Page:The Analyst; or, a Discourse Addressed to an Infidel Mathematician.djvu/47

Rh XXIV. For the fuller illutration of this Point, I hall conider it in another light, and proceeding in finite Quantities to the Concluion, I hall only then make ue

of one Infiniteimal. Suppoe the traight Line MQ cuts the Curve AT in the Points R and S. Suppoe LR a Tangent at the Point R, AN the Abcie, NR and OS Ordinates. Let AN be produced to O, and RP be drawn parallel to NO. Suppofe AN = x, NR = y, NO = v, PS = z, the ubecant MN = S, Let the Equation y = xx expres the nature of the Curve: and uppoing y and x increaed by their finite Increments, we get y + z = xx + 2xv + vv: whence the former Rh