Page:Œuvres de Fermat, Tannery, tome 1, 1891.djvu/146

idemque continget, licet homogenea omnino data Tequationibus misceantur.

Sit

Eq. cuale D in A.

In pracedenti figura, vertice N, circa diametrum NZ, describatur parabole, cujus rectum latus sit D, et applicatæ rectæ NP parallelse prsestabit propositum, ut patet.

Ponatur

Bq.- Aq.. Tq. DinE.

Ergo

B q.-DinE æquabitur A q.

Applicetur Bq. ad D et sit eequale D in R. Ergo

D in R - D in E æquabitur A q.

ideoque

D in(R-E) æquabitur Aq.

Ideoque hæc æquatio reducetur ad prsecedentem: recta quippe B -- E succedet ipsi E.

Fiat quippe (fig. 83) NM parallela ZI et æqualis R, et per pun ctum M3 ducatur MO parallela NZ: datur punctum M, et recta MO positione. In

Fig. 83.

hæ constructione, OI æquatur R - E: ergo D in 01 æquatur NZ quad., sive MO quad. Yertice M, circa diametrum MN, descripta parabole, cujus rectum latus D, et applicatæ ipsi NZ parallelx, prsestabit propositum, ut patet ex constructione.

Si

Bq. + A q. eq. D in E, D in E - Bq. aquabitur Aq.,