An Elementary Treatise on the Differential Calculus: In Which the Method of Limits Is (Classic Reprint)

The method of Limits is generally allowed to be the best and most natural basis upon which to found the principles of theD ifferential Calculus; in the following pages this method is exclusively adopted, no use whatever being made of series in the demonstration of fundamental propositions. The following is an outline of the work, which is by no means offered to the reader as a complete treatise on the subject, but merely as an exposition of its more prominent and useful principles. In Chap. I, certain terms, afterwards to be used, are defined and explained. In Chap. II the nature of a Limiting Value is fully set forth, and the important distinction (which ought never to be overlooked) between an actual and a limiting value is pointed out and illustrated hy examples. Chap. Ill contains a set of Lemmas, which arc necessary in order to render the use made of limiting values in theD ifferential Calculus perfectly legitimate; and here I have endeavoured to confine myself to what seems really essential. In Chap. IV certain important limiting values are obtained. Chap. Vcontains theE
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