Apollonius <Pergaeus> - Apollonii Pergaei Conicorvm Lib. V. VI. VII. paraphraste Abalphato Asphahanensi : nunc primum editi ; additvs in calce Archimedis assvmptorvm liber, ex codibvs arabicis mss Abrahamus Ecchellensis Maronita latinos reddidit, Jo. Alfonsvs Borellvs curam in geometricis versione contulit & [et] notas vberiores in vniuersum opus adiecit

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150112Apollonij Pergæi

Lineæ vero breuiſſimæ, quæ ca-

136[Figure 136]11d 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-
2226. 27.
huius. quiorem vertici, minorem ipſo angulo
C; & propterea quælibet breuiſsima,
ad peripheriam A B extenſa ſecabit ne-
3328. huius. 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-
44Conuerſ.
8. lib. 2.
26. 27.
huius.
28. huius. 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.

SECTIO DECIMASEXTA

Continens XVI. XVII. XVIII. Propoſ.
Apollonij.

SI menſura comparata ſumpta fuerit in axe recto minore elli-
55a 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.

Sit D C rectus a-

137[Figure 137] 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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