10870Apollonij Pergæi
SECTIO VNDECIMA
Continens Propoſ. LXVIII. LXIX. LXX.
& LXXI. Apollonij.
& LXXI. Apollonij.
PROPOSITIO LXVIII. LXIX.
SI occurrant duæ tangentes alicui ſectioni A B C, vt ſunt A
11a F, E F, vtique quod abſcinditur ex tangente proximiori
vertici ſectionis, qui eſt B minus eſt ſegmento abſciſſo ex alia,
nempe E F minor eſt, quàm A F.
11a F, E F, vtique quod abſcinditur ex tangente proximiori
vertici ſectionis, qui eſt B minus eſt ſegmento abſciſſo ex alia,
nempe E F minor eſt, quàm A F.
Iuncta enim A E,
22b
88[Figure 88]&
in parabola ex F
producta linea F I
parallela axi B D e-
rit illa diameter, bi-
fariam ſecans E A in
G (34. ex 2.) Simi-
3330. lib. 2. liter ex centro H pro-
ducamus H F G, quæ
eſt quoque diameter
(34. ex 2.) bifariam
44Ibidem. ſecans E A in G, &
ducamus A D in pa-
rabola, & hyperbola perpendicularem ſuper axim D B. Ergo angulus
A I G in parabola eſt rectus, & in hyperbola obtuſus; ergo F G A erit
obtuſus in illis omnibus; quare maior eſt, quàm angulus F G E, & A
G æqualis eſt ipſi G E, & F G communis; igitur E F minor eſt, quàm
F A.
22b
producta linea F I
parallela axi B D e-
rit illa diameter, bi-
fariam ſecans E A in
G (34. ex 2.) Simi-
3330. lib. 2. liter ex centro H pro-
ducamus H F G, quæ
eſt quoque diameter
(34. ex 2.) bifariam
44Ibidem. ſecans E A in G, &
ducamus A D in pa-
rabola, & hyperbola perpendicularem ſuper axim D B. Ergo angulus
A I G in parabola eſt rectus, & in hyperbola obtuſus; ergo F G A erit
obtuſus in illis omnibus; quare maior eſt, quàm angulus F G E, & A
G æqualis eſt ipſi G E, & F G communis; igitur E F minor eſt, quàm
F A.