Page:Œuvres de Fermat, Tannery, tome 1, 1891.djvu/200

Ut autem plenius innotescat utriusque hujus nostræ methodi usum esse generalem, dispiciamus novas æquationum correlatarum species de quibus < tacet > Vieta, ex libro Apollonii De determinata sectione (propositione apud Pappum 6r Libri VII), cujus determinationes ipse Pappus innuit et profitetur difficiles ^[1].

Sit recta BDEF (fig. 97), in qud data puncta B, D, E, F. Intrapuncta D et E sumendum punctum N, ut rectangulum BNF ad rectangulumn DNE habeat minimam rationem.

Fig. 97.

Recta DE vocetur B, DF vocetur Z, BD vocetur D; ponatur DN esse A: ergo

ratio DinZ-Din A +Zin A-Aq. ad Bin A-Aq. est minima.

Ratio correlata similis et æqualis esto

D in Z-D in E+Z in E-Eq. ad B in E-Eq.,

juxta priorem methodum. Factum itaque sub mediis equabitur facto sub extremis: hoc est, ex una parte,

D in Z in B in E - Din Zin Eq. - Din Ain B inE + D in A in Eq. + Z in A inB in E- Zin A inEq. -Aq. in B in E Aq. inEq.,

ex altera parte,

D in Z in B in A - D in Z in Aq. -D in E in B in A + D in E in Aq. + Z in E in B in A - Z in E in Aq. -Eq. in B in A Eq. in Aq.

Demptis communibus et facta congrua metathesi,

D in Z in B in A - D in Z in B in E + D in E in Aq. - D in A in Eq. -Z in E in Aq. + Z in A in Eq. + Aq. in B in E - Eq. in B in A æquabitur D in Z in Aq. - D in Z in Eq.

1. Voir plus haut la même question traitée, page 142.