nnrr — nn (x-^ff = (E-+-Bx)-— ACxx— 2 CDx— FC, 

 quae aequatio euoluta ita fe habebit: 

 nnrr — n nff — 2 n nfx — nn x x 



= EE-FC-f-2(BE-CD)x+(BB-AC)xx, 



Hinc pateteffe debere i°.) nn — AC — BB, ideoque 

 n~-i/(AC — BB); 2°.) effe debet nnf^CD — BK, 

 ideoque / = ^^~^^ - ', 3°) vero neceffe eft vt fiat 



rr=ff-^-'-^. 

 vbi fi valores inuentos fubftituamus, prodibit : 



„ „ (CD — B E]2 ■ EE — FC 



(AC — iJB)2 "• AC — BB' 



liue 



CCDD — 2 ^CDE+ ACEE CF 



rr 



(AC — BBp AC — BB 



His valoribus inuentis area tota noftrae elliplis debet effe 

 — t: mnr r fm. b), vnde fada fubftitutione obtinebitur fe- 

 quens expreffio: 



(C D D - 2 B D E H- A E E) fin. r;j — '^ ^ ^"^' " 



(A^~^ /(AC-BB)' 



quae area etiam hoc modo exhiberi poteft: 



r /CDD-HAEE-2BDE F V 



71 iin. co / — \« 



i (AC-BBf >^(AC-BB)j 



Haec expreffio ideo maxime eft notatu digna, quod eius ope 

 omnium eUipfium . areae totae fatis expedite affignari pof- 

 funt ex fola aequatione inter coordinatas, fiue eae fint re- 

 ftangidae fiue obUquangLilae. Ita fi habeatur aequatio no- 

 tiffima pro eUipfi : ffxx-hggyy~ffgg, inter coordi- 

 NouaAUa Acad. Imp, Sdent. Jom. /X S natas 



