MAXIMA ET MINIMA. 151 



Ut autem plenius innotescat utriusque hujus nostrse methodi usuni 

 esse generalem, dispiciamus novas sequationum correlatarum species 

 de quibus < tacet > Vieta, ex libro Apollonii De determinata sectione 

 (propositione apud Pappum 6t Libri VII), cujus determinationes ipse 

 Pappiis innuit et profitetur difficiles ('). 



Sit recta BDEF {fig. 97), in quâ datapuncta B, D, E, F. Intra puncta 

 D ei E sumendum punctuni N, ul rectangulum BNF ad rectaiiguliun DNE 

 haheat minimam rationem. 



Fig- 97- 

 ^^ ^ ^^ 



RectaDE voceturfi, DFvoceturZ, BD vocetur D; ponatur DN esse .4 : 

 ergo 



ratio D'inZ — DmA-\-Z\nA — Aq. ad BmA — Aq. esl minima. 



Ratio correlata similis et aequalis esto 



D\nZ~D\nE + Z\nE — Eq. ad BinE-Erj., 



juxta priorem methodum. Factum itaque sub mediis aequabitur facto 

 sub extremis : hoc est, ex una parte, 



DinZinBln £" — D'in Z in Eq. — £>'m Ain BinE -\- D in A in Et/. 

 -+■ Zin AinBin E — Z in Ain Eq. — Aq. in BinE -¥ Aq. in Eq., 



ex altéra parte, 



D in Z in B in .1 — Z> in Z in Aq. — DinE in Bin A + Din E in Aq. 

 -I- Z in £" in 5 in /l — Z in £" in Aq. — Eq. in B in A -+- Eq. in Aq. 



Demptis communibus et facta congrua metathesi, 



/> in Z in // in .4 — i» in Z in BinE -^D in E in Aq. — DinA in Eq. 

 — Zin£'in Aq. -y- Zin A in Eq. + Aq. in B in E — Eq. in Z?in A 

 aequabitur D in Z in Aq. — Din Zin Eq. 



(1) f^uir plus haut la même question traitée, page 142. 



