Page:The Analyst; or, a Discourse Addressed to an Infidel Mathematician.djvu/52

This page has been validated.
42
The Analyst.

as a Knack, an Art or rather an Artifice, but not a ſcientific Demonſtration.


XXVI. The Doctrine premiſed may be farther illuſtrated by the following ſimple and eaſy Caſe, wherein I ſhall proceed by evaneſcent Increments. Suppofe AB = x,

BC = y, BD = o, and that xx is equal to the Area ABC: It is propoſed to find the Ordinate y or BC. When x by flowing becomes x + o, then xx becomes xx + 2xo + oo: And the Area ABC becomes ADH, and the Increment of xx will be equal to BDHC the Increment of the

Area,