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.

222184Apollonij Pergæi

248[Figure 248]

Secentur diametrorum abſciſſæ G B, & H E in ĳſdem rationibus in L, M,
N, O, & ab ĳſdem punctis educantur baſibus æquiſtantes, ſeu ad diametros or-
dinatim applicatæ P Q, R S, T V, X Y. Quoniam ex hypotheſi G B ad B I
eſt, vt H E ad E K; eſtque A G media proportionalis inter G B, & B I; pari-
11II. lib. I. terque D H media proportionalis eſt inter H E, & E K; igitur A G ad G B
eſt, vt D H ad H E; Et quoniam inuertendo L B ad B G eſt, vt N E ad E H,
atque B G ad B I poſita fuit, vt H E ad E K; ergo ex æquali ordinata L B ad
B I erit, vt N E ad E K, quare vt L B ad P L, mediã proportionalẽ inter L B,
& I B, ita erit N E ad N T mediam proportionalem inter N E, & E K. Eo-
dem modo oſtendetur, quod R M ad M B eandem proportionem habet, quàm X
O ad O E: & hoc ſemper continget in quibuslibet alĳs diuiſionibus proportiona-
libus abſciſſarum, ſuntque anguli G, & H æquales; igitur ſegmenta A B C, &
D E F ſimilia ſunt inter ſe. Quod erat oſtendendum.

22Defin. 7.
huius.

LEMMA VII.

S I in duobus ſegmentis A B C, & D E F hyperbolicis, aut ellipti-
cis, baſes A C, & D F cum diametris G B, & H E, æquales
angulos G, & H obliquos continentes, efficiant abſciſſas G B, & H E
proportionales lateribus rectis B I, & E K, atque tranſuerſis B Z, &
E a, erunt ſegmenta ſimilia inter ſe.

249[Figure 249]

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