Page:The Analyst; or, a Discourse Addressed to an Infidel Mathematician.djvu/57

Rh algebraical Quantity to be an infinitely mall or evanecent Quantity, and therefore to be neglected, mut have produced an Error, had it not been for the curvilinear Spaces being equal thereto, and at the ame time ubducted from the other Part or Side of the Equation agreeably to the Axiom, If from Equals you ubduct Equals, the Remainders will be equal. For thoe Quantities which by the Analyts are aid to be neglected, or made to vanih, are in reality ubducted. If therefore the Concluion be true, it is abolutely neceary that the finite Space CFH be equal to the Remainder of the Increment expreed by $$\frac{nn-n}{2}oox^{n-2}$$ &c. equal I ay to the finite Remainder of a finite Increment.

XXIX. Therefore, be the Power what you pleae, there will arie on one Side an algebraical Expreion, on the other a geometrical Quantity, each of which naturally divides it elf into three Members: The algebraical or fluxionary Expreion, into one which includes neither the  preion