Page:The Analyst; or, a Discourse Addressed to an Infidel Mathematician.djvu/67

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The Analyst.
57

to conceive ſeems quite impoſſible. Yet ſome there are, who, though they ſhrink at all other Myſteries, make no difficulty of their own, who ſtrain at a Gnat and ſwallow a Camel.


XXXV. I know not whether it be worth while to obſerve, that poſſibly ſome Men may hope to operate by Symbols and Suppoſitions, in ſuch ſort as to avoid the uſe of Fluxions, Momentums, and Infiniteſimals after the following manner. Suppoſe x to be one Abſciſs of a Curve, and z another Abſciſs of the ſame Curve. Suppoſe alſo that the reſpective Areas are xxx and zzz: and that zx is the Increment of the Abſciſs, and zzzxxx the Increment of the Area, without conſidering how great, or how ſmall thoſe Increments may be. Divide now zzzxxx by z - x and the Quotient will be zz + zx + xx: and, ſuppoſing that z and x are equal, this ſame Quotient will be 3xx which in that caſe is the Ordinate, which therefore may be thus obtained independently of Fluxions and Infiniteſimals. But herein is a direct Fallacy: for

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