Elementary algebra
By: by H. S. Hall and S. R. Knight; rev. and enl. for the use of American schools by F. L. Sevenoak.
Contributors: Knight, S. R.; Sevenoak, Frank L.
Edition: 2d. ed.
Publisher: Macmillan
Published: 1896
Place of publication: New York; London
Language: eng
Number of pages: 516
Subjects: Algebra.
Table of contents: label: I
title: Definitions. Substitutions
pagenum: 1; label: II
title: Negative Quantities. Addition of Like Terms
pagenum: 9; label: III
title: Simple Brackets. Addition and Subtraction
pagenum: 13; title: Commutative Law for Addition and Subtraction
pagenum: 15; title: Associative Law for Addition and Subtraction
pagenum: 15; title: Dimension, Degree, Ascending and Descending Powers
pagenum: 17; title: Miscellaneous Examples I
pagenum: 23; label: IV
title: Multiplication
pagenum: 24; title: Commutative Law for Multiplication
pagenum: 25; title: Associative Law for Multiplication
pagenum: 25; title: Index Law for Multiplication
pagenum: 25; title: Distributive Law for Multiplication
pagenum: 26; title: Multiplication of Compound Expressions
pagenum: 27; title: Rule of Signs
pagenum: 28; title: Note on Arithmetical and Symbolical Algebra
pagenum: 29; title: Distributing the Product
pagenum: 31; title: Products Written by Inspection
pagenum: 35; title: Multiplication by Detached Coefficients
pagenum: 37; label: V
title: Division
pagenum: 38; title: Index Law for Division
pagenum: 39; title: Division of Compound Expressions
pagenum: 40; title: Important Cases in Division
pagenum: 44; title: Horner's Method of Synthetic Division
pagenum: 46; label: VI
title: Removal and Insertion of Brackets
pagenum: 48; title: Miscellaneous Examples II
pagenum: 53; label: VII
title: Simple Equations
pagenum: 55; label: VIII
title: Symbolical Expression
pagenum: 60; label: IX
title: Problems Leading to Simple Equations
pagenum: 65; label: X
title: Resolution into Factors
pagenum: 70; title: Trinomial Expressions
pagenum: 72; title: Difference of Two Squares
pagenum: 78; title: Important Cases
pagenum: 82; title: Sum or Difference of Two Cubes
pagenum: 82; title: Miscellaneous Cases
pagenum: 83; title: Converse Use of Factors
pagenum: 85; title: The Factor Theorem
pagenum: 87; label: XI
title: Highest Common Factor
pagenum: 92; title: Factor Theorem Employed
pagenum: 98; label: XII
title: Lowest Common Multiple
pagenum: 102; label: XIII
title: Fractions
pagenum: 107; title: Reduction to Lowest Terms
pagenum: 108; title: Multiplication and Division
pagenum: 110; title: Addition and Subtraction
pagenum: 114; title: Rules for Change of Sign
pagenum: 121; title: Cyclic Order
pagenum: 124; label: XIV
title: Complex Fractions. Mixed Expressions
pagenum: 126; title: Miscellaneous Exercise on Fractions
pagenum: 132; label: XV
title: Fractional and Literal Equations
pagenum: 136; label: XVI
title: Problems
pagenum: 141; title: Miscellaneous Examples III
pagenum: 144; label: XVII
title: Simultaneous Equations
pagenum: 147; title: Elimination by Addition or Subtraction
pagenum: 148; title: Elimination by Substitution
pagenum: 149; title: Elimination by Comparison
pagenum: 150; title: Equations Involving Three Unknown Quantities
pagenum: 152; title: Reciprocal
pagenum: 154; title: Literal Simultaneous Equations
pagenum: 157; label: XVIII
title: Problems
pagenum: 160; label: XIX
title: Indeterminate and Impossible Problems. Negative Results
pagenum: 165; title: Meaning of a/0, a/∞, 0/0, ∞/∞
pagenum: 167; label: XX
title: Involution
pagenum: 169; title: To Square a Multinomial
pagenum: 171; title: To Cube a Multinomial
