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

Table of contents

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[171.] PROPOSITIO IV.
[172.] PROPOSITIO X.
[173.] Notæ in Propoſit. I.
[174.] Notæ in Propoſit. II.
[175.] Notæ in Propoſit. IV.
[176.] Notæ in Propoſit. X.
[177.] SECTIO SECVNDA Continens Propoſit. III. VI. VII. & IX. PROPOSITIO III.
[178.] PROPOSITIO VI.
[179.] PROPOSITIO VII.
[180.] PROPOSITIO IX.
[181.] Notæ in Propoſit. III.
[182.] Notæ in Propoſit. VI.
[183.] Notæ in Propoſit. VII.
[184.] Notæ in Propoſit. IX.
[185.] LEMMAI.
[186.] SECTIO TERTIA Continens Propoſit. V. & VIII. PROPOSITIO V.
[187.] PROPOSITIO VIII.
[188.] Notæ in Propoſit. V.
[189.] Notæ in Propoſit. VIII.
[190.] SECTIO QVARTA Continens Propoſit. XI. XII. XIII. & XIV. PROPOSITIO XI.
[191.] PROPOSITIO XII.
[192.] PROPOSITIO XIII.
[193.] PROPOSITIO XIV.
[194.] MONITVM.
[195.] LEMMA II.
[196.] COROLLARIVM.
[197.] LEMMA III.
[198.] LEMMA IV.
[199.] COROLLARIVM.
[200.] LEMMAV.
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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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