Examples and Solutions of the Differential Calculus, Vol. 1 of 2 (Classic Reprint)

Doctrine of Limits is now very generally adopted as the basis of theD ifferential and Integral Calculus. Of the methods which were formerly in use it may be advantageous to the mathematical student to glance at some of the most prominent. By inscribing successively in a circle, regular polygons of four, eight, sixteen, thirty-two, c. sides, we may at length suppose a polygon to be inscribed whose area shall be less than that of the circle by a quantity so small as to be unas signable. In this manner the area of the circle may be said to be exhausted. Hence, the method which was based upon this mode of operation was termed theM ethod of ExJ taustions. In the early part of the seventeenth century a work was published, in which all quantity was assumed to be composed of elements so small that it would be impossible to divide them. An infinite number of points in continued contact were supposed to form a line, an infinite number of lines to form a surface, and an infinite number of surfaces to form a solid.
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