THE

ANALYSIS

OF

WRITTEN ARITHMETIC.

BOOK SECOND,

DESIGNED FOR

PUBLIC AND PRIVATE SCHOOLS,

CONTAINING

MENTAL, SLATE, AND BLACKBOARD EXERCISES;

BY

S. A. FELTER, A. M.,

GRADUATE OF THE STATE NORMAL SCHOOL, AND LATE OF THE BROOKLYN COLLEGIATE
AND POLYTECHNIC INSTITUTE, AUTHOR OF PRIMARY ARITHMETIC, ETC.

SCHERMERHORN, BANCROFT & CO.,

NEW YORK, 130 GRAND ST PHILADELPHIA, 512 ARCH ST.

Entered according to Act of Congress in the year 1864, by
S. A. FELTER,

In the Clerk's Office of the District Court for the Southern District
of New York.

CASE, LOCKWOOD & CO.,
ELECTROTYPERS AND PRINTERS,

HARTFORD, CONN.

PREFACE.

In the preparation of this work the author has labored to secure, 1st, discipline of mind by requiring a formula for each step of the analysis; 2nd, rapidity, accuracy, and complete familiarity with commercial transactions, by giving a large number of abstract and practical examples and problems; 3rd, thoroughness, by a systematic daily review.

Upon the introduction of Mental Arithmetic into our schools, the solution of problems by rule gave place, in some degree, to analysis, which has, however, been applied but little to the more advanced subjects of Commercial Arithmetic. A complete system of analysis constitutes an important, and it is hoped, a very advantageous feature of this work.

In most published text books on arithmetic more attention has been given to the development of the science and the properties of numbers, and the logical arrangement of subjects than to their application to business transactions. Most of the examples are prepared with particular reference to the subject which they are to illustrate, much time and space are devoted to arithmetical puzzles, and the commercial examples often contain most improbable conditions. While the arrangement of subjects is logical, it is not natural, and does not follow the order of simplicity, thereby involving the pupil in diffiulties before his mind is sufficiently developed to master them. The subject

of Proportion, or the Rule of Three, has received undue prominence; for all commercial questions can be more easily solved by Analysis. Reduction of Currencies, Duodecimals, Permutation, and the Progressions are superfluous in a commercial arithmetic, and should be discussed in a higher arithmetic only. In this work an effort has been made to avoid these and similar faults.

The work is divided into two parts; the first containing a complete theoretical review of the subjects contained in the First Book, with important additions of principles and contractions in the fundamental rules and denominate numbers. Exercises in the composition of examples may be carried to any desirable extent. The second part commences with the Properties of Numbers, and Fractions, and is, really, the continuation of Book First. No pupil should begin it without being thoroughly acquainted with the subjects treated in that volume; for a neglect of this precaution will greatly embarrass both pupil and teacher.

The author wishes to acknowledge his indebtedness to those teachers who have shown their interest in this series by kindly offering valuable suggestions, as well as to R. S. Delisser, Esq., for his method of averaging accounts by interest, which he has kindly given permission to use.

COLLEGIATE AND POLYTECHNIC INSTITUTE,
BROOKLYN, N. Y., May, 1864.

INTRODUCTION.

IN presenting this work to his fellow teachers, the author deems it proper to exhibit its peculiarities more fully than he can do in a preface for the general reader.

ANALYSIS. This work is intended to continue the subject of commercial arithmetic as left in Book First; and, also, to make it in some measure complete for those who wish a theoretical review of the subjects treated in that volume. All the tables, principles, analyses, formulas, &c., given in the First Book are, therefore, reproduced in the second, with model examples for composition, by which the key to the formation of problems as well as their true analysis is clearly exhibited. (See Anal., page 27.)

Every complex, concrete, or commercial problem, can be separated into elementary questions, and each question involves one of six arithmetical formulas. Using the symbols x and y, we have:

I. If some oranges cost x cts., and some apples cost y cts., both will cost the sum of these quantities, which are x+y cts.

II. If the oranges cost x cts., and the apples cost y cts., the oranges will cost as many more cents than the apples as the difference of these quantities, which is x-y cts.

III. If one orange cost x cts., y oranges will cost y times x cts., which is xxy cts.

IV. If x cts. are equally divided among y boys, each boy will receive one y part of x cts., which is x÷y cts.

V. If one orange costs y cts., as many oranges can be bought for x cts. as y cts. are contained times in x cts., which are x÷y times. VI. If a boy have a cts. and he give away y cts., he will give the part of his money.

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