Page:The Analyst; or, a Discourse Addressed to an Infidel Mathematician.djvu/76

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The Analyst.

ceeds the Particle Lm. And in general, as the Iſochronal Velocities deſcribing the Particles of MN exceed the Iſochronal Velocities deſcribing the Particles of LM, even ſo the Particles of the former exceed the correſpondent Particles of the latter. And this will hold, be the ſaid Particles ever ſo ſmall. MN therefore will exceed LM if they are both taken in their naſcent States: and that exceſs will be proportional to the exceſs of the Velocity b above the Velocity a. Hence we may ſee that this laſt account of Fluxions comes, in the upſhot, to the ſame thing with the firſt[1].


XLII. But notwithſtanding what hath been ſaid it muſt ſtill be acknowledged, that the finite Particles Lm or Mp, though taken ever ſo ſmall, are not proportional to the Velocities a and b; but each to a Series of Velocities changing every Moment, or which is the ſame thing, to an accelerated Velocity, by which it is generated, during a certain minute Particle of time: That the naſcent beginnings or evaneſcent endings of finite Quantities

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