(i5o) ==3 



^, j* — c p . c f^ vndc ob c a = C A, omnino concluditur forc 

 C P . C F — f/) . c/. At ob QR paralklam ipfi G P et qr 

 parallelam ipfi gp ^t 



CR:CP = CG:CQi=:DQ:DE et 



D F : C R =z C F : D Q, 

 quoriim pofterius demonftratur vti §. 6. flnflum eft, crit igi- 

 tur ex aequo perturbate DF:CPr=CF:DE, vnde colli- 

 gitur DF . DE = C P . C F, et quum fimili ratione fiat cp.cf 



— df . d Cy crit omnino D¥.DE=:df.de. Tum vero 

 quum fit 



G M^ : C O» 1= Q C' - G C' : Q C rz Q D* - D E' : Q D% 

 tt fimili modo 



g m" : C O^ :=: q c* — g c- : q c- zn q d^ — d e' : q d^ , 

 ob GM=zg?n et Q^V z=: q d erit C O" (QD' — D E') =z 

 c 0'' (q d^ — c) O' hinc quum pcr Lemma I. fit C O* rz: Q D' 



— D ¥' et c 0' z=: q d' — df% ob D F . D E :=: 3/. 5 f , iit 

 quoque D E' H- D F' = 3 f" -r- 3/% vnde demum concludi- 

 tur efle D F n: df; D E rr 3 f ; et C O z= c o. Pro fegmen- 

 tis autem Ellipticis NQMN, nqmn quum ordinatarum ra- 

 tio fit ea aequalitatis, erunt ifta fegmenta in ratione com>po/ita 

 abfciffarum QG, q g.> et finuum ang. QGE, qge., ideoque 

 ctiam vt producT:a Q E fm. QEG, qeiaw.qge.i vel fimplici- 

 ter vt fin. QE G : fin.^ e ^, quia Q^E — qe. Sunt \ero quo- 

 que triangula N F M, nfm in eadem ratione, proinde inte- 

 ger fedor EUipticus NFMQ ad fedorem nfmq., vt fin. 

 Q E G : fin. ^ ^ ^ = fin. Q D C : fin. ^ a <r :zi ^ : ^ 1=: C H : <• ^, 



ob C O zzic 0. 



§. 10. Quicunque ad tenorem quo demonftrationcs 

 propofitae procedunt, animum aduerteie voluerit, facile per- 

 Ipiciet easdcm loci adhibita mutatione ad Hyperbolas aeque 



ac 



