Excerpt from Elements of Analytical Geometry and of the Differential and Integral Calculus The following treatise on Analytical Geometry and the Cal culus constitutes the fourth volume of a course of Mathematics designed for Colleges and High Schools, and is prepared upon substantially the same model as the preceding volumes. It was written, not for mathematicians, nor for those who have a pe culiar talent or fondness for the mathematics, but rather for the mass of college students of average abilities. I have, there fore, labored to smooth down the asperities of the road so as not to discourage travelers of moderate strength and courage; but have purposely left some difficulties, to arouse the energies and strengthen the faculties of the beginner. In a course of liberal education, the primary object in studying the mathe maties should be the discipline of the mental powers. This discipline is alike important to the physician and the divine, the jurist and the statesman, and it is more effectually secured by mathematical studies than by any other method hitherto proposed. Hence the mathematics should occupy a prominent place in an education preparatory to either of the learned pro fessions. But, in order to secure the desired advantage, it is indispensable that the student should comprehend the reasons of the processes through which he is conducted. How can he be expected to learn the art of reasoning well, unless he see clearly the foundations of the principles which are taught? This remark applies to every branch of mathematical study, but perhaps to none with the same force as to the Differential and Integral Calculus. The principles of the Calculus are fur ther removed from the elementary conceptions of the mass of mankind than either Algebra, Geometry, or Trigonometry, and they require to be developed with corresponding care. It is quite possible for a student to learn the rules of the Calculus. 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.