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NUMBERS APPLIED

A COMPLETE ARITHMETIC

BY

Andrew 7. RickoFF, A.M., LL.D

NEW YORK, BOSTON, AND CHICAGO
D. APPLETON AND COMPANY

1888

Edte f TT 8: 86.5

HARVARD COLLEGE LIBRARY

GIFT OF
MRS. CHARLES S. PEIRCE

JUNE 28, 1915

Ecluetua,sr.745

COPYRIGHT, 1886,
By D. APPLETON AND COMPANY.

PREFACE. .

This work is not the result of any ambition on the part of the publishers to add another title to their already long list of text-books, but of a desire to meet a wide-spread and growing demand for a treatise on arithmetic adapted to the objective methods of instruction now so common in all educational institutions which have been reached directly or indirectly by the influence of normal schools, teachers' institutes, etc.

In its preparation the author has kept steadily in view these two thoughts: (1) That words are useless in the ratio that they fail to call up in the mind vivid images of the things signified. Hence the aim to vitalize the relation of words and things by the aid of the best practicable illustrations at every point; and (2) That, to the learner, the operations of arithmetic are apt to be but manipulations of figures after prescribed models, unless he realizes the fact that they are representative of processes that may be applied to material objects.

The book is intended to be put into the hands of the learner as soon as he has completed a course in primary arithmetic; but it would be well for him to begin the study of it with the first chapter, that he may get a better technical knowledge of the fundamental rules and their relations to each other, and that he may become rapid and reliable in computations involving integers before he takes up the more complicated subject of fractions.

Great care has been taken to adapt the work as far as possible to the needs of the great number of children who are withdrawn from school before a full course in arithmetic can be completed. With this object in view, the more useful business applications of elementary principles are made as soon as they are learned. Thus, familiar measures are introduced before reduction is mentioned; federal money before decimals; many practical measurements before mensuration; and questions even in percentage and interest are to be met with before those subjects are reached in due course. The conditions of these problems are so presented as to be within

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