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AN

ELEMENTARY ARITHMETIC,

DESIGNED FOR

ACADEMIES AND SCHOOLS:

ALSO SERVING AS AN INTRODUCTION TO THE

HIGHER ARITHMETIC,

BY GEORGE R. PERKINS, LL.D.,

PRINCIPAL AND PROFESSOR OF MATHEMATICS IN THE NORMAL SCHOOL OF THE STATE &
NEW YORK; AUTHOR OF TREATISE ON ALGEBRA; ELEMENTS OF ALGEBRA,
HIGHER ARITHMETIC; GEOMETRY, ETC.

STEREOTYPE EDITION, REVISED AND IMPROVED.

NEW-YORK:

D. APPLETON & CO., 346 & 348 BROADWAY.

M.DCCC.LV.

MAKYAND COLLEGE LIBRARY

BY EXCHANGE FROM

NEW YORK STATE LIBRARY

FEB 27, 1932

ENTERED, according to Act of Congress, in the year 1849 By George R. Perkins,

in the Clerk's Office of the Northern District of New York.

3May17

Mrs. R.T. Saville

PUBLISHERS' NOTICE

IN offering the present edition of Perkins' Elementary Arithmetic to the public, the Publishers desire to call attention to what they deem the peculiar merits of the work.

I. They regard as a prominent feature of the book, the presence throughout of the distinguished mathematical mind of the Author. It is not everything labelled "an explanation," in an Archmetic, that brings reasons to view; nor every operation marked an "analysis" that reveals principles or essential relations. There is still a "lower deep" where the groundmatter lies; and this we think Professor Perkins has ploughed up. The examiner may select, at random, proofs of this radical excellence.

We, therefore, believe that the Arithmetic which we submit, is peculiarly adapted to discipline the minds of those who study it, in the science of Numbers, and to advance them to a higher level of intellectual capability; in short, to train them fitly for advanced departments in Mathematics.

We are confident that the present work will maintain a longer than usual hold on the interest of both teachers and pupils; for it is not, like a cistern, to be exhausted by a few drawings, but like nature's reservoirs, it has the fountain within itself.

II. The Publishers would present as another excellence of the book, its freedom from minute repetitional details which cum ber a page, and obstruct a pupil's progress. It is believed that no principle is left unelucidated; and that new light is thrown upon many, heretofore imperfectly illustrated. It is regarded as no small merit of the work, that it does not so dilute principles and crumble reasons as to enfeeble their

ower or obscure their clearness. There is such a thing as lebilitating a pupil's mind through excess of illustration; as nducing a passive reception rather than an active grasp of ruths. It is with the intellectual as with the physical system. The digestive process would be less complete, if he who eats hould be deprived of the action and the relish of chewing and swallowing his own food; so a true digestion of knowledge requires that the pupil should masticate his own intellectua. aliments. We think Professor Perkins' book is happily adapted 'o secure this result.

III. The general arrangement of the subjects treated is hought to be philosophical. Those are brought into con ¡unction which are related in idea. The subject of Fractions, of Decimals, of Interest, of Partial Payments, etc., will, in their perspicuousness and their thoroughness, commend themselves to the examiner.

The subject of Proportion and Ratio is presented with peculiar force; as also, in Equation of Payments, the method of finding the Cash Balance.

IV. The method of Extraction of the Cube Root is greatly preferable to the old method. It is far more concise and more comprehensive; saving nearly half the labor, and being anplicable, with little variation, to the extraction of all ro The new method is fully and beautifully explained in t work.

V. The properties of the significant figures, and the use of the zero, are, we think, philosophically and concisely presented.

VI. Lastly, we may say, no subject has been omitted on account of any inherent difficulty in elucidating it.

The Publishers take pleasure in the appearance of the Book, which certainly invites the interest of the schc lar.

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