Beek: See 17

A

PRACTICAL ARITHMETIC.

BY

G. P. QUACKENBOS, LL. D.,

AUTHOR OF

66

99 66
AN ELEMENTARY ARITHMETIC;

"A PRIMARY ARITHMET1;" 66
AN ENGLISH GRAM-
MAR; FIRST LESSONS IN COMPOSITION;" "ADVANCED COURSE OF COMPO-
SITION AND RHETORIC; A NATURAL PHILOSOPHY; 19 ILLUSTRATED

99.66

SCHOOL HISTORY OF THE UNITED STATES; """PRIMARY HIS-

EducT 118.72.723

HARVARD COLLEOR LIBRARY

BY EXCHANGE

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 in 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 full Account of the Aborigines, Biographical Notices of Distin-
guished Men, numerous Maps, Plans of Battle-fields, 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 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