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G. P. QUACKENBOS, LL. D.,

AUTHOR OF

POSITION ;*“ ADVANCED course or com

"A PRIMARY ARITHMETIU;" “ AN ELEMENTARY ARITHMETIC; " "AN ENGLISII GRAN-
MAR;" “ FIRST LESSONS IN COMPOSITION; " " ADVANCED COURSE OF COMPO-
SITION AND RHETORIC; " " A NATURAL PHILOSOPHY;" "ILLUSTRATED
SCHOOL HISTORY OF THE UNITED STATES ; " " PRIMARY HIS-

TORY OF THE UNITED STATES ; " ETC.

UPON TIE BASIS OF THE WORKS OF

GEO. R. PERKINS, LL. D.

D. APPLETON COMPANY

NEW YORK:
D. APPLETON & COMPANY,

549 & 651 BROADWAY.

1872.
33162
WITHDRAWN Nur towy

EducT

118.72.723

MAGVARD COLL OF US PAVY
i savetiGE

NOV 29 1939
By the same Author:

A PRIMARY ARITHMETIC: Handsomely Illustrated. 16mo, pp. 108. 30 cts.
AN ELEMENTARY ARITHMETIC: 12mo, pp. 144. 50 cts.
A MENTAL ARITHMETIC: Designed to impart readiness in mental calcula.

tions, and extending them to the various operations needed iu business

life. 16mo, pp. 168. 45 cts. KEY TO PRACTICAL ARITHMETIC: 12mo, pp. 72. 20 cts. FIRST BOOK IN GRAMMAR: 16mo, pp. 120. 50 cts. AN ENGLISH GRAMMAR: 12mo, pp. 288. 90 cts. FIRST LESSONS IN COMPOSITION: In which the Principles of the Art are

developed in connection with the Principles of Grammar. 12mo, pp. 182.

90 cts. ADVANCED COURSE OF COMPOSITION AND RHETORIC: A Series of

Practical Lessons on the Origin, History, and Peculiarities of the English
Language, Punctuation, Taste, the Pleasures of the Imagination, Figures.
Style and its Essential Properties, Criticism, and the various Departments
of Prose and Poetical Composition: Illustrated with copious Exercises.

12mo, pp. 450. $1.50. ELEMENTARY HISTORY OF THE UNITED STATES: With numerous

Illustrations and Maps. 12mo, pp. 216. 75 cts ILLUSTRATED SCHOOL HISTORY OF THE UNITED STATES: Em

bracing a ful! Account of the Aborigines, Biographical Notices of Distinguished Men, numerous Maps, Plans of Battle-fielde, and Pictorial Illustra

tions. 12mo, pp. 538. $1.75. A NATURAL PHILOSOPHY: Embracing the most recent Discoveries in

Physics. Adapted to use with or without Apparatus, and accompanied with Practical Exercises and 335 Illustrations. New Edition, revised and brought in all respects up to date. 12mo, pp. 450. $1.75.

ENTERED, according to Act of Congress, in the year 1866, by

D. APPLETON & COMPANY, in the Clerk's Office of the District Court of the United States, for the Southern

District of New York.

- Lena Malone

PREFACE.

The Third of our Series of Arithmetics, designed for all ordinary classes in our Public and Private Schools, is now presented to the public. The aim has been to make it comprehensive, clear, free from verbiage in its definitions and explanations, inductive in its development of the subject, and well adapted to the schoolroom.

It is believed that the study of Arithmetic, apart from its necessity as a practical branch, may be rendered invaluable as a mental discipline. Every device has been resorted to in this work to make it useful as a means of intellectual training, of teaching the young learner to reflect and reason, at the same time without requiring anything that is not fairly within his reach. Acting on this principle, the author has not laid down rules arbitrarily, but shown the reasons for them by means of preliminary analyses. He has also placed occasional questions or suggestions after examples, in the belief that such hints, starting the learner in the right direction, would encourage him to attempt the solution for himself, rather than apply for aid to his teacher,-a practice as destructive of self-reliance in the one as it is annoying to the other.

To impress principles on the mind, as well as to impart facility in operating, much practice is necessary; and, to secure this, numerous examples are presented, applying the rules in a great variety of ways. The answers in most cases are given, but, to test the learner, a few under almost every rule are omitted. Answers are apt to suggest the processes used; and, if they are invariably given, even the most faithful will unconsciously fall.

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