Page:The Analyst; or, a Discourse Addressed to an Infidel Mathematician.djvu/73

Rh the econd the Velocities of the econd Differences, the third Fluxions the Velocities of the third Differences, and o on ad infinitum. But not to mention the inurmountable difficulty of admitting or conceiving Infiniteimals, and Infiniteimals of Infiniteimals, &c. it is evident that this notion of Fluxions would not conit with the great Author's view; who held that the minutet Quantity ought not to be neglected, that therefore the Doctrine of Infiniteimal Differences was not to be admitted in Geometry, and who plainly appears to have introduced the ue of Velocities or Fluxions, on purpoe to exclude or do without them.

XXXIX. To others it may poibly eem, that we hould form a juter Idea of Fluxions, by auming the finite unequal iochronal Increments KL, LM, MN, &c. and conidering them in tatu nacenti, alo their Increments in tatu nacenti, and the nacent Increments of thoe Increments, and o on, uppoing the firt nacent Increments to be proportional to the firt Fluxions or Velocities, the nacent Increments of thoe Increments to be  tional