Excerpt from An Elementary Treatise on the Differential Calculus: Containing the Theory of Plane Curves, With Numerous Examples IN the following Treatise I have adopted the method of Limiting Ratios as my basis; at the same time the co ordinate method of Infinitesimals or Difierentials has been largely employed. In this latter respect I have followed in the steps of all the great writers on the Calculus, from N ewton and Leibnitz, its inventors, down to Bertrand, the author of the latest great treatise on the subject. Ah ex elusive adherence to the method of. Differential Coefficients is by no means necessary for eleamess and simplicity; and, indeed, I have found by experience that many fundamental investigations in Mechanics and Geometry are made more intelligible to beginners by the method of Differentials than by that of Differential Coefficients. While in the more ad vanced applications of the Calculus, Which we find in such works as the Mecam'que Celeste of Laplace and the Meca m'que Analytz'gue of Lagrange, the investigations are all conducted on the method of Infinitesimals. The principles on which this method is founded are given in a concise form in Arts. 38 and 39. 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.