Page:The Analyst; or, a Discourse Addressed to an Infidel Mathematician.djvu/80

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70
The Analyst.

may be eaſily conceived, in Lines, in Surfaces, in Species, to be continued without end or limit. But it will not be found ſo eaſy to conceive a Series, either of mere Velocities or of mere naſcent Increments, diſtinct therefrom and correſponding thereunto. Some perhaps may be led to think the Author intended a Series of Ordinates, wherein each Ordinate was the Fluxion of the preceding and Fluent of the following, i. e. that the Fluxion of one Ordinate was it ſelf the Ordinate of another Curve; and the Fluxion of this laſt Ordinate was the Ordinate of yet another Curve; and ſo on ad infinitum. But who can conceive how the Fluxion (whether Velocity or naſcent Increment) of an Ordinate ſhould be it ſelf an Ordinate? Or more than that each preceding Quantity or Fluent is related to its Subſequent or Fluxion, as the Area of a curvilinear Figure to its Ordinate; agreeably to what the Author remarks, that each preceding Quantity in ſuch Series is as the Area of a curvilinear Figure, whereof the Abſciſs is z, and the Ordinate is the following Quantity.

XLVII. Upon