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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[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)
[91.] Notæ in Propoſ. XLV.
Page: 107 (69)
[92.] SECTIO VNDECIMA Continens Propoſ. LXVIII. LXIX. LXX. & LXXI. Apollonij. PROPOSITIO LXVIII. LXIX.
Page: 108 (70)
[93.] PROPOSITIO LXX.
Page: 109 (71)
[94.] PROPOSITIO LXXI.
Page: 109 (71)
[95.] Notæ in Propoſit. LXVIII. LXIX. LXX. & LXXI.
Page: 109 (71)
[96.] SECTIO DVODECIMA Continens XXIX. XXX. XXXI. Propoſ. Appollonij.
Page: 110 (72)
[97.] Notæ in Propoſit. XXIX. XXX. & XXXI.
Page: 111 (73)
[98.] SECTIO DECIMATERTIA Continens Propoſ. LXIV. LXV. LXVI. LXVII. & LXXII. Apollonij. PROPOSITIO LXIV. LXV.
Page: 112 (74)
[99.] PROPOSITIO LXVI.
Page: 113 (75)
[100.] PROPOSITIO LXVII.
Page: 114 (76)
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page |< < (203) of 458 > >|
241203Conicor. Lib. VI. 274[Figure 274]
Notæ in Propoſit. XXI.
QVoniam G B ad B I, ſuppoſita eſt vt H E ad E K, & c. Quia L B
11a ad B G ex bypotheſi erat, vt M E ad E H, & inuertendo G B ad B I
erat vt H E ad E K; ergo ex æqualitate L B ad B I erit vt M E
ad E K; & per conuerſionem rationis B L ad L I erit vt E M ad M K.
Et propter ſimilitudinem duarum ſectionum N L ad A I, nempe L O
22b ad O I eſt, vt P M ad F K, nempe M Q ad Q K, & c. Quoniam duæ ſe-
ctiones N B, & P E ſimiles ſuppoſitæ ſunt, & axiũ abſciſſæ L B, M E, nec non
I B, K E ad latera recta B G,
275[Figure 275]Cc 2& H E proportionales ſunt; igitur N L ad A I eandem 33ex 12.
huius. portionem habebit, quàm P M ad D K: & quia triangula N L O, & A I O ſimilia ſunt pro- pter parallelas N L, & I A, pariterque triangula P M Q,& D K Q ſimilia ſunt; igitur L O ad O I erit vt N L ad I A; pariterque M Q ad Q K erit vt P M ad D I, ſeu vt N L ad A I: & propterea L O ad O I erit vt M Q ad QK.
Et ex æqualitate L O ad
44c L B erit vt Q M ad M E, ſed
L B ad L N eſt vt M E ad
M P, cum ex ſuppoſitione
ſectiones ſint ſimiles, &

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