not to cut another given Line, which is a manifeſt Contradiction, ſuch as ſubverts the Hypotheſis and gives a Demonſtration of its Falſhood. Sixthly, If this be not admitted, I demand a Reaſon why any other apagogical Demonſtration, or Demonſtration ad abſurdum ſhould be admitted in Geometry rather than this: Or that ſome real Difference be aſſigned between this and others as ſuch. Seventhly, I obſerve that it is ſophiſtical to ſuppoſe NO or RP, PS, and SR to be finite real Lines in order to form the Triangle RPS, in order to obtain Proportions by ſimilar Triangles; and afterwards to ſuppoſe there are no ſuch Lines, nor conſequently ſimilar Triangles, and nevertheleſs to retain the Conſequence of the firſt Suppoſition, after ſuch Suppoſition hath been deſtroyed by a contrary one. Eighthly, That although, in the preſent caſe, by inconſiſtent Suppoſitions Truth may be obtained, yet that ſuch Truth is not demonſtrated: That ſuch Method is not conformable to the Rules of Logic and right Reaſon: That, however uſeful it may be, it muſt be conſidered only as a Preſumption,
