Page:The Analyst; or, a Discourse Addressed to an Infidel Mathematician.djvu/48

38 Equation being ubducted there remains z = 2xv + vv. And by reaon of imilar Triangles PS : PR :: NR : NM, i.e. z : v :: y : s = $$\frac{vy}{z}$$ wherein if for y and z we ubtitute their values, we get $$\frac{vxx}{2xv+vv}$$. And uppoing NO to be infinitely diminihed, the ubecant NM will in that cae coincide with the ubtangent NL, and v as an Infiniteimal may be rejected, whence it follows that $$S = NL = \frac{xx}{2x} = \frac{x}{2}$$ which is the true value of the Subtangent. And ince this was obtained by one only error, i. e. by once rejecting one only Infiniteimal, it hould eem, contrary to what hath been aid, that an infiniteimal Quantity or Difference may be neglected or thrown away, and the Concluion nevertheles be accurately true, although there was no double mitake or rectifying of one error by another, as in the firt Cae. But if this Point be throughly conidered, we hall find there is even here a double mitake, and that one compenates or rectifies the other. For in the Firt