THE

ELEMENTS OF ALGEBRA.

WITH NUMEROUS EXAMPLES,

For the Use of Schools.

BY REV. ROBERT FOWLER, M. A.,

LATE FELLOW OF CHRIST'S COLLEGE, CAMBRIDGE;

AND PRINCIPAL OF THE MILITARY SCHOOL, TUNBRIDGE WELLS,

LONDON:
SIMPKIN, MARSHALL, AND CO.

1861.

100.066

181. C

150

LONDON: PRINTED BY W. CLOWES AND SONS, STAMFORD STREET, AND CHARING CROSS.

VII. The Greatest Common Measure and the Least Common

X. On the Resolution of Algebraical Expressions into

Factors..

94

XI. Fractional and Negative Indices, and Surds

107

XII. Quadratic Equations of one or more Unknown Quantities 137

Problems requiring the solution of Quadratic Equations

XIV. Arithmetic, Geometric, and Harmonic Progression..

200

XVIII. Indeterminate Coefficients, Partial Fractions, and Re-

XXI. Summation of Series- - Piles of Balls, Shells, &c.

-

282

APPENDIX. Application of the Methods of Finding the Square

and Cube Roots to Numbers

291

....

PREFACE.

My apology for writing the following pages is that I have taught more or less of Algebra to above five hundred pupils; and my motive has been to supply some of those aids to beginners which a twelve years' experience has shown me to be necessary, but which are not to be found in the works in Algebra with which I am acquainted.

Three of the main difficulties in the way of beginners are the following:

1. The want of model examples to guide them in working out their solutions in a neat and methodical form.

2. The want of experience and dexterity in resolving algebraical expressions into their simple factors.

3. Indistinct conceptions of the meanings of the symbols employed in general formulæ.

I have therefore placed models of the working out of questions at the head of each chapter of examples.

A chapter is devoted to the resolution of algebraical expressions into their factors; and I would recommend all teachers who use this book to put their pupils through this chapter before they begin fractions.