pagenum: 173; title: Application of Binomial Theorem
pagenum: 173; label: XXI
title: Evolution
pagenum: 176; title: Square Root of a Multinomial
pagenum: 177; title: Cube Root of a Multinomial
pagenum: 181; title: Some Higher Roots
pagenum: 185; title: The nth Root of a Multinomial
pagenum: 186; title: Square and Cube Root of Numbers
pagenum: 187; label: XXII
title: The Theory of Indices
pagenum: 191; title: Meaning of Fractional Exponent
pagenum: 193; title: Meaning of Zero Exponent
pagenum: 193; title: Meaning of Negative Exponent
pagenum: 194; label: XXIII
title: Surds (Radicals)
pagenum: 203; title: Reduction of Surds
pagenum: 205; title: Addition and Subtraction of Surds
pagenum: 207; title: Multiplication of Surds
pagenum: 208; title: Division of Surds
pagenum: 209; title: Compound Surds
pagenum: 211; title: Factor Which Will Rationalize Any Binomial Surd
pagenum: 214; title: Properties of Quadratic Surds
pagenum: 216; title: Square Root of a Binomial Surd
pagenum: 217; title: Square Root of a Binomial Surd by Inspection
pagenum: 218; title: Equations Involving Surds
pagenum: 220; label: XXIV
title: Imaginary Quantities
pagenum: 222; title: Imaginary Unit
pagenum: 223; title: Fundamental Algebraic Operations
pagenum: 225; label: XXV
title: Problems
pagenum: 227; title: Miscellaneous Examples IV
pagenum: 232; label: XXVI
title: Quadratic Equations
pagenum: 235; title: Pure Quadratic Equations
pagenum: 236; title: Affected Quadratic Equations
pagenum: 237; title: Solution by Formula
pagenum: 239; title: Solution by Factoring
pagenum: 241; title: Formation of Equations with Given Roots
pagenum: 242; title: Values Found for the Unknown Quantity Which Do Not Satisfy the Original Equation
pagenum: 243; label: XXVII
title: Equations in Quadratic Form
pagenum: 245; label: XXVIII
title: Simultaneous Equations Involving Quadratics
pagenum: 249; title: Homogeneous Equations of the Same Degree
pagenum: 253; title: Symmetrical Equations
pagenum: 254; title: Miscellaneous Cases
pagenum: 255; label: XXIX
title: Problems
pagenum: 258; label: XXX
title: Theory of Quadratic Equations
pagenum: 264; title: Number of the Roots
pagenum: 264; title: Character of the Roots
pagenum: 265; title: Relation of Roots and Coefficients
pagenum: 266; title: Formation of Equations with Given Roots
pagenum: 267; title: Miscellaneous Theorems
pagenum: 272; title: Remainder Theorem
pagenum: 272; title: Symmetry
pagenum: 273; label: XXXI
title: Indeterminate Equations of the First Degree
pagenum: 276; label: XXXII
title: Inequalities
pagenum: 279; title: Miscellaneous Examples V
pagenum: 283; label: XXXIII
title: Ratio
pagenum: 286; title: Proportion
pagenum: 291; title: Transformations that May Be Made in a Proportion
pagenum: 293; title: Variation
pagenum: 296; label: XXXIV
title: Arithmetical Progression
pagenum: 301; title: Geometrical Progression
pagenum: 308; title: Harmonical Progression
pagenum: 313; label: XXXV
title: Permutations and Combinations
pagenum: 319; label: XXXVI
title: Probability (Chance)
pagenum: 331; title: Miscellaneous Examples VI
pagenum: 334; label: XXXVII
title: Binomial Theorem: Proof for Positive Integral Index
pagenum: 338; title: The General Term
pagenum: 341; title: Simplest Form of the Binomial Theorem
pagenum: 342; title: Proof by Mathematical Induction
pagenum: 343; title: Equal Coefficients
pagenum: 345; title: Greatest Coefficient
pagenum: 345; title: Greatest Term
pagenum: 345; title: Sum of the Coefficients
pagenum: 347; title: Expansion of Multinomials
