Excerpt from Algebra for Schools and Colleges As it has frequently been a part of the author's duty to ascertain what is really left of a course of mathematical study in the minds of those who have been through college, some hints on the best methods of study in connection with the present work may be excused. If asked to point out the greatest error in our usual system of mathematical instruction from the common school upward, he would reply that it con sisted in expending too much of the mental power of the student upon problems and exercises above his capacity. With the exception of the fundamental routine-operations, problems and exercises should be confined to insuring a proper understanding of the principles involved: this once ascertained, it is better that the student should go on rather than expend time in doing what it is certain he can do. Problems of some difficulty are found among the exercises of the present work; they are inserted rather to give the teacher a good choice from which to select than to require that any student should do them all. It would, the author conceives, be found an improvement on our usual system of teaching algebra and geometry successively if the analytic and the geometric courses of mathematics were pursued simultaneously. The former would include algebra and the calculus, the latter elementary geometry, trigonometry, and analytic geometry. The analytic course would then furnish methods for the geometric one, and the latter would furnish applications and illustrations for the analytic one. The Key to the work, which will be issued as soon as practicable, will contain not only the usual solutions, but the explanations and demonstra tions of the less familiar theorems, and a number of additional problems. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com 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.