(i4a) 



Mncqiie AAlQa, Qaf fimilia et aequalk, qiiare IQrfQ 

 et FI ™ F Q4-/Q~ AB. lam fi iungatiir centrum El- 

 lipfeos C cum pmido a, linea re«fla C a, ob I a ~ a/ 

 et F C zi: fC , erit omnino parallela ipfi F I, et C a : F I 

 ™ C f- F/rr I : 2 , hinc C a m C A. In parallelogrammo 

 Q a C D erit igitur QDrrCa=CA. Tum vero ob F Q 

 izrQD— FD et FQH-Q/=2QD, fiet/Q — QD + FD 

 hincque 2FD=/Q-FQ. Denique ob FQ./Q=QD'-FD% 

 quia eil F Q . /Q = C O* (vide Simfon Eknmt : SeCiiQn, 

 Conkar. Lib. V. Prop. XXX.), erit omnino 

 QD^ — FD' = CO% 



§. 3. Lemma II. Eadem adhibita conJiruCtlone ae fu^ 

 pra, dico fore: 



fin. ang. TQF:i=AC:OC. 

 Ducantur ex centro C et foco F normales ad tangentem C U, 

 F|3, tumque per pundum Q normalis QV quae axi maiori 

 in V, diametro vero coniugatae in X occurrit, tumque ex Q 

 in axin maiorem demittatur perpendicularis QR. lam quia 

 in Elementis Sedlion. Conicar. paifim demonftratur efle CR:VR 

 r:CA':CH^ hincque CR :C V = C A^:CA^-CH^ = CA^:CF=; 

 tum vero quia eft CA:CR=:CT:CA, fit CA*=CR.CT, 

 hincoue CR:CV=:CR.CT:CF% ex quo omnino colli- 

 gitur' C V . C T =z C F% fiue C F : C V = C T : C F. Hinc 

 autem deducitur CF:CF-f-CVzr:CT:CT-}-CF, fiue 

 CF:/V==CT:fT, et alternando C F : C T =:/V :/T, 

 tumque C T — C F : C T ziz/T — /V :/T, id eft FT:CI 

 VT:/T. lam ob redas F(3, VQ, CU et /a inter fe 

 parallelas, habebitur F(3:VQrrCU:/a, vnde F(3./ar= 

 VQ.CU; ateft VQ.CUi=CH% ( Conf. Simfon Ele- 

 mem, SeSlion. Conic. Lib. V. Prop. Xlll. Coroh), erit pro- 



inde 



