incorporates text from a publication now in the public domain: Rich, Anthony (1849). The illustrated companion to the Latin dictionary, and Greek lexicon. p. vi. OCLC 894670115. https://archive.org/details/illustratedcompa00rich.
GRADUS. A set of bed-steps, consisting of several stairs (Varro, L. L. v. 168.), which were requisite when the bedstead was of such a height from the ground that it could not be reached by a simple scamnum. The illustration (Gradus/1.1) represents Dido's marriage bed in the Vatican Virgil, with a set of these steps at its foot.
2. A flight of steps leading up to the porch (pronaos) of a temple. (Cic. Att. iv. 1. Virg. Aen. i. 448.) In Greek temples it usually consisted of only three steps; but the Roman architects added a dozen or more, and sometimes divided them into two flights, as in the annexed example (Gradus/2.1) from the ruins of a small temple in the Forum at Pompeii. In all cases, however, the steps were of an uneven number, in order that the person ascending, who naturally commenced with his right foot, might place the same one on the topmost step by which he entered the porch (Vitruv. iii. 4. 4.); the superstition of the people leading them to think a contrary course ill-omened.
3. The seats upon which the spectators sat in a theatre, amphitheatre, or circus. (Inscript. ap. Marini. Frat. Arv. pp. 130. 23. Compare TESSERA THEATRALIS.) These were deep steps rising over one another in tiers, as shown by the annexed view (Gradus/3.1) from the larger theatre at Pompeii, in which the seats (gradus) are the larger steps; the smaller ones, running directly from the doors of entrance, being only staircases (scalae), by which the spectator descended until he arrived at the particular gradus, on which the place belonging to him was situated.
4. The parallel ridges, like steps, on the inside of a dice-box (fritillus), for the purpose of mixing the dice when shaken, and giving them a disposition to rotate when cast from it (Auson. Profess. i. 28.); as shown by the section in the annexed engraving (Gradus/4.1), from an original discovered at Rome.
5. The lines or wrinkles on the roof of a horse's mouth, which resemble those in a dice-box. Veg. Vet. i. 22. 11. Ib. 2. 4.
6. A studied and feminine arrangement of the hair, when artificially disposed in parallel waves or gradations rising one over the other, like steps (Quint. xii. 10. 47.), the same as now termed "crimping." Nero is said to have had his head always dressed in this manner (Suet. Nero, 51); and a statue representing that emperor in the character of Apollo Citharoedus (Mus. Pio-Clem. iii. 4.) has the hair parted in the centre, and regularly crimped on both sides, like a girl's.
* Gradus/1.1
* Gradus/2.1
* Gradus/3.1
* Gradus/4.1
# Illustrated Companion to the Latin Dictionary/Graecostadium

This article incorporates text from a publication now in the public domain: Rich, Anthony (1849). The illustrated companion to the Latin dictionary, and Greek lexicon. p. vi. OCLC 894670115. https://archive.org/details/illustratedcompa00rich.
GRAECOSTAD'IUM. Capitol. Antonin. 8. Same as GRAECOSTASIS.
# Illustrated Companion to the Latin Dictionary/Graecostasis

This article incorporates text from a publication now in the public domain: Rich, Anthony (1849). The illustrated companion to the Latin dictionary, and Greek lexicon. p. vi. OCLC 894670115. https://archive.org/details/illustratedcompa00rich.
GRAECOS'TASIS. The foreign embassy; a building in the Roman Forum, near the Comitium, in which ambassadors from foreign states were lodged at the public expense during their mission. (Varro, L. L. v. 155. Cic. Q. Fr. ii. 1.) Three magnificent Corinthian columns, with a portion of their entablature, still standing under the north-east corner of the Palatine hill, are supposed by some antiquaries to be the remains of the edifice; but the style of the architecture, which presents one of the most perfect models now remaining in Rome, is certainly antecedent to the reign of Antoninus, to which period any ruins of the Graecostasis, if they now remained, must belong, as it was rebuilt by that emperor, after having been totally destroyed by fire. Capitol. Antonin. 8.
# Illustrated Companion to the Latin Dictionary/Grallae

