Publisher's Synopsis
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.
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