Page:The Analyst; or, a Discourse Addressed to an Infidel Mathematician.djvu/30

20 Propoition, a certain Point is uppoed, by virtue of which certain other Points are attained; and uch uppoed Point be it elf afterwards detroyed or rejected by a contrary Suppoition; in that cae, all the other Points, attained thereby and conequent thereupon, mut alo be detroyed and rejected, o as from thence forward to be no more uppoed or applied in the Demontration." This is o plain as to need no Proof.

XIII. Now the other Method of obtaining a Rule to find the Fluxion of any Power is as follows. Let the Quantity x flow uniformly, and be it propoed to find the Fluxion of xn. In the ame time that x by flowing becomes x + o, the Power xn becomes $$\overline{x + o}|^n$$, i. e. by the Method of infinite Series $$x^n + nox^{n-1} + \frac{nn-n}{2} oox^{n-2} + $$ &c. and the Increments o and $$nox^{n-1} + \frac{nn-n}{2} oox^{n-2} + $$ &c. are one to another as 1 to $$nx^{n-1} + \frac{nn-n}{2}ox^{n-2} + $$ &c. Let now the Increments vanih, and their lat Proportion will be 1 to $$nx^{n-1}$$. But it hould eem that