An Elementary Treatise on the Differential: Calculus, Containing the Theory of Plane Curves, With Numerous Examples (Classic Reprint)

Treatise I have adopted the method of Limiting Eatios as my basis; at the same time the co ordinate method of Infinitesimals or Differentials has been largely employed. In this latter respect I have followed in the steps of all the great writers on the Calculus, from Newton and Leibnitz, its inventors, down to Bertrand, the author of the latest great treatise on the subject. An exclusive adherence to the method of Differential Coefficients is by no means necessary for clearness 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 advanced applications of the Calculus, which we find in such works as theM ecanique Celeste of Laplace and theM ecanique Analytique of Lagrange, the investigations are all conducted on the method of I nfinitesimals. The principles on which this method is founded are given in a concise form in A rts. 38 and 39.
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