Elements of the Infinitesimal Calculus: With Numerous Examples and Applications to Analysis and Geometry (Classic Reprint)

The Infinitesimal Calculus is generally considered to be the most diffieiilt branch of pure mathematics to which the attention of the student is directed. It is certainly the most powerful instrument of investigation known to the mathematician, and its philosophy is as profound as its methods are far-reaching and comprehensive. But we believe that its difficulties, in so far as they are not purely algebraic, are due quite as much to the manner in which its first princ ples are usually exhibited, as to any inherent obscurity in the subject itself. In the preparation of the following treatise, the attempt has been made to remove all grounds for that feeling of uncertainty which often possesses the student at the very outset, and from which he rarely finds it possible afterward to extricate himself. With this end in view, considerable space has been devoted to an exposition of the doctrine of limits, which has been made the basis of both theD iiferential and the Integral Calculus. Many demonstrations might have been abridged, and apparently simplified, by the adoption of the ordinary method of infinitely small quantities; but this would have been, in the opinion of the writer, at the expense of a sound philosophy, for which, in a work intended primarily for educational purposes, the advantage of mere brevity could ofler no compensation.
(Typographical errors above are due to OCR software and don't occur in the book.)

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