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

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

[91.] Notæ in Propoſ. XLV.

[92.] SECTIO VNDECIMA Continens Propoſ. LXVIII. LXIX. LXX. & LXXI. Apollonij. PROPOSITIO LXVIII. LXIX.

[93.] PROPOSITIO LXX.

[94.] PROPOSITIO LXXI.

[95.] Notæ in Propoſit. LXVIII. LXIX. LXX. & LXXI.

[96.] SECTIO DVODECIMA Continens XXIX. XXX. XXXI. Propoſ. Appollonij.

[97.] Notæ in Propoſit. XXIX. XXX. & XXXI.

[98.] SECTIO DECIMATERTIA Continens Propoſ. LXIV. LXV. LXVI. LXVII. & LXXII. Apollonij. PROPOSITIO LXIV. LXV.

[99.] PROPOSITIO LXVI.

[100.] PROPOSITIO LXVII.

[101.] PROPOSITIO LXXII.

[102.] MONITVM.

[103.] LEMMA IX.

[104.] LEMMA X.

[105.] LEMMA XI.

[106.] Notæ in Propoſ. LXIV. & LXV.

[107.] Notæ in Propoſ. LXVI.

[108.] Ex demonſtratione præmiſſa propoſitionum 64. & 65. deduci poteſt conſectarium, à quo notæ ſubſe-quentes breuiores reddantur. COROLLARIVM PROPOSIT. LXIV. & LXV.

[109.] Notæ in Propoſ. LXVII.

[110.] COROLLARIVM PROPOSIT. LXVII.

[111.] Notæ in Propoſit. LXXII.

[112.] SECTIO DECIMAQVARTA Continens Propoſ. LXXIII. LXXIV. LXXV. LXXVI. & LXXVII. PROPOSITIO LXXIII.

[113.] PROPOSITO LXXIV.

[114.] PROPOSITO LXXV.

[115.] PROPOSITIO LXXVI.

[116.] PROPOSITIO LXXVII.

[117.] Notæ in Propoſit. LXXIII.

[118.] LEMMA XII.

[119.] Notæ in Propoſ. LXXIV.

[120.] Notæ in Propoſit. LXXV.

244206Apollonij Pergæi ſeu axium (in hoc caſu) L B, & M E ſiguræ ſimiles inter ſe; & ideò ſectiones
11ex 11. 12.
huius. A B C, & D E F ſimiles erunt.

Itaque propter ſimilitudinem duorum ſegmẽtorum ſimlia erunt B N L,
22b E O M, & pariter L B P, & M E Q atque quadratum B P ad L P in P
N nempe, & c. Huius ſecundæ partis demonſtrationem, quàm non ſinceram Pa-
raphraſtes Arabicus nobis tranſmiſit omittere opere pretium erit, eandemq; bre-

279[Figure 279] uius demonſtrare hac ratione. Quia ſegmenta C B G, & F E H ſimilia ponun-
tur; ergo erunt figuræ diametrorum B I, E K ſimiles inter ſe in angulis I, K
33Lem. 8.
huius. æqualibus, & ſectiones ipſæ C B G, & F E H ſimiles inter ſe erunt; quod eſt
44Prop. 15.
huius. contra hypotheſin.

Notæ in Propoſit. XXIII.

SI enim ſimilia eſſent haberent conditiones ſimilitudinis, quod eſt im-
55a poſſibile, & c. Si enim concedantur ſegmenta G B C in parabola, & H E
F in hyperbole, vel ellipſi, ſimilia inter ſe; igitur in vnaquaque earũ duci poſ-
66Defin. 7.
huius. ſent ad diametros ordinatim applicatæ numero æquales, efficientes angulos æqua-

280[Figure 280]

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