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PRINCIPLES

OF

ARITHMETIC.

THE

PRINCIPLES

OF

ARITHMETIC:

I Comprehensive Text-Book

FOR TIIE USE OF

TEACHERS AND ADVANCED PUPILS.

BY

D. O'SULLIVAN, PED, M.R.I.A.,

ONE OF THE PROFESSORS IN THE TRAINING DEPARTMENT OF THE

COMMISSIONERS OF NATIONAL FOUCATION (IRELAND).

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ALEXANDER THOM, PRINTER AND PUBLISHER,

87 & 88, ABBEY-STREET.
SIMPKIN, MARSHALL, & CO., LONDON.

JOHN MENZIES & CO., EDINBURGH,

.

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PREFACE.

This book, which is detailed as well as comprehensive, and which is the result of a long and varied experience, will, I hope, enable persons of ordinary capacity and intelligence to acquire for themselves, by diligent and patient study, a sound knowledge of the rationale of Arithmetic. The want of such a treatise has, in numerous instances, been complained of by the Irish National Teachers, with whom-as Inspector of National Schools, as Head Master of the Central Model Schools, and as Professor-I have, for many years, been officially connected.

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In the following pages, Arithmetic is reduced to a series of distinct “ Principles,” which—for facility of reference-are printed in large type, and numbered. The student is asked to take nothing for granted. Every Principle is logically established, and is, moreover, illustrated by a sufficient number of carefully selected examples.

In the arrangement and treatment of the Principles, I have exercised my own judgment. Many

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