THE PRINCIPLES OF ARITHMETIC: A Comprehensive Text-Book FOR THE USE OF TEACHERS AND ADVANCED PUPILS. BY D. O'SULLIVAN, PHD, M.R.I.A., ONE OF THE PROFESSORS IN THE TRAINING DEPARTMENT OF THE DUBLIN: ALEXANDER THOM, PRINTER AND PUBLISHER, SIMPKIN, MARSHALL, & CO., LONDON. 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 |