Page:The Analyst; or, a Discourse Addressed to an Infidel Mathematician.djvu/50

40 Subecant when v vanihes or becomes nothing.

XXV. Upon the whole I oberve, Firt, that v can never be nothing o long as there is a ecant. Secondly, That the ame Line cannot be both tangent and ecant. Thirdly, that when v or NO vaniheth, PS and SR do alo vanih, and with them the proportionality of the imilar Triangles. Conequently the whole Expreion, which was obtained by means thereof and grounded thereupon, vaniheth when v vaniheth. Fourthly, that the Method for finding Secants or the Expreion of Secants, be it ever o general, cannot in common ene extend any further than to all Secants whatoever: and, as it necearily uppoeth imilar Triangles, it cannot be uppoed to take place where there are not imilar Triangles. Fifthly, that the Subecant will always be les than the Subtangent, and can never coincide with it; which Coincidence to uppoe would be aburd; for it would be uppoing, the ame Line at the ame time to cut and not