This article incorporates text from a publication now in the public domain: Rich, Anthony (1849). The illustrated companion to the Latin dictionary, and Greek lexicon. p. vi. OCLC 894670115. https://archive.org/details/illustratedcompa00rich.
GRALLAE. A pair of stilts made, as they still are, with a fork to embrace the foot; and originally invented for the actors who personated Pan or the satyrs on the stage, in order that they might appear with the thin and slender legs ascribed to these goat-footed deities. Festus. s. Grallatores. Varro ap. Non. p. 115. and CAPRIPES.
# Illustrated Companion to the Latin Dictionary/Grallator

This article incorporates text from a publication now in the public domain: Rich, Anthony (1849). The illustrated companion to the Latin dictionary, and Greek lexicon. p. vi. OCLC 894670115. https://archive.org/details/illustratedcompa00rich.
GRALLA'TOR (καλοβάμων, καλοβάτης). One who walks upon stilts. Plaut. Poen. iii. 1. 27. Varro, ap. Non. p. 115, and GRALLAE.
# Illustrated Companion to the Latin Dictionary/Granarium

This article incorporates text from a publication now in the public domain: Rich, Anthony (1849). The illustrated companion to the Latin dictionary, and Greek lexicon. p. vi. OCLC 894670115. https://archive.org/details/illustratedcompa00rich.
GRANA'RIUM. Often used in a general sense as synonymous with horreum, a granary or magazine for storing corn (Varro, R. R. i. 57. Hor. Sat. i. 1. 53.); but more accurately distinguished by Palladius (i. 19. 2.), as a cell or bin in the general dépôt, which contained a great number of these, each destined for the reception of a different kind of grain.
# Illustrated Companion to the Latin Dictionary/Graphiarium

This article incorporates text from a publication now in the public domain: Rich, Anthony (1849). The illustrated companion to the Latin dictionary, and Greek lexicon. p. vi. OCLC 894670115. https://archive.org/details/illustratedcompa00rich.
GRAPHIA'RIUM or Graphiaria Theca. A sheath or case for holding the sharp-pointed graver (graphium), employed for writing on tablets covered with wax. Mart. xiv. 21. Suet. Claud. 35.
# Illustrated Companion to the Latin Dictionary/Graphium

This article incorporates text from a publication now in the public domain: Rich, Anthony (1849). The illustrated companion to the Latin dictionary, and Greek lexicon. p. vi. OCLC 894670115. https://archive.org/details/illustratedcompa00rich.
GRAPH'IUM (γραφίον). A sharp-pointed instrument, or sort of graver made of iron or bronze, employed for writing on wooden tablets covered with wax. (Isidor. Orig. vi. 9. Ov. Am. i. 11. 23.) The example (Graphium/1.1) represents an original between eight and nine inches long, found in an excavation at Rome, which is made to open, and shut (top figure), and affords ample testimony to the truth of the anecdotes which speak of persons being wounded, even mortally, with this instrument. Suet. Caes. 82. Id. Cal. 28. Senec. Clem. i. 14.
# Illustrated Companion to the Latin Dictionary/Gregarius

This article incorporates text from a publication now in the public domain: Rich, Anthony (1849). The illustrated companion to the Latin dictionary, and Greek lexicon. p. vi. OCLC 894670115. https://archive.org/details/illustratedcompa00rich.
GREGA'RIUS sc. miles. An orderly or common foot-soldier of the rank and file. (Cic. Planc. 30. Tac. Hist. v. 1.) Their accoutrements, of course, varied according to the class of troops to which they belonged, and whether Romans, allies, or auxiliaries.
2. Gregarius eques. A cavalry trooper below the rank of an officer. Tac. Hist. iii. 51.
# Illustrated Companion to the Latin Dictionary/Gremium

This article incorporates text from a publication now in the public domain: Rich, Anthony (1849). The illustrated companion to the Latin dictionary, and Greek lexicon. p. vi. OCLC 894670115. https://archive.org/details/illustratedcompa00rich.
GREM'IUM. A lap; that is, the seat or cavity formed by the belly and thighs of a person in sitting posture; upon which, for instance, nurses and mothers place their children (Cic. Div. ii. 41. Virg. Aen. i. 689. Pedo Albin. i. 116.); thence applied in a more special sense to the lap or hollow made by raising up the lower part of a tunic or mantle, as women do their aprons, in order to form a receptacle for holding anything. (Pet. Sat. 60. 4.) Thus, in strictness it differs from sinus, which was formed over the chest, whereas the gremium fell lower down and over the belly, as in the annexed illustration (Gremium/1.1) from a terra-cotta lamp; but this distinction is not always preserved.
# Illustrated Companion to the Latin Dictionary/Griphus

