Page:The Analyst; or, a Discourse Addressed to an Infidel Mathematician.djvu/46

From Wikisource
Jump to navigation Jump to search
This page has been validated.
36
The Analyst.

which themſelves are not accurate, it being a rule in Logic that Concluſio ſequitur partem debiliorem. Therefore I obſerve in the third place, that when the Concluſion is evident and the Premiſes obſcure, or the Concluſion accurate and the Premiſes inaccurate, we may ſafely pronounce that ſuch Concluſion is neither evident nor accurate, in virtue of thoſe obſcure inaccurate Premiſes or Principles; but in virtue of ſome other Principles which perhaps the Demonſtrator himſelf never knew or thought of. I obſerve in the laſt place, that in caſe the Differences are ſuppoſed finite Quantities ever ſo great, the Concluſion will nevertheleſs come out the ſame: inaſmuch as the rejected Quantities are legitimately thrown out, not for their ſmallneſs, but for another reaſon, to wit, becauſe of contrary errors, which deſtroying each other do upon the whole cauſe that nothing is really, though ſomething is apparently thrown out. And this Reaſon holds equally, with reſpect to Quantities finite as well as infiniteſimal, great as well as ſmall, a Foot or a Yard long as well as the minuteſt Increment.

XXIV. For