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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[11.] PRÆFATIO AD LECTOREM.
[12.] INDEX
[13.] APOLLONII PERGAEI CONICORVM LIB. V. DEFINITIONES. I.
[14.] II.
[15.] III.
[16.] IV.
[17.] V.
[18.] VI.
[19.] VII.
[20.] VIII.
[21.] IX.
[22.] X.
[23.] XI.
[24.] XII.
[25.] XIII.
[26.] XIV.
[27.] XV.
[28.] XIV.
[29.] NOTÆ.
[30.] SECTIO PRIMA Continens propoſitiones I. II. & III. Apollonij. PROPOSITIO I.
[31.] PROPOS. II.
[32.] PROPOS. III.
[33.] Notæ in Propoſitionem primam.
[34.] Notæ in Propoſitionem ſecundam.
[35.] Notæ in Propoſitionem tertiam.
[36.] SECTIO SECVNDA Continens propoſitiones IV. V. VI. Apollonij.
[37.] PROPOSITIO IV.
[38.] PROPOSITIO V. & VI.
[39.] Notæ in pro poſitionem quartam.
[40.] Notæ in propoſitionem quintam.
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page |< < (70) of 458 > >|
10870Apollonij Pergæi
SECTIO VNDECIMA
Continens Propoſ. LXVIII. LXIX. LXX.
& 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.
Iuncta enim A E,
22b88[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.
89[Figure 89]

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