Page:The Analyst; or, a Discourse Addressed to an Infidel Mathematician.djvu/49

Rh firt place, it was uppoed, that when NO is infinitely diminihed or becomes an Infiniteimal, then the Subecant NM becomes equal to the Subtangent NL. But this is a plain mitake, for it is evident, that as a Secant cannot be a Tangent, o a Subecant cannot be a Subtangent. Be the Difference ever o mall, yet till there is a Difference. And if NO be infinitely mall, there will even then be an infinitely mall Difference between NM and NL. Therefore NM or S was too little for your uppoition, (when you uppoed it equal to NL) and this error was compenated by a econd error in throwing out v, which lat error made s bigger than its true value, and in lieu thereof gave the value of the Subtangent. This is the true State of the Cae, however it may be diguied. And to this in reality it amounts, and is at bottom the ame thing, if we hould pretend to find the Subtangent by having firt found, from the Equation of the Curve and imilar Triangles, a general Expreion for all Subecants, and then reducing the Subtangent under this general Rule, by conidering it as the Rh