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A RITHMETIC

SECOND BOOK

BY

EDWIN P. SEAVER, A.M., LL.B.

SUPERINTENDENT OF PUBLIC SCHOOLS, BOSTON

AND

GEORGE A. WALTON, A.M.
AGBNT OF MASSACHUSETTS BOARD OF EDUCATION; AUTHOR OF

WALTON'S ARITHMETICS, ARITHMETICAL TABLES, ETC.

BUTLER, SHELDON & COMPANY

.

NEW YORK, PHILADELPHIA, CHICAGO

HARVARD
UNIVERSITY
LIBRARY

COPYRIGHT, 1895,
BY SHELDON AND COMPANY.

PREFACE.

This book is not merely a revised edition of the Franklin Written Arithmetic published by the authors seventeen years ago. In its general plan and method, it preserves all the essential characteristics of that favorably known and widely used text-book, but it has been constructed out of new material. All the illustrations are fresh, nearly all the examples are new, and the text has been rewritten throughout. The principles of arithmetic do not change, neither do the essential elements of good teaching change, but there is infinite room for variety in the application of principles and in the exemplification of method. In these respects the authors trust that their new book may be found fully up with the times.

The method of the book is thoroughly inductive. Every new topic is introduced, as it should be in good teaching, by easy oral questions designed to bring the subject matter clearly before the learner's mind. Then follow illustrative examples, definitions, principles and rules in true inductive order. · The number of examples provided for practice and drill is unusually large, particularly in the earlier half of the book. There appears to be a demand for an abundance of such material, which this book aims to satisfy. But the authors are very far from recommending that all the examples under one topic should be worked before a pupil or a ciass of pupils is permitted to take up the next topic.

Opinions may differ as to whether topics like taxes, insurance, foreign exchange, stocks and bonds, equation of payments, and average of accounts should be included in the course of study for common schools, but there seems to be no doubt that such topics should be included in a book that aims at ordinary completeness. In this book the treatment of the topics mentioned is unusually simple and practical, the illustrations being not the old-fashioned imaginary transactions, but the actual ones occurring daily in the course of mercantile business. By means of them a considerable amount of accurate and useful information is conveyed.

An important feature of the book is the anticipation of topics. In the earlier sections are found well-chosen examples which serve to familiarize the learner with matters that are to be presented in a more formal and complete shape in the later sections. Thus a knowl. edge of compound numbers is conveyed by the examples given to illustrate the applications of multiplication and division of simple numbers ; many examples in percentage and interest are given among the applications of decimal fractions; and the simpler examples in mensuration are introduced long before the systematic treatment of that subject in the last section is reached.

It is this same principle of anticipation that has led the authors to make a somewhat free use of algebraic notation and methods in the treatment of problems in interest, proportions, square and cube root, and some other topics.

Proportion has received a somewhat broader treatment than has been usual in arithmetical text-books of late years. It is believed that proportion affords a straightforward, simple, and clear form of analysis, the training in which is highly useful for general purposes and cannot be too strongly recommended for all who are to be concerned with the further study of mathematics or with the physical sciences. In this book the range of examples is enlarged so as to include some of the simpler applications of proportion to similar geometrical figures.

The section on mensuration has been enlarged so as to contain a considerable amount of practical geometry. This, with the practical exercises suggested for the purpose of making the principles objectively clear, will, it is hoped, make mensuration a less dry and forbidding topic than children usually find it.

In conclusion, the authors desire to express their hearty acknowledgments for the favorable reception accorded to their former book, and venture to hope that the present one may be found no less worthy of public favor.

E. P. S.

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TABLE OF CONTENTS.

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