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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[111.] Notæ in Propoſit. LXXII.
Page: 123 (85)
[112.] SECTIO DECIMAQVARTA Continens Propoſ. LXXIII. LXXIV. LXXV. LXXVI. & LXXVII. PROPOSITIO LXXIII.
Page: 126 (88)
[113.] PROPOSITO LXXIV.
Page: 128 (90)
[114.] PROPOSITO LXXV.
Page: 128 (90)
[115.] PROPOSITIO LXXVI.
Page: 129 (91)
[116.] PROPOSITIO LXXVII.
Page: 130 (92)
[117.] Notæ in Propoſit. LXXIII.
Page: 130 (92)
[118.] LEMMA XII.
Page: 130 (92)
[119.] Notæ in Propoſ. LXXIV.
Page: 134 (96)
[120.] Notæ in Propoſit. LXXV.
Page: 135 (97)
[121.] Notæ in Propoſ. LXXVI.
Page: 137 (99)
[122.] Notæ in Propoſit. LXXVII.
Page: 138 (100)
[123.] COROLLARIVM.
Page: 143 (105)
[124.] SECTIO DECIMAQVINTA Continens Propoſ. XXXXI. XXXXII. XXXXIII. Apollonij. PROPOSITIO XXXXI.
Page: 147 (109)
[125.] PROPOSITO XXXXII.
Page: 147 (109)
[126.] PROPOSITIO XXXXIII.
Page: 148 (110)
[127.] Notæ in Propoſ. XXXXI.
Page: 148 (110)
[128.] Notæ in Propoſ. XXXXII.
Page: 149 (111)
[129.] Notæ in Propoſit. XXXXIII.
Page: 149 (111)
[130.] SECTIO DECIMASEXTA Continens XVI. XVII. XVIII. Propoſ. Apollonij.
Page: 150 (112)
[131.] Notæ in Propoſit. XVI. XVII. XVIII.
Page: 152 (114)
[132.] SECTIO DECIMASEPTIMA Continens XIX. XX. XXI. XXII. XXIII. XXIV. & XXV. Propoſ. Apollonij. PROPOSITIO XIX.
Page: 154 (116)
[133.] PROPOSITIO XX. XXI. & XXII.
Page: 155 (117)
[134.] PROPOSITIO XXIII. & XXIV.
Page: 156 (118)
[135.] PROPOSITIO XXV.
Page: 157 (119)
[136.] Notæ in Propoſit. XIX.
Page: 157 (119)
[137.] Notæ in Propoſit. XX. XXI. XXII.
Page: 158 (120)
[138.] Notæ in Propoſ. XXIII. XXIV.
Page: 161 (123)
[139.] Notæ in Propoſ. XXXV.
Page: 161 (123)
[140.] SECTIO DECIMAOCTAVA Continens XXXII. XXXIII. XXXIV. XXXV. XXXVI. XXXVII. XXXVIII. XXXIX. XXXX. XXXXVII. XXXXVIII. Propoſit. Apollonij. PROPOSITIO XXXII.
Page: 162 (124)
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167129Conicor. Lib. V.
PROPOSITIO XXXXVIII.
T Res lineæ maximæ E F, G H,
11a164[Figure 164] I K ad vnum ellipſis quadrã-
tem A F B cadentens non cõueniunt
in vno puncto.
Alioquin cõueniant in O, & quia ſunt
lineæ maximæ erunt M K, H N, L F, li-
neæ breuiſſimæ (32. ex 5.) & conueniunt
in puncto O; quod eſt abſurdũ (54. ex 5.)
oſtenſum ergo eſt, quod fuerat propoſitũ.
Notæ in Propoſit. XXXII.
L Inea maxima ſecat tranſuerſam in pũ-
22a165[Figure 165] cto, cuius intercepta inter punctum
illud, & ſectionem, eſt linea breuiſſima,
& c. Verba, quæ in textu Arabico deſideran-
tur ſupplenda cenſui, vt æquiuocationes tolle-
rentur.
Quia G H eſt linea maxima, erit D A
33b ad A F, nempe B E ad B D, & c. Quia
in 22. huius oſtenſum eſt, lineæ maximæ G
H potentialem H O ſecare ſemiaxim minorẽ
A D in O, vt ſit D O ad O G in eadẽ propor-
tione figuræ axis minoris A C; ſcilicet erit,
vt D A ſemiaxis minor ad A F eius ſemie-
rectum; ſed vt A D ad A F, ita eſt B E ſe-
miſsis lateris recti axis tranſuerſi ad B D
ſemiſſem eiuſdem tranſuerſi; igitur D O ad
O G eandem proportionem habebit, quàm E
B ad B D; ſed propter parallelas N D, H O,
eſt N H ad H G, vt D O ad O G; pariter-
que propter parallelas D G, H P, erit N P ad P D, vt N H ad H G; & pro-
pterea N P ad P D eandem proportionem habebit, quàm D O ad O G, ſeu
quàm E B ad B D; & permutando D P ad P N erit, vt D B ad B E, ſeu vt
4415. huius. axis tranſuerſus ad eius, erectum; & propterea linea N H erit breuiſsima.
Notæ in Propoſit. XXXIII. XXXIV.
E Contra oſtendetur, quod duæ breuiſſimæ, ſi educantur ex parte ſuæ
55a originis ad rectum, fient duo maximi cum relatione ad rectum:

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