An edition of Elementary algebra (1895)

Elementary algebra

2d. ed.

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  • 12 Want to read
Cover of: Elementary algebra by Henry Sinclair Hall, Henry Sinclair Hall
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Last edited by Drini
June 18, 2025 | History
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An edition of Elementary algebra (1895)

Elementary algebra

2d. ed.

by

  • 12 Want to read

This edition doesn't have a description yet. Can you add one?

Publish Date
Publisher
Macmillan
Language
English
Pages
516

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Previews available in: English

Subjects

Algebra
Edition Availability
Cover of: Elementary algebra
Elementary algebra
1896, Macmillan
in English - 2d. ed.
Cover of: Elementary algebra
Elementary algebra
1895, Macmillan and co.
in English - Rev. and enl. for the use of American schools by F. L. Sevenoak ...

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Book Details

Table of Contents

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

Edition Notes

Published in
New York, London

The Physical Object

Pagination
x, 516 p. ;
Number of pages
516

Edition Identifiers

Open Library
OL23416611M
Internet Archive
elementaryalgebr00hall

Work Identifiers

Work ID
OL5230280W

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Download catalog record: RDF / JSON / OPDS | Wikipedia citation
June 18, 2025 Edited by Drini Add TOC from Tocky
April 13, 2010 Edited by Open Library Bot Linked existing covers to the edition.
December 15, 2009 Edited by WorkBot link works
July 7, 2009 Created by ImportBot Imported from Internet Archive item record