PREFACE

TABLE OF CONTENTS

Book I

THE FUNDAMENTAL OPERATIONS OF COMMON ALGEBRA—

THEIR LAWS AND APPLICATIONS

INTRODUCTION

-

The Nature of Numbers and the Fundamental Postulate of Arithmetic

The Equality of Two Groups

Symbolic Representation of Numbers

The Equation and Inequalities

Counting

CHAPTER I

ADDITION AND MULTIPLICATION

The Sum of Two Groups-Parenthesis

Addition of Positive Integers and its Fundamental Laws
Multiplication of Positive Integers and its Fundamental Laws.
The Exponent and Index Law of Multiplication

Addition and Multiplication of Monomials and Polynomials

V

11

12

13

14

15

17

18

19

21

24

27

29

30

32

35

36

Determinateness of Numerical Subtraction-Formal Rules of Subtraction 40

Indeterminateness of Division by 0-Determinateness of Symbolic Division 69

The Vanishing of a Product

70

An Identity-An Equation of Condition-The Unknown Quantity

Axioms

Transposition

Case VII: To Factor Polynomials which have a Binomial Factor

Case VIII: To Factor a Polynomial of Four Terms

Solution of Equations — Imaginary Numbers

CHAPTER IX

GREATEST COMMON DIVISOR AND LEAST COMMON MULTIPLE

93

94

96

98

99

G. C. D. of Quantities Readily Factored

101

G. C. D. of Two or more Algebraic Expressions

102

Least Common Multiple of Quantities readily Factored and those not

Formulae for the Solution of an Equation of the First Degree in One

Unknown Quantity

158

The Solution of two Equations of the First Degree - Elimination by

Addition and Subtraction

Elimination by Substitution.

Elimination by Comparison

Elimination by Undetermined Multiplier

198

199

200

201

204

207

212

218

Two Equations of the First Degree which have a Common Root

237

CHAPTER VIII

GENERAL SOLUTION OF A SYSTEM OF THREE EQUATIONS

Examples of Three Equations of the First Degree

Number of Solutions of a System of n Linear Equations

Problems involving Three or More Unknown Numbers

CHAPTER IX

GRAPHICAL REPRESENTATION OF POINTS AND LINES

Graphical Representation of a Point

Graph of the Solution of a Conditional Equation

Graph of the Line y=mx+b

Intercepts

Intersections of Pairs of Lines

CHAPTER X

DIOPHANTIAN EQUATIONS OF THE FIRST DEGREE

Simple Indeterminate Equations

Rule for Solution of ax + by = c

General Solution

Given One Solution of ax-by=c in Positive Integers, to Find the

General Solution of Two Equations

272

274

BOOK III

INVOLUTION-EVOLUTION-FRACTIONAL AND NEGATIVE EXPONENTS

Index Law of Involution.

CHAPTER I

INVOLUTION

Powers of Monomials, Fractions, Binomials, and Polynomials