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ARITHMETIC:

ON THE

INDUCTIVE SYSTEM,

BY

ANALYSIS AND SYNTHESIS.

CONTAINING

LUCID DEMONSTRATIONS OF THE RULES, ARITHMETICAL
IMPROVEMENTS, AND CURIOSITIES, MENSURATION OF PLANEN

AND SOLIDS, PHILOSOPHICAL PROBLEMS, ETC. ETC.

BEING ALSO,

A KEY

TO ANY ARITHMETICAL WORK,

ON THE

PRINCIPLES OF ASSOCIATION AND VISIBLE ILLUSTRATION,

WITH THIRTY ENGRAVINGS:

FOR THE USE OF
SCHOOLS AND ACADEMIES

IN THE UNITED STATES.

BY CHARLES WATERHOUSE, A. M.

STEREOTYPE EDITION.

SOLD BY BOOKSELLERS GENERALLY.

Peitsrum

HARYAD COLLEGE LIBRARY

BY EXCHANGE

FEL 12 1932
PROSPECTUS.

TAE author of this treatise proposes to publish a monthly periodical, termed - The Mathematical Directory," commencing January 1, A. D. 1846.

It is designed as a Key and Supplement to the works of the various authors on the different branches of the mathematics.

It will be written in simple and perspicuous language, and illustrated by facts and experiments, made level to the capacity of ordinary minds.

Engravings, to assist the illustrations, will be interspersed throughout the numbers.

Competent assistance is engaged to effect this object, but those disposed to contribute matter for the Directory, are assured it will be gratefully received and considered.

Each number will be twenty-four pages, octavo, at two dollars

a year.

It will not

ot be published except there be a sufficient number of subscriptions

Letters, postage paid, containing money or matter for the work, will be punctually attended to, or the money refunded.

Address WATERHOUSE & Co., Portland, (Me.)

Editors noticing the above for three months, (weekly,) shall receive the several numbers, when published.

NOTE.—Just published--An Introduction to any Arithmetic. (Price-6 cts.)

Entered according to act of Congress, A. D. 1844,

By CHARLES WATERHOUSE,
In the Clerk's Office of the District Court of Maine.

PREFACE.

In offering this treatise to the public, we would suggest the following as the reasot.

I. Because the community is taxed too much for defective works of little or no merit, which are crowded upon it by the avaricious and inconsiderate book-monger.

II. Because there are too many works on this science, which it is believed can be supplanted by a single treatise, if it be the cheapest and best. This book was calculated expressly for either, the best, or the CHEAPEST, being offered at about half for which others are sold. If it is also the best, we have no fear of any objections being offered against it-its rapid and unparalleled introduction already implies this. By it is enjoyed what is very desirable, an entire uniformity.

III. A large part of those arbitrary rules given in most textbooks on arithmetic, are erroneous, only approximating to the required result.

IV. Much valuable and necessary matter has been omitted, which should have been found in those works.

V. Also, abstruse matter has been given in such, and that without containing any precedent for its solution.

VI. Bad arrangement, by endeavoring to render the work more immediately practical.

This would most certainly render it much less practical, as it would necessarily lead the scholar into a habit of performing the operations, without comprehending the principles, which are their basis.

For this reason also, much of arithmetic is practised at school, and but little learned, for the scholar is put to cyphering without understanding the reason of the rule, as it cannot be properly demonstrated, unless it is taken in its natural order of the science. But by a tedious course of practice, perhaps the pupil acquires only a mechanical dexterity of performing the operations, which is soon forgot.

VII. A want of demonstrations of rules founded on axioms and illustrations of much other matter, is a source of no inconsiderable complaint among our school teachers.

The preceding kind of frame-work serves only to lead the pupil over the science, but not into it.

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