Page:Œuvres de Fermat, Tannery, tome 1, 1891.djvu/292

ct, vicissim et convertendo, erit

axis AC ad axem XF sive basis DC (ex suppositione) ad basim GF ut curva DOA ad curvam GIX.

Quod erat demonstrandum.

Propositio III.

Esto, in tertia figura (fig. 136), curva AO, cujus axis AC, basis CO, et ab ea intelligatur formari alia cturva ejulsdem e i e eti verticis, in qua applicatce silt senmper zi ratione applicatarllu prioris curvæ: sit nempe

ut basis CO ad basini CV, ita applicata BP prioris curvæ ad applicatam BR posterioris curvæ et ita applicata DE ad applicatam DN,

et sic in infinitum; si ad punctun quodlibet prioris curivo, uit 0, clucaflr tan gens OH cCinZ axe cozienieens in puncto H, et continuetur CO donlec occurral secrndce curvce in aV, aio rectanm, qual puncta V et H cot1jiC/g'it, Iangere sectndamn curcamn, et seNzper contingere at ttngentes correlater in ultratqule cutva cad idem punctlun axi occurrant.

Fig. 136 (3).

Ducantur enini applicatw BPR, DEN, occurrentes curvis in punctis,, E, N, et rectis 011O, VY productis in punctis Q, S, F, MI.

Si probaverimus rectam BS, supra rectan CV ductam, semper majorem esse recta BR, item rectam DM, inferius ductarn, esse etiam scmper rmajorem applicata DN, patebit rectam MVSH tangere secundam curvam in puncto V.