This article incorporates text from a publication now in the public domain: Rich, Anthony (1849). The illustrated companion to the Latin dictionary, and Greek lexicon. p. vi. OCLC 894670115. https://archive.org/details/illustratedcompa00rich.
GRI'PHUS (γρῖφος and γρῖπος). Properly a Greek word, denoting one of the various kinds of fishing-nets employed in Greece (Oppian. Hal. iii. 81.); but of what precise nature is not ascertained. The Romans used the same term to designate an engine of war (Not. Tires. p. 126.), the characteristic properties of which are equally unknown. From some analogy with these objects the same word was used in a metaphorical sense to signify any thing doubtful or obscure, such as a riddle or enigma. Aristoph. Vesp. 20. Aul. Gell. i. 2. 2.
# Illustrated Companion to the Latin Dictionary/Aspergillum

This article incorporates text from a publication now in the public domain: Rich, Anthony (1849). The illustrated companion to the Latin dictionary, and Greek lexicon. p. vi. OCLC 894670115. https://archive.org/details/illustratedcompa00rich.
ASPERGIL'LUM (περιῤῥαντήριον). See the next word.
# Illustrated Companion to the Latin Dictionary/Aspersio

This article incorporates text from a publication now in the public domain: Rich, Anthony (1849). The illustrated companion to the Latin dictionary, and Greek lexicon. p. vi. OCLC 894670115. https://archive.org/details/illustratedcompa00rich.
ASPER'SIO. The act of sprinkling with water, as a purification, before making sacrifice to the gods below (Cic. Leg. ii. 10. Compare Ov. Fast. v. 67. Virg. Aen. iv. 635.); whereas the whole body, or the hands and face, were immersed previous to a sacrifice offered to the gods above. (Broüer, de Adorat. cap. 12.) This ceremeony was performed either with a branch of laurel; as in the example (Aspersio/1.1) from a medal, which represents Lucilla, the daughter of M. Aurelius, breaking off a branch to sprinkle the young children, whilst a priestess is drawing water from the river; or with a whisk made expressly for the purpose, as in the annexed engraving (Aspersio/1.2), also from a medal, and which the Greeks termed περιῤῥαντήριον or ῥάντιστρον. The corresponding Latin term is unknown; for the word aspergillum, employed by modern philologists, is not supported by any ancient authority.
* Aspersio/1.1
* Aspersio/1.2
# Illustrated Companion to the Latin Dictionary/Cataracta

This article incorporates text from a publication now in the public domain: Rich, Anthony (1849). The illustrated companion to the Latin dictionary, and Greek lexicon. p. vi. OCLC 894670115. https://archive.org/details/illustratedcompa00rich.
CATARAC'TA or CATARAC'TES (καταῤῥάκτης). A cataract, cascade, or sudden fall of water from a higher to a lower level, like the falls of Tivoli or Terni. Plin. H. N. v. 10. Vitruv. viii. 2. 6.
2. A sluice, flood-gate, or lock in a river, either for the purpose of moderating the rapidity of the current (Plin. Ep. x. 69.), or for shutting in the water, so as to preserve a good depth in the stream. (Rutil. i. 481.) The illustration (Cataracta/2.1) is copied from one of the bas-reliefs on the arch of Septimius Severus. It will be observed, that the Roman artist, in accordance with the practice of his school, has omitted to insert the flood-gate, contenting himself with carving the uprights by which it was kept in its place, and made to slide up and down.
3. A portcullis, suspended over the entrance of a city or fortified place, so that it could be let down or drawn up by iron rings and chains at pleasure. (Liv. xxvii. 28. Veget. Mil. iv. 4.) In one of the ancient gate-ways still remaining at Rome, another at Tivoli, and also at Pompeii, the grooves in which the portcullis worked are plainly aparent; and the example here introduced (Cataracta/3.1), from an ancient fresco painting, where it defends the entrance to a bridge, exhibits the chains and ring by which it was worked, precisely as mentioned by Vegetius. The grating which closed the entrance does not appear in the original, which may be the effect of age; or, perhaps, it was not a regular portcullis, but only a movable bar raised and lowered at certain hours to close the passage against travellers or cattle; but in either case, it is sufficient to exhibit the character of such contrivances amongst the ancients.
* Cataracta/2.1
* Cataracta/3.1
# Illustrated Companion to the Latin Dictionary/Craticula

