I4(J tlSSERTATlO GEOMETRICA 



"hfn—nH-fnz^CD^-hCA". Q. E. D. 



Theorema. 



Fig. 3. §. 3. Sint EUipfeos axes dimidii CA , CD, et 



lemidi:imetri coniugatae quaecunque MC, CH : atque 

 redangulum fub dimidiis axibus aequale erit paralielg- 

 ^rammo fub dimidiis diametris coniugatis. 



Demonflratio. 



Per extremum diametri M ducatur tangensTME 

 crit haec parallela ipfi CH ; per extremum diametri H 

 ducatur alia tangens HE ; erit haec iam parallela ipfi 

 CM ; adeoque erit parallelogrammum fiib dimidiis dia^ 

 jnetris coniugatis CMEH. Ponantur denuo AC — m 

 CD — «, MCrzrtf, CH— (5', CP— x ; atque habebitur 

 (§. i)CP(.v): CA{m)— CA (»/) : CT( ^) ; PTzz 

 ^-x-VM—Via-x"), confequenter TM=:=y(^-H 

 a—zm^). Sed eft ex -natura Ellipfeos PM*(«*— a*): 

 C D* ( «* ) =r A P X P B ( ;«*— x* ) : A C* ( m'' ) , vnde deducitur 

 •^' — ~ J»-n ^ ; qui valor fubftitutus efRcit P M — 



V(w»-fi») j ^ ^ V^a^-fi*} > ^ * ^^ V(a^~n'j > 



Tel, ob m'-\-n'-a'-\-b' (§.2), eritTMzr^^^; 



adeoque pofito finu toto — i , erit finus T — — — 



j^-^y Porro in triangulo CTM eft CM(«):fin.T 



Wi^x_CT/ ii^^^v fin.CMT( ^ )=:fm.MCH 



:^fin.HCF, ob parallelas MEetCH. Demifla nunc 

 ex H perpendiculari HF in produftam MC, erit in 



txm.- 



