Page:The Analyst; or, a Discourse Addressed to an Infidel Mathematician.djvu/65

From Wikisource
Jump to navigation Jump to search
This page has been validated.
The Analyst.
55

proceeding is not clear nor your method ſcientific. For inſtance, it is ſuppoſed that AB being the Abſciſs, BC the Ordinate,

and VCH a Tangent of the Curve AC, Bb or CE the Increment of the Abſciſs, Ec the Increment of the Ordinate, which produced meets VH in the Point T, and Cc the Increment of the Curve. The right Line Cc being produced to K, there are formed three ſmall Triangles, the Rectilinear CEc, the Mixtilinear CEc, and the Rectilinear Triangle CET. It is evident theſe three Triangles are different from each other, the Rectilinear CEc being leſs than the Mixtilinear CEc, whoſe Sides are the three Increments abovementioned, and this ſtill leſs than the Triangle CET. It is ſuppoſed that the Ordinate bc moves into the place BC, ſo that the Point c is coincident with the Point C; and the right Line CK,

E 4
and