Subſecant when v vaniſhes or becomes nothing.
XXV. Upon the whole I obſerve, Firſt, that v can never be nothing ſo long as there is a ſecant. Secondly, That the ſame Line cannot be both tangent and ſecant. Thirdly, that when v or NO[1] vaniſheth, PS and SR do alſo vaniſh, and with them the proportionality of the ſimilar Triangles. Conſequently the whole Expreſſion, which was obtained by means thereof and grounded thereupon, vaniſheth when v vaniſheth. Fourthly, that the Method for finding Secants or the Expreſſion of Secants, be it ever ſo general, cannot in common ſenſe extend any further than to all Secants whatſoever: and, as it neceſſarily ſuppoſeth ſimilar Triangles, it cannot be ſuppoſed to take place where there are not ſimilar Triangles. Fifthly, that the Subſecant will always be leſs than the Subtangent, and can never coincide with it; which Coincidence to ſuppoſe would be abſurd; for it would be ſuppoſing, the ſame Line at the ſame time to cut and
- ↑ See the foregoing Figure,