This article incorporates text from a publication now in the public domain: Rich, Anthony (1849). The illustrated companion to the Latin dictionary, and Greek lexicon. p. vi. OCLC 894670115. https://archive.org/details/illustratedcompa00rich.
CRATI'CULA (ταῤῥίον). Diminutive of CRATES; whence, in a more special sense, a gridiron (Cato, R. R. 13. 2. Mart. Ep. xiv. 221.) The example (Craticula/1.1) is taken from an original of bronze found in a tomb at Paestum, but without the handle, which is restored in the engraving, from a similar specimen painted in a sepulchre of the Christian era on the Via Tiburtina.
# Illustrated Companion to the Latin Dictionary/Gerrae

This article incorporates text from a publication now in the public domain: Rich, Anthony (1849). The illustrated companion to the Latin dictionary, and Greek lexicon. p. vi. OCLC 894670115. https://archive.org/details/illustratedcompa00rich.
GERRAE (γέῤῥον). Any thing made of wicker work; whence trifles, trumpery, mere bagatelles. Plaut. Poen. i. 1. 9. Ep. ii. 2. 45.
# Cauchy-Riemann Equations
## Theorem

Let $G\subseteq \mathbb {C}$ be an open subset. Let the function $f=u+iv$ be differentiable at a point $z=x+iy\in G$. Then all partial derivatives of $u$ and $v$ exist at $\left(x,y\right)$ and the following Cauchy-Riemann equations hold:
    ${\dfrac {\partial u}{\partial x}}\left(x,y\right)={\dfrac {\partial v}{\partial y}}\left(x,y\right)\quad \quad {\dfrac {\partial u}{\partial y}}\left(x,y\right)=-{\dfrac {\partial v}{\partial x}}\left(x,y\right)$
In this case, the derivative of $f$ at $z$ can be represented by the formula
    $f'\left(z\right)={\dfrac {\partial u}{\partial x}}\left(x,y\right)-i{\dfrac {\partial u}{\partial y}}\left(x,y\right)={\dfrac {\partial v}{\partial y}}\left(x,y\right)+i{\dfrac {\partial v}{\partial x}}\left(x,y\right)$

## Proof

The proof can be decomposed into 3 main steps:
* calculate the partial derivative for the real part,
* calculate the partial derivative for the imaginary part,
* due to property of $f$ being complex differentiable both derivatives yield the same complex value. This leads to Cauchy-Riemann equations.

### Proof - Step 1

Let $h:=k+i0\left(k\in \mathbb {R} \right)$. Then
${\begin{array}{rcl}f'\left(z\right)&=&\lim \limits _{h\to 0}{\dfrac {f\left(z+h\right)-f\left(z\right)}{h}}\\&=&\lim \limits _{k\to 0}{\dfrac {u\left(x+k,y\right)+iv\left(x+k,y\right)-u\left(x,y\right)-iv\left(x,y\right)}{k}}\\&=&\lim \limits _{k\to 0}{\dfrac {u\left(x+k,y\right)-u\left(x,y\right)}{k}}+i{\dfrac {v\left(x+k,y\right)-v\left(x,y\right)}{k}}\\&=&{\dfrac {\partial u}{\partial x}}\left(x,y\right)+i{\dfrac {\partial v}{\partial x}}\left(x,y\right)\end{array}}$

### Proof - Step 2

Let $h:=0+il\left(l\in \mathbb {R} \right)$. Then
${\begin{array}{rcl}f'\left(z\right)&=&\lim \limits _{h\to 0}{\dfrac {f\left(z+h\right)-f\left(z\right)}{h}}\\&=&\lim \limits _{l\to 0}{\dfrac {u\left(x,y+l\right)+iv\left(x,y+l\right)-u\left(x,y\right)-iv\left(x,y\right)}{il}}\\&=&\lim \limits _{l\to 0}{\dfrac {1}{i}}{\dfrac {u\left(x,y+l\right)-u\left(x,y\right)}{l}}+{\dfrac {v\left(x,y+l\right)-v\left(x,y\right)}{l}}\\&=&{\dfrac {\partial v}{\partial y}}\left(x,y\right)-i{\dfrac {\partial u}{\partial y}}\left(x,y\right)\end{array}}$

