Page:The Analyst; or, a Discourse Addressed to an Infidel Mathematician.djvu/51

Rh not to cut another given Line, which is a manifet Contradiction, uch as ubverts the Hypotheis and gives a Demontration of its Falhood. Sixthly, If this be not admitted, I demand a Reaon why any other apagogical Demontration, or Demontration ad aburdum hould be admitted in Geometry rather than this: Or that ome real Difference be aigned between this and others as uch. Seventhly, I oberve that it is ophitical to uppoe NO or RP, PS, and SR to be finite real Lines in order to form the Triangle RPS, in order to obtain Proportions by imilar Triangles; and afterwards to uppoe there are no uch Lines, nor conequently imilar Triangles, and nevertheles to retain the Conequence of the firt Suppoition, after uch Suppoition hath been detroyed by a contrary one. Eighthly, That although, in the preent cae, by inconitent Suppoitions Truth may be obtained, yet that uch Truth is not demontrated: That uch Method is not conformable to the Rules of Logic and right Reaon: That, however ueful it may be, it mut be conidered only as a Preumption, as