Page:The Analyst; or, a Discourse Addressed to an Infidel Mathematician.djvu/72

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The Analyst.

Minds the things, which we ſuppoſe to be ſignified by them. To conſider the Exponents, whether Geometrical, or Algebraical, or Fluxionary, is no difficult Matter. But to form a preciſe Idea of a third Velocity for inſtance, in it ſelf and by it ſelf, Hoc opus, hic labor. Nor indeed is it an eaſy point, to form a clear and diſtinct Idea of any Velocity at all, excluſive of and preſcinding from all length of time and ſpace; as alſo from all Notes, Signs or Symbols whatſoever. This, if I may be allowed to judge of others by my ſelf, is impoſſible. To me it ſeems evident, that Meaſures and Signs are abſolutely neceſſary, in order to conceive or reaſon about Velocities; and that, conſequently, when we think to conceive the Velocities, ſimply and in themſelves, we are deluded by vain Abſtractions.


XXXVIII. It may perhaps be thought by ſome an eaſier Method of conceiving Fluxions, to ſuppoſe them the Velocities wherewith the infiniteſimal Differences are generated. So that the firſt Fluxions ſhall be the Velocities of the firſt Differences,

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