Elements of Algebra (Classic Reprint)

Excerpt from Elements of Algebra<br><br>In the preparation of this work the authors have followed their usual plan of attempting to allow the light of modern mathematics to shine in upon the old, and to do this by means of a text-book which shall be usable in American high schools, academies, and normal schools.<br><br>In general, the beaten paths have been followed, experience having developed these and having shown their safety and value. But where there is an unquestionable gain in departing from these paths the step has been taken. For example, the subject of factoring has recently attracted the attention it deserves; in fact, several writers have carried it to an unjustifiable extreme; but there are few text-books that mention the subject after the chapter is closed; it is taught with no applications, and the student is usually left with the idea that it has none. The authors have departed from this plan, and have followed the chapter with certain elementary applications, using the method in solving easy quadratic and higher equations, making much use of it in fractions, and not ceasing to review it and its applications until it has come to be a familiar and indispensable tool. By following such a scheme the student knows much of quadratics before he reaches the chapter on the subject, and he enters upon it with increased intelligence and confidence.<br><br>The arrangement of chapters has been the subject of considerable experiment of late. But the plan adopted in this work is, in general, based upon the following:<br><br>1. The new should grow out of the old, as the expressions of algebra out of those of arithmetic, the negative number out of familiar concepts, factors out of elementary functions, quadratic and higher equations out of factoring, the theory of indices out of the three fundamental laws for positive integral indices, the complex number out of the surd, and so on.<br><br>About the Publisher<br><br>Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com<br><br>This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.