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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[61.] LEMMA VII.
Page: 69 (31)
[62.] SECTIO OCTAVA Continens Prop. IL. L. LI. LII. LIII. Apoll.
Page: 70 (32)
[63.] PROPOSITIO IL. & L.
Page: 71 (33)
[64.] PROPOSITIO LI.
Page: 72 (34)
[65.] PROPOSITIO LII. LIII.
Page: 73 (35)
[66.] PROPOSITIO LIV. LV.
Page: 77 (39)
[67.] PROPOSITIO LVI.
Page: 77 (39)
[68.] PROPOSITIO LVII.
Page: 78 (40)
[69.] Notæ in Propoſit. IL. L.
Page: 78 (40)
[70.] Notæ in Propoſit. LI.
Page: 79 (41)
[71.] Demonſtratio ſecundæ partis. PROPOSITIONIS LI.
Page: 81 (43)
[72.] Notæ in Propoſ. LII. LIII.
Page: 83 (45)
[73.] Secunda pars buius propoſitionis, quam Apollonius non expoſuit hac ratione ſuppleri poteſt.
Page: 87 (49)
[74.] Notæ in Propoſ. LIV. LV.
Page: 92 (54)
[75.] Notæ in Propoſit. LVI.
Page: 93 (55)
[76.] LEMMA VIII.
Page: 95 (57)
[77.] Notæ in Propoſ. LVII.
Page: 96 (58)
[78.] SECTIO NONA Continens Propoſ. LVIII. LIX. LX. LXI. LXII. & LXIII.
Page: 98 (60)
[79.] PROPOSITIO LVIII.
Page: 98 (60)
[80.] PROPOSITIO LIX. LXII. & LXIII.
Page: 98 (60)
[81.] PROPOSITIO LX.
Page: 100 (62)
[82.] PROPOSITIO LXI.
Page: 100 (62)
[83.] Notæ in Propoſit. LVIII.
Page: 101 (63)
[84.] Notæ in Propoſit. LIX. LXII. & LXIII.
Page: 102 (64)
[85.] Notæ in Propoſit. LX.
Page: 103 (65)
[86.] Notæ in Propoſit. LXI.
Page: 103 (65)
[87.] SECTIO DECIMA Continens Propof. XXXXIV. XXXXV. Apollonij.
Page: 105 (67)
[88.] PROPOSITIO XXXXIV.
Page: 105 (67)
[89.] PROPOSITIO XXXXV.
Page: 106 (68)
[90.] Notæ in Propoſ. XXXXIV.
Page: 106 (68)
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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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