AN ELEMENTARY ARITHMETIC, DESIGNED FOR ACADEMIES AND SCHOOLS: ALSO SERVING AS AN INTRODUCTION TO THE HIGHER ARITHMETIC, BY GEORGE R. PERKINS, A. M. PRINCIPAL AND PROFESSOR OF MATHEMATICS IN THE NORMAL SCHOOL OF THE STATE STEREOTYPE EDITION, REVISED AND IMPROVED. NEW YORK: PUBLISHED BY D. APPLETON AND CO. UTICA: HAWLEY, FULLER AND CO. HARVARD ENTERED, according to Act of Congress, in the year 1949 By George R. Perkins, in the Clerk's Office of the Northern District of New York. 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 Arithmetic, 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 filly 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 |