Page:The Analyst; or, a Discourse Addressed to an Infidel Mathematician.djvu/71

Rh on: that a is the Velocity of LM in tatu nacenti, and b, c, d, e, &c. are the Velocities of the Increments MN, NO, OP, &c. in their repective nacent etates. You may proceed, and conider thee Velocities themelves as flowing or increaing Quantities, taking the Velocities of the Velocities, and the Velocities of the Velocities of the Velocities, i. e. the firt, econd, third, &c. Velocities ad infinitum: which ucceeding Series of Velocities may be thus expreed. a. b — a. c — 2b + a. d — 3c + 3b - a &c. which you may call by the names of firt, econd, third, fourth Fluxions. And for an apter Expreion you may denote the variable flowing Line KL, KM, KN, &c. by the Letter x; and the firt Fluxions by $$\dot{x}$$, the econd by $$\ddot{x}$$, the third by $$\dot{\ddot{x}}$$, and o on ad infinitum.

XXXVII. Nothing is eaier than to aign Names, Signs, or Expreions to thee Fluxions, and it is not difficult to compute and operate by means of uch Signs. But it will be found much more difficult, to omit the Signs and yet retain in our Minds