### Proof - Step 3

Both partial derivatives must provide a same complex value due to the fact that $f$ is complex differentiable: $f'\left(z\right)={\dfrac {\partial u}{\partial x}}\left(x,y\right)+i{\dfrac {\partial v}{\partial x}}\left(x,y\right)={\dfrac {\partial v}{\partial y}}\left(x,y\right)-i{\dfrac {\partial u}{\partial y}}\left(x,y\right)$

### Proof - Step 4

Equating the real and imaginary parts, we get the Cauchy-Riemann equations. The representation formula follows from the above line and the Cauchy-Riemann equations.
# Algebra 1

Welcome to Algebra 1. We will cover everything from Elementary Algebra and work our way up to Geometry with some great discussions along the way. Mathematics is a language and if you can become fluent in it (which if you complete this course, I promise you will be!), then that is simply one more step in your great knowledge bank.

## Course Outline

You may notice that some weeks seem to be duplicated. Please know that this is not the case, but it basically means that we will be going up levels in those concepts. As you can see, they are the same main ideas, but you will be learning new things in each week.

### Semester I

* Week 1: Introduction To Algebra
* Week 2: The Translation of Algebra
* Week 3: Linear and Literal Equations
* Week 4: Functions
* Week 5: Graphing Linear Equations
* Week 6: X-intercepts and Y-intercepts, Slopes
* Week 7: Inequalities
* Week 8: Graphing Inequalities
* Week 9: Six rules of Exponents
* Week 10: Polynomials, Binomials, Trinomials
* Week 11: Cube Roots
# Linear mapping/Field/Definition

Let $K$ be a field, and let $V$ and $W$ be $K$-vector spaces. A mapping
    $\varphi \colon V\longrightarrow W$
is called a linear mapping if the following two properties are fulfilled.
* $\varphi (u+v)=\varphi (u)+\varphi (v)$ for all $u,v\in V$.
* $\varphi (sv)=s\varphi (v)$ for all $s\in K$ and $v\in V$.
# Linear mapping/Field/Definition/Explanations/Remark

Here, the first property is called additivity and the second property is called compatibility with scaling. When we want to stress the base field, then we say $K$-linear. The identity $\operatorname {Id} _{V}\colon V\rightarrow V$, the null mapping $V\rightarrow 0$, and the inclusion $U\subseteq V$ of a linear subspace are the simplest examples of a linear mapping. For a linear mapping, the compatibility with arbitrary linear combination holds, that is,
    $\varphi {\left(\sum _{i=1}^{n}s_{i}v_{i}\right)}=\sum _{i=1}^{n}s_{i}\varphi (v_{i})\,,$
see exercise.
# Derivation/Linear/Example

Let $C^{0}(\mathbb {R} ,\mathbb {R} )$ denote the space of continuous functions from $\mathbb {R}$ to $\mathbb {R}$, and let $C^{1}(\mathbb {R} ,\mathbb {R} )$ denote the space of continuously differentiable functions. Then the mapping
    $D\colon C^{1}(\mathbb {R} ,\mathbb {R} )\longrightarrow C^{0}(\mathbb {R} ,\mathbb {R} ),f\longmapsto f',$
which assigns to a function its derivative, is linear. In analysis, we prove that
    $(af+bg)'=af'+bg'\,$
holds for $a,b\in \mathbb {R}$ and another function $g\in C^{1}(\mathbb {R} ,\mathbb {R} )$.
# Linear mapping/Determination on basis/Fact/Proof

Since we want $f(v_{i})=w_{i}$, and since a linear mapping respects all linear combinations, that is
    $f{\left(\sum _{i\in I}s_{i}v_{i}\right)}=\sum _{i\in I}s_{i}f{\left(v_{i}\right)}\,$
holds, and since every vector $v\in V$ is such a linear combination, there can exist at most one such linear mapping. We define now a mapping
    $f\colon V\longrightarrow W$
in the following way: we write every vector $v\in V$ with the given basis as
    $v=\sum _{i\in I}s_{i}v_{i}\,$
(where $s_{i}=0$ for almost all $i\in I$) and define
    $f(v):=\sum _{i\in I}s_{i}w_{i}\,.$
Since the representation of $v$ as such a linear combination is unique, this mapping is well-defined. Also, $f(v_{i})=w_{i}$ is clear. Linearity. For two vectors $u=\sum _{i\in I}s_{i}v_{i}$ and $v=\sum _{i\in I}t_{i}v_{i}$, we have
    ${\begin{aligned}f{\left(u+v\right)}&=f{\left({\left(\sum _{i\in I}s_{i}v_{i}\right)}+{\left(\sum _{i\in I}t_{i}v_{i}\right)}\right)}\\&=f{\left(\sum _{i\in I}{\left(s_{i}+t_{i}\right)}v_{i}\right)}\\&=\sum _{i\in I}(s_{i}+t_{i})f{\left(v_{i}\right)}\\&=\sum _{i\in I}s_{i}f{\left(v_{i}\right)}+\sum _{i\in I}t_{i}f(v_{i})\\&=f{\left(\sum _{i\in I}s_{i}v_{i}\right)}+f{\left(\sum _{i\in I}t_{i}v_{i}\right)}\\&=f(u)+f(v).\end{aligned}}$
The compatibility with scalar multiplication is shown in a similar way, see exercise.
# Isometry of space/Rotation axis/Complement/Unitary/Section
## Theorem
### Proof