pagenum: 347; title: Application When Index is Negative or Fractional
pagenum: 347; label: XXXVIII
title: Logarithms
pagenum: 352; title: Properties of Logarithms
pagenum: 353; title: Characteristic and Mantissa
pagenum: 354; title: Advantages of Common Logarithms
pagenum: 355; title: Logarithms Transformed from Base a to Base b
pagenum: 357; title: Logarithms in Arithmetical Calculation
pagenum: 358; title: Four-Place Table of Logarithms
pagenum: 360; title: Use of the Table
pagenum: 362; title: Cologarithms
pagenum: 365; title: Exponential Equations
pagenum: 366; label: XXXIX
title: Interest and Annuities
pagenum: 367; label: XL
title: Limiting Values and Vanishing Fractions
pagenum: 370; label: XLI
title: Convergency and Divergency of Series
pagenum: 377; title: Tests for Convergency
pagenum: 377; title: Auxiliary Series
pagenum: 383; label: XLII
title: Undetermined Coefficients
pagenum: 386; title: Functions of Finite Dimensions
pagenum: 386; title: Functions of Infinite Dimensions
pagenum: 390; title: Expansion of Fractions into Series
pagenum: 391; title: Expansion of Surds into Series
pagenum: 392; title: Reversion of Series
pagenum: 393; title: Partial Fractions
pagenum: 394; title: The General Term
pagenum: 397; label: XLIII
title: Continued Fractions
pagenum: 400; title: Formation of Successive Convergents
pagenum: 403; title: Limits to Error
pagenum: 407; title: Recurring Continued Fractions
pagenum: 409; label: XLIV
title: Summation of Series
pagenum: 413; title: Scale of Relation
pagenum: 413; title: The Sum of n Terms
pagenum: 415; title: The General Term
pagenum: 417; title: The Method of Differences
pagenum: 418; title: Any Required Term
pagenum: 419; title: The Sum of n Terms
pagenum: 420; title: Piles of Shot and Shells
pagenum: 422; title: Interpolation
pagenum: 425; label: XLV
title: Binomial Theorem: Proof for Any Index
pagenum: 426; label: XLVI
title: Exponential and Logarithmic Series
pagenum: 430; label: XLVII
title: Determinants
pagenum: 435; title: Minors
pagenum: 437; title: Vanishing of a Determinant
pagenum: 438; title: Multiplication of a Determinant
pagenum: 438; title: A Determinant Expressed as the Sum of Two Other Determinants
pagenum: 439; title: Simplification of Determinants
pagenum: 440; title: Solution of Simultaneous Equations of the First Degree
pagenum: 444; title: Signs of the Terms
pagenum: 447; title: Determinant of Lower Order
pagenum: 448; label: XLVIII
title: Theory of Equations
pagenum: 450; title: Horner's Method of Synthetic Division
pagenum: 451; title: Number of the Roots
pagenum: 453; title: Depression of Equations
pagenum: 453; title: Formation of Equations
pagenum: 454; title: Relations between the Roots and the Coefficients
pagenum: 454; title: Fractional Roots
pagenum: 458; title: Imaginary Roots
pagenum: 458; title: Transformation of Equations
pagenum: 460; title: Standard Form of Reciprocal Equations
pagenum: 466; title: Descartes' Rule of Signs
pagenum: 469; title: Derived Functions
pagenum: 472; title: Equal Roots
pagenum: 472; title: Location of the Roots
pagenum: 474; title: Sturm's Theorem and Method
pagenum: 476; title: Graphical Representation of Functions
pagenum: 480; title: Solution of Higher Numerical Equations
pagenum: 483; title: Newton's Method
pagenum: 483; title: The Cube Roots of Unity
pagenum: 486; title: Cardan's Method
pagenum: 487; title: Biquadratic Equations
pagenum: 488; title: Incommensurable Roots
pagenum: 491; title: Horner's Method of Approximation
pagenum: 492; title: Any Root of Any Number
pagenum: 495; title: Miscellaneous Examples VII
pagenum: 496