Page:The Analyst; or, a Discourse Addressed to an Infidel Mathematician.djvu/53

From Wikisource
Jump to navigation Jump to search
This page has been validated.
The Analyst.
43

Area, i. e. to BCFD + CFH. And if we ſuppoſe the curvilinear Space CFH to be qoo, then 2xo + oo = yo + qoo which divided by o gives 2x + o = y + qo. And, ſuppoſing o to vaniſh, 2x = y, in which Caſe ACH will be a 'ſtraight Line, and the Areas ABC, CFH, Triangles. Now with regard to this Reaſoning, it hath been already remarked[1], that it is not legitimate or logical to ſuppoſe o to vaniſh, i. e. to be nothing, i. e. that there is no Increment, unleſs we reject at the ſame time with the Increment it ſelf every Conſequence of ſuch Increment, i. e. whatſoever could not be obtained but by ſuppoſing ſuch Increment. It muſt nevertheleſs be acknowledged, that the Problem is rightly ſolved, and the Concluſion true, to which we are led by this Method. It will therefore be asked, how comes it to paſs that the throwing out o is attended with no Error in the Concluſion? I anſwer, the true reaſon hereof is plainly this: Becauſe q being Unite, qo is equal to o: And therefore 2x + o - qo = y = 2x,

the
  1. Sect. 12 and 13. ſupra.