$\Box$
A proper linear isometry of the space transforms the unit sphere into itself. One might imagine an isometry as a rotation of a ball lying in a suitable bowl.

## Theorem
### Proof

$\Box$

## Theorem
### Proof

$\Box$
# Euclidean vector space/R^3/Isometry/Eigenvector/Fact

Let
    $\varphi \colon \mathbb {R} ^{3}\longrightarrow \mathbb {R} ^{3}$
be a linear isometry.
eigenvector with eigenvalue
$1$
$-1$
# Euclidean vector space/R^3/Isometry/Eigenvector/Fact/Proof

The characteristic polynomial $P$ of $\varphi$ is a normed polynomial of degree three. For $t\to +\infty$, we have $P(t)\to +\infty$, and for $t\to -\infty$, we have $P(t)\to -\infty$. Due to the intermediate value theorem, $P$ has a real zero. Such a zero is an eigenvalue of $\varphi$. Because of fact, this eigenvalue equals $1$ or $-1$.
# Euclidean vector space/R^3/Proper isometry/Fact

A proper isometry
    $\varphi \colon \mathbb {R} ^{3}\longrightarrow \mathbb {R} ^{3}$
eigenvector with eigenvalue
$1$
that is, there exists a line (through the origin) that is a fixed line for $\varphi$.
# Euclidean vector space/R^3/Proper isometry/Fact/Proof

We consider the characteristic polynomial of $\varphi$, that is,
    $P(\lambda )=\det {\left(\lambda E_{3}-\varphi \right)}\,.$
This is a normed real polynomial of degree three. For $\lambda =0$, we have
    $P(0)=\det {\left(-\varphi \right)}=-\det \varphi =-1\,.$
As the polynomial $P(\lambda )\to \infty$ as $\lambda \to \infty$, there must be a positive $\lambda$ that is a zero of $P$. Due to fact, we must have $\lambda =1$.
# Illustrated Companion to the Latin Dictionary/Groma

This article incorporates text from a publication now in the public domain: Rich, Anthony (1849). The illustrated companion to the Latin dictionary, and Greek lexicon. p. vi. OCLC 894670115. https://archive.org/details/illustratedcompa00rich.
GROMA and GRUMA (γρώμων). An instrument used by land-surveyors, engineers, and persons of that class; which was set up as an index for the purpose of enabling them to draw their lines, or direct their roads perfectly straight to any given point. (Non. s. v. p. 63. Hyg. de Limit. p. 164. Goes.) Hence degrumari, to make straight (Lucil. Sat. iii. 15. Gerlach.); and grumae, the central point at which four cross-roads meet. Non. l. c.
# Illustrated Companion to the Latin Dictionary/Gryps

This article incorporates text from a publication now in the public domain: Rich, Anthony (1849). The illustrated companion to the Latin dictionary, and Greek lexicon. p. vi. OCLC 894670115. https://archive.org/details/illustratedcompa00rich.
GRYPS and GRYPHUS (γρύψ). A griffin; a fabulous animal (Plin. H. N. x. 69.), mostly represented with the body and legs of a lion, surmounted by the head and wings of an eagle; thus combining strength with agility. It was, consequently, employed as an emblem of vigilance, and is frequently represented in tombs and on sepulchral lamps, as it were in the act of guarding the remains deposited therein. The example (Gryps/1.1), from a terra-cotta lamp, possesses all the qualities and characteristics described.