Page:The Analyst; or, a Discourse Addressed to an Infidel Mathematician.djvu/55

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The Analyst.
45

the other Side of the Equation: So it muſt be allowed a very logical and juſt Method of arguing, to conclude that if from Equals either nothing or equal Quantities are ſubducted, they ſhall ſtill remain equal. And this is a true Reaſon why no Error is at laſt produced by the rejecting of o. Which therefore muſt not be aſcribed to the Doctrine of Differences, or Infiniteſimals, or evaneſcent Quantities, or Momentums, or Fluxions.


XXVIII. Suppoſe the Caſe to be general, and that xn is equal to the Area ABC whence by the Method of Fluxions the Ordinate is found which we admit for true, and ſhall inquire how it is arrived at. Now if we are content to come at the Concluſion in a ſummary way, by ſuppoſing that the Ratio of the Fluxions of x and xn are found [1] to be 1 and , and that the Ordinate of the Area is conſidered as its Fluxion; we ſhall not ſo clearly ſee our way, or perceive how the truth comes out, that Method as we have ſhewed before being ob-

ſcure