Full text: Pergaeus, Apollonius: Apollonii Pergaei Conicorvm Lib. V. VI. VII. paraphraste Abalphato Asphahanensi

Aſſumpt. Liber. tũ O B, ſiue X S in parabola
æquale eſt rectangulo S FN,
ergo AO ad A C eſt vt qua-
dratum E B ad quadratum
O B, & propterea parallele-
pipedum, cuius baſis quadra-
tum O B, altitudo O A æ-
quale erit parallelepipedo ba-
ſe quadrato E B, altitudine
A C contento, quod erat
propoſitum.

383.1.

Prop. 52.
lib. 1.
Prop. 11.
lib. 1.
0450-01
Prop. 4. &
12. lib. 2.
Prop. 26.
lib. 1.
ex 1. & 2.
lib. 2.
Prop. 12.
lib. 2.
0451-01
Prop. 11.
lib. 1.

Ex hiſce propoſitionibus de-
ducit inſuper Eutocius aliqua,
quæ non omnino firma, & cer-
ta mihi videntur, nam ex eo
quod recta linea vt I X tangit
vtramq; coniſectionem (hyper-
bolen ſcilicet B X, & parabo-
len F X) in eodem puncto X
concludit hyperbolen interius
contingere parabolen quàm de-
inceps non ſecat ad eaſdem par-
tes axis illius. Hoc autem omnino
neceſſarium nõ [?] eſt ex demonſtra-
tis à me in prop. 20. 21. & 22. Adàit. lib. 6. Apoll. fieri
enim poteſt vt Parabole exte-
rius hyperbolen tangat in X, & poſtea hinc inde eam ſecet. Poteſt inſuper hyperbole ſecare eandem parabolam
in eodem puncto X, licet ambo in eodem puncto tangantur ab aliqua recta li-
nea, vt eſt I X; quod quidem adnotaſſe fuit operepretium.

384. FINIS.

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