Page:The Analyst; or, a Discourse Addressed to an Infidel Mathematician.djvu/21

Rh our modern Analyts are not content to conider only the Differences of finite Quantities: they alo conider the Differences of thoe Differences, and the Differences of the Differences of the firt Differences. And o on ad infinitum. That is, they conider Quantities infinitely les than the leat dicernible Quantity; and others infinitely les than thoe infinitely mall ones; and till others infinitely les than the preceding Infiniteimals, and o on without end pr limit. Inomuch that we are to admit an infinite ucceion of Infiniteimals, each infinitely les than the foregoing, and infinitely greater than the following. As there are firt, econd, third, fourth, fifth, &c. Fluxions, o there are Differences, firt, econd, third, fourth, &c. in an infinite Progreion towards nothing, which you till approach and never arrive at. And (which is mot trange) although you hould take a Million of Millions of thee Infiniteimals, each whereof is uppoed infinitely greater than ome other real Magnitude, and add them to the leat given Quantity, it hall be never the bigger. For this is one of the modet potulata of our