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HIGHER ARITHMETIC. .

BY

G. P. QUACKENBOS, LL.D.,

AUTHOR OF

" A PRACTICAL ARITHMETIC; AN ELEMENTARY ARITHMETIC;" " A PRIMARY AR'TE
NETIC;
A MENTAL ARITHMETIO;
" "AN ENGLISH GRAMMAR ;

" "FIRST LES-
BONS IN COMPOSITION; ADVANCED COURSE OF COMPOSITION AND
RHETORIO; " "A NATURAL PHILOSOPHY ; "JLLUSTRATED

SCHOOL HISTORY OF THE UNITED STATES; " ETC.

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NEW YORK ::: CINCINNATI ::: CHICAGO
A MERICAN BOOK COMPANY.

FROM THE PRESS OF
D. APPLETON & COMPANY.

KD34784

ia UNIVER: LIBRARY

42X120

[PUBLISHERS' NOTICE.] APPLETONS MATHEMATICAL SERIES.

By G. P. QUACKENBOS, LL.D.

A Primary Arithmetic. Beautifully illustrated; carries the

beginner through the first four Rules and the simple Tables,
combining mental exercises with examples for the slate. 16mo.

1

108 pages.

An Elementary Arithmetic. Reviews the subjects of the

Primary in a style adapted to somewhat maturer minds. Also
embraces Fractions, Federal Money, Reduction, and the Com-

pound Rules. 12mo. 144 pages.
A Practical Arithmetic. Prepared with direct reference to

the wants Common Schools, giving special prominence to the

branches of Mercantile Arithmetic. 12mo. 336 pages.
Key to Practical Arithmetic. 12mo. 72 pages.
A Higher drithmetic. A comprehensive text-book on the

science of Arithmetic and its practical applications; specially
designed as an aid in preparing for the counting-house. 12mo.

420 pages.

Key to Higher Arithmetic. 12mo. 96 pages.
A Mental Arithmetic Designed to impart readiness in mental

calculations, and extending them to the various operations needed
in business life. Introduces short methods, and new and beauti-
ful processes. 16mo. 168 pages.

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

D. APPLETON & CO.,
In the Office of the Librarian of Congress, at Washington.

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PREFAOE.

This work, which completes our Arithmetical Series, is designed for the use of high-schools, academies, business colleges, advanced classes in private and grammar schools, and all who desire a thorough preparation for the duties of the countinghouse, and have had such previous training as will enable them to enter on a higher course intelligently and profitably. It is complete in itself, furnishing, in addition to a comprehensive course in all the higher topics, a brief summary also of the elementary parts of the subject. When it was remembered how easy it is to forget notation and numeration while laboring in partial payments, cube root, etc., it was deemed unsafe to leave out any link in the chain. Yet, in treating the elementary topics referred to, the fact that they had already been studied was distinctly kept in view: they are discussed in a manner adapted to maturer minds; more has been left for the student himself to develop; additional matter, of interest and importance, has been introduced; and subjects have been presented in new connections and different combinations. Classes may, therefore, be placed at the very commencement of this book, with no risk of losing time by a useless re-traversing of ground too familiar to be again gone over with profit.

Merchants often complain that young men who have had the best school advantages, on entering stores, are quite ignorant of business processes, and unable to make a prompt and efficient use of their arithmetical knowledge in off-hand calculations even of the simplest character. One great aim in preparing the present work has been to remove all ground for this complaint, by treating the various branches of commercial arithmetic with special

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