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).

ALEXANDER THOM, PRINTER AND PUBLISHER,

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

JOHN MENZIES & CO., EDINBURGH,

.

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.

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