9961Conicor. Lib. V.
76[Figure 76]
ſimiliter C L ad L E, vt proportio figuræ, &
producamus per L ip-
ſam O M parallelam A I F, & per F ipſam G M parallelam C E, & fa-
ciamus ſectionem H C B hyperbolen tranſeuntem per punctum C circa
114. lib. 2. continentes G M, O M, quæ occurret ſectioni A B (in ellipſi quidem vt
2256.
huius. demonſtrauimus) in hyberbola vero eo quod O M parallela axi D A in-
33b clinato ſubtendit, ſi producatur, angulum ſubſequentem continentiæ an-
gulum ſecabit A B, & corda, ſi producatur, occurret ſectioni; Ergo O
M ingreditur ſectionem A B, & ampliatur ſectio A B per extenſionem,
longè à duabus lineis O M, M G, & ſectio B C prope illas ducitur (deci-
4414. lib. 2. moſexta, ex ſecundo) igitur duæ ſectiones A B, C B ſibi occurrunt, vt
in B, & ducamus per B, C lineam occurrentem D F A in I, & G F in G;
Et quia B O æqualis eſt ipſi C G (octaua ex ſecundo) erit O N æqualis
55c ipſi M L, & O L ipſi N M; ergo O L, nempe N M, ſeu K F ad E I eſt,
vt C L ad C E, nempe D F ad D E, ergo K F ad E I eſt, vt D F
ad E D comparando homologorum ſummas in hyperbola, & eorundem
66d77Lem. 3. differentias in ellipſi, & iterum comparando antecedentes ad differen-
88Lem. 1. tias terminorum
77[Figure 77]
fiet D K ad K
I, vt D F ad F
E, quæ eſt vt
proportio figu-
ræ; igitur B I eſt
linea breuiſſima
(9. 10. ex quin-
to) & hoc erat
probandum.
ſam O M parallelam A I F, & per F ipſam G M parallelam C E, & fa-
ciamus ſectionem H C B hyperbolen tranſeuntem per punctum C circa
114. lib. 2. continentes G M, O M, quæ occurret ſectioni A B (in ellipſi quidem vt
2256.
huius. demonſtrauimus) in hyberbola vero eo quod O M parallela axi D A in-
33b clinato ſubtendit, ſi producatur, angulum ſubſequentem continentiæ an-
gulum ſecabit A B, & corda, ſi producatur, occurret ſectioni; Ergo O
M ingreditur ſectionem A B, & ampliatur ſectio A B per extenſionem,
longè à duabus lineis O M, M G, & ſectio B C prope illas ducitur (deci-
4414. lib. 2. moſexta, ex ſecundo) igitur duæ ſectiones A B, C B ſibi occurrunt, vt
in B, & ducamus per B, C lineam occurrentem D F A in I, & G F in G;
Et quia B O æqualis eſt ipſi C G (octaua ex ſecundo) erit O N æqualis
55c ipſi M L, & O L ipſi N M; ergo O L, nempe N M, ſeu K F ad E I eſt,
vt C L ad C E, nempe D F ad D E, ergo K F ad E I eſt, vt D F
ad E D comparando homologorum ſummas in hyperbola, & eorundem
66d77Lem. 3. differentias in ellipſi, & iterum comparando antecedentes ad differen-
88Lem. 1. tias terminorum
I, vt D F ad F
E, quæ eſt vt
proportio figu-
ræ; igitur B I eſt
linea breuiſſima
(9. 10. ex quin-
to) & hoc erat
probandum.