Office Sec. B's Education Newark, NJ,

C

BY DANIEL W. FISH, A.M.,

EDITOR OF ROBINSON'S SERIES OF PROGRESSIVE ARITHMETICS.

IVISON, BLAKEMAN, TAYLOR & CO.,

NEW YORK AND CHICAGO.

1874.

HARVARD COLLEGE LIBRARY

FROM THE GIFT OF

CHARLES HEART THURBER
MAR 5 1926

ROBINSON'S

SHORTER COURSE

OF MATHEMATICS.

Of this Course, the Publishers have just issued,
the “INTERMEDIATE ARITHMETIC,” and the “cOM-

PLETE ALGEBRA."

The "FIRST BOOK IN ARITHMETIC,” And the "com-
PLETE ARITHMETIC," will appear about the 1st of
January, 1875.

The "GEOMETRY,” “EXAMPLES," and "KEYS,"
will follow, as soon as practicable.

Entered according to Act of Congress, in the year 1874,

BY DANIEL W. FISH.

In the Office of the Librarian of Congress, at Washington.

Electrotyped by SMITH & MCDOUGAL, 82 Beekman St., N. Y.

Cambridge: Printed by Welch, Bigelow, & Co.

PREFACE.

HOW to save the time of both teacher and pupil, and at the

same time enhance the mental discipline and practical knowledge of the latter, is an object, the attainment of which must not only be a source of economy, but a real educational improvement.

At the present time there is an obvious demand that the books composing an arithmetical series should not only be fewer in number but more comprehensive; and, moreover, that one of the books of such a series should be adapted to that numerous class of pupils whose time and opportunities are too limited to permit their acquiring more than the elementary principles of arithmetic and the applications of these to the most familiar business transactions.

In the preparation of this treatise, the author has endeavored to supply such a book, by confining the treatment to a limited number of topics of the most useful and practical character, and by so thoroughly developing each, both in theory and applications, as to obviate entirely the necessity of studying these portions of the subject again in any larger book.

Scarcely too much importance can be given to the study of mental arithmetic in our elementary schools. There is no doubt, that when properly taught, it is one of the most effective means of intellectual training; and yet, although the mental exercises should always precede the written, this part of the subject is too generally neglected for want of time.

In this work, oral and written exercises have been thoroughly combined the oral preceding and made preparatory to the written. Sufficient oral arithmetic has been introduced to answer the purpose of a separate book, thus ensuring attention to the subject and the saving of much valuable time.