('43) 



inde F(?.fa = CH*. Atqui eft 



fin. TQF: I =F^:FQ=:/a: /Q, hincqiie 



fin. TQF': I — Ff3./a: FQ./Q— C H* : C O'. 



Eadem autem atfeclio hunc quoque in modum demonftratur: 

 quia ert D C parallcla ipf: T Q, fit ang. T QF — Q D C, 

 atqui eft fin. Q D C : i ~ Q X : Q D. At per Piop. XX. Lib. 

 II. Elewcnt. Sinifoni eft parallclogrammum contentum diamerris 

 coniugatis QC, CO aequale ledangulo A C . H C. Atqui 

 iftud parallelogrammum aequatur reclangulo Q X . C O , hinc- 

 que omnino colligitur QX.CO ~CA. CH, ideoque 

 QX:CAi=CH:CO, vnde fiet 



fin. T Q D : I =: C H : C O. 



§. 4. Lemma. HI. In ElHpfi AHB axihus C A, Tab. IV. 

 C H defcripta.^ ducaniur a focis ad punitum eius quodcunque K S- ^* 

 lineae rcctae F K, f K , tuvique fi ex K ad axem principalem du- 

 catur perpendicularis K P, f/ Kf normalis ad Ellipfin quae axi in 

 ^ ociurrit , ^.v ^ i-ero in F Q perpendicularis ducatur ^ X , erit 



FK:F?=:FP:FXz=:CA:CF. 



Quia angulus F K/ in binas partes aequiles fecatur linea K^ 

 rormali ad Ellipfin in K, erit FK:/K— Ff:/^, hincque 

 F K : F K -r-/K — F f : F f -4-/?, et alternando F K : F ^ z=: 

 F K-h/K:F?-f-f?:=C A:CF. Et ob AKFPcvj^FX, 

 fit F P : F X in' F K : F ? — C A : C F. lam quia vt in Eh^ 

 Tfirntis Scclion. Conic. Sinifoni Lib. V. Prop. XXXI. demon- 

 ftrarur, e(l K X . C A ~ C H% hoc eft K X acqualis paramctro 

 principali Ellipfeos, deducitur hinc pcr modiim Corollurii 



F K . C A iz: (K X -4- F X) C A =z C li' -f- F P . F Ci 

 tum autem ob C H' — C A* — C F% erit 



FK.CAi;:CA'— CF*-i-FP.CF — CA'— CF.CP. 



llla 



