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

[81.] PROPOSITIO LX.

[82.] PROPOSITIO LXI.

[83.] Notæ in Propoſit. LVIII.

[84.] Notæ in Propoſit. LIX. LXII. & LXIII.

[85.] Notæ in Propoſit. LX.

[86.] Notæ in Propoſit. LXI.

[87.] SECTIO DECIMA Continens Propof. XXXXIV. XXXXV. Apollonij.

[88.] PROPOSITIO XXXXIV.

[89.] PROPOSITIO XXXXV.

[90.] Notæ in Propoſ. XXXXIV.

[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.

348309Conicor. Lib. VII.

Quia C G ad A G, nempe quadratum A C ad ſuam figuram in ma-
11c iori, & in figura ſecunda ellipſi in minori proportione, & c. Ideſt. In,

409[Figure 409] prima, & ſecunda figura hyperboles,
& in prima figura ellipſis habet C G ad
G A maiorem proportionem, quàm ad
G E, eo quod G E maior eſt, quàm G
A: at in ſecunda figura ellipſis propor-
tio minor eſt; quia G E minor eſt, quã
A G. Propoſitum verò aliter oſtendetur
hac ratione.

Quoniam ex demonſtratis in nota
propoſit. 27. in hyperbola, atquè ex
propoſitione 11. libri quinti in ellipſi
erit axis minor, & rectus Q R minor
diametro recta N O, & N O minor
remotiore V X, ideoquè quadratum Q
R minus erit quadrato N O, & qua-
dratum N O minus quàm quadratum
V X : eſt verò figura, ſeu rectangulum
C A F ſub extremis contentum ęquale
quadrato Q R ex media proportionali
2215. lib. 1. inter illas deſcriptum: pariterquè re-
ctangulum L I K ęquale eſt quadrato
diametri ei coniugatę N O, nec non,
rectangulum T S Z ęquale erit qua-
drato V X, ergo rectangulum C A F
minus eſt rectangulo L I K, atque rectangulum L I K minus eſt rectangulo T

410[Figure 410] S Z. E contra in ellipſi ſecunda. Quia. Q R maior eſt, quàm N O, & hęc
maior, quàm V X ; ergo rectangulum C A F maius eſt rectangulo L I K, &
hoc maius erit rectangulo T S Z.

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