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

Lineæ vero breuiſſimæ, quæ ca-
dunt ad peripheriam ſectionis B
A, continent angulos minores,
quàm B C D, vtique non occur-
runt D F, & c. Ideſt: quia quælibet
breuiſsima ex puncto peripheriæ A B
ad axim ducta efſicit angulum propin-
quiorem vertici, minorem ipſo angulo
C; & propterea quælibet breuiſsima,
ad peripheriam A B extenſa ſecabit ne-
ceſſario ipſam B C vlterius productam
ad partes C: ſed prius oſtenſa fuit B
C parallela asymptoto D F; igitur quæ-
libet breuiſsima ad peripheriam A B
educta ideſt inter parallelas poſita non
occurret alteri æquidiſtantium D F ad partes F, ſed ad partes oppoſitas verſus
D; eo quod quælibet recta linea intra hyperbolam ducta non ſecat peripheriam ſe-
ctionis in ea parte, in qua continentem D F nõ ſecat; At quælibet alia breuiſsima
infra C B ducta, neceſſario efſiciet ad axim angulum maiorem, quàm C; & pro-
pterea vlterius producta ſecabit ipſam B C ad partes C; ſed quælibet breuiſsima
extra parallelas poſita quæ ſecat vnam æquidiſtantium B C, ſecabit quoq; reli-
quam ad eaſdem partes F C; quare prius ſectioni occurret, vt dictum eſt.

129.1.

0150-01
d
26. 27.
huius.
28. huius.
Conuerſ.
8. lib. 2.
26. 27.
huius.
28. huius.

130. SECTIO DECIMASEXTA
Continens XVI. XVII. XVIII. Propoſ.
Apollonij.

SI menſura comparata ſumpta fuerit in axe recto minore elli-
pſis, erit maximus ramorum ab eius origine egredientium,
& illi propinquior maior eſt remotiore: minimus vero ramorũ
eſt differentia recti, & comparatæ, & illi propinquior, minor
eſt remotiore, atque exceſſus quadrati comparatæ ſupra qua-
dratum cuiuſcunque rami aſſignati æqualis eſt exemplari appli-
cato ad abſciſſam illius rami, ſiue comparata ſit minor, aut
æqualis, aut maior recto.

130.1.

a

Sit D C rectus a-
xis minor ſectionis
ellipticæ A B C ſit-
que C I comparata,
& rami I H, I K, I
B, I L, I A, I D, & ſemiſſis erecti ſit C
F, & centrum E, &

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