Lowdermilk

9-30.30 22611

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ADVERTISEMENT.

میر ناف بال اور علاج

As UTILITY is the great object aimed at in this Publication, I have spared no pains to • make a careful selection of materials, from

the most approved sources, which may tend to elucidate, in a full and clear manner, the Elements of Algebra, both in theory and practice.

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Those author's of whose labours I have principally availed myself, are Euler, Clairaut, Lacroix, Garnier, Bezout, Lagrange, Newton, Simpson, Emerson, Wood, Bonnycastle, Bridge, and Bland.

To Bland's Algebraical Problems, (a work compiled for the use of Students in one of the first Universities in Europe), I am chiefly indebted for the problems in Simple, Pure, and Quadratic Equations.

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By permission of the learned Dr. Adrain, I have added, as an Appendix, his method of demonstrating algebraically_the propositions in the fifth book of Euclid's Ele. ments.

JAMES RYAN.

New-York, July 1, 1824,

CONTENTS.

INTRODUCTION.

Page

Explanation of the Algebraic method of notation :

Definitions and Axioms,

1

CHAPTER I.

On the Addition, Subtraction, Multiplication and Division

of Algebraic Quantities.

Sect.

1. Addition of algebraic quantities,

14

II. Subtraction of algebraic quantities,

25

III. Multiplication of algebraic quantities,

30

IV. Division of algebraic quantities,

45

V. Some general theorems, observations, &c.

63

CHAPTER II.

.

On Algebraic Fractions.

Sect.

1. Theory of algebraic fractions,

II. Method of finding the greatest common divisor

of two or inore quantities,

83

III. Method of finding the least common multiple

of two or more quantities,

101

IV. Reduction of algebraic fractions,

104

V. Addition and subtraction of algebraic fractions, 122

VI. Multiplication and division of algebraic frac-

tions,

129

VII. Resolution of algebraic fractions or quotients

into infinite series,

135

161

On Simple Equations involving only one unknown

Quantity,

Sect.

I. Reduction of simple equations,

II. Resolution of simple equations, involving only

one unknown quantity,

III. Examples in simple equations, involving only

one unknown quantity,

162

169

• 179

CHAPTER IV.

193

191

On Simple Equations, involving two or more un-

known Quantities,

Sect.

1. Elimination of unknown quantities from any

number of simple equations,

II. Resolution of simple equations, involving two

unknown quantities,

Examples in which the preceding rules are ap-

plied, in the solution of simple equations,

involving two unknown quantities,

III. Resolution of simple equations, involving three

or more unknown quantities,

230

248

257

CHAPTER V.

26.3

On the Solution of Problems, producing Simple

Equations,

Sect.

1. Solution of problems producing simple equa-

tions, involving only one unknown quantity,

II. Solution of problems producing simple equa-

tions, involving more than one unknown

quantity,