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Ellen A. Store

E. Lpingim Mocean ,"IB70

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PRACTICAL ARITHMETIC.

BY

G. P. QUACKENBOS, LL. D.,

AUTHOR OP

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"Á PRINARY ARITHMETIC; " AN ELEMENTARY ARITHMETIO; AX ENGLISH GRAX
MAR;

FIRST LESSONS IN COMPOSITION; ADVANCED COURSE OP COMPO-
BITION AND RIETORIC;
" " A NATURAL PHILOSOPHY ;

" ILLUSTRATED
SCHOOL HISTORY OF THE UNITED STATES;” “PRIMARY HIS-

TORY OF THE UNITED STATES ; " ETO.

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90, 92 & 94 GRAND ST.
PHILADELPHIA: ELDREDGE & BROTHER

1869.

Fructus ep.720

HARVARD";.'GE L'.

uiti OF GEORGE ARTHUR ?

JANUARY 25, 154

By the same Author:

A PRIMARY ARITHMETIC: Handsomely Illustrated. 16mo, pp. 108. 10 cta
AN ELEMENTARY ARITHMETIC: 12mo, pp. 144. 60 cts.
FIRST BOOK IN GRAMMAR: 16mo, pp. 120. 50 cts.
AN ENGLISH GRAMMAR: 12mo, pp. 288. $1.20.
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. $1.75. PRIMARY HISTORY OF THE UNITED STATES: Made easy and interosting for Beginners. Child's Quarto, splendidly illustrated, pp. 192

75 cts. ILLUSTRATED SCHOOL HISTORY OF THE UNITED STATES: Em

bracing a full Account of the Aborigines, Biographical Notices of Distinguished

len, numerous Maps, Plans of Battle-fields, and Pictorial Illustrations. 12mo,

pp. 538. $2.00. A NATURAL PHILOSOPHY: Embracing the most recent Discoveries in Physics.

Adapted to use with or without Apparatus. and accompanied with Practical Exercises and 835 Illustrations. 12mo, pp. 450. $2.00.

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.

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 school

room.

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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