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.

9860Apollonij Pergæi

SECTIO NONA
Continens Propoſ. LVIII. LIX. LX. LXI.
LXII. & LXIII.

I Am ex puncto dato C extra, vel intra ſectionem A B (quod
11a in axi I A non ſit) poſſumus rectam lineam ducere, cuius
portio intercepta inter ſectionem, & axim ſit linea breuiſſima.

PROPOSITIO LVIII.

Sit ſectio parabole, & producamus perpendicularem C E ſu-
per I E A, & ponamus E F æqualem dimidio erecti, & du-
camus G F parallelam ipſi C E, & per C ducamus hyperbolen
224. lib. 2.33b H C B circa duas continentes illam G F, I F, quæ occurat ſe-
ctioni A B in B, & per B, C producatur linea occurrens con-
tinenti I A in I, & continenti G F in G: Dico, quod B I eſt
linea breuiſsima.

75[Figure 75]

Producatur perpendicularis B K. Quoniam C I æqualis eſt B G (sexta
44C ex ſecundo) erit E I æqualis K F, & E F, K I erunt æquales, atque ſup-
558. lib. 2. poſita, eſt E F æqualis dimidio erecti; ergo K I ita eſt pariter; Quare
B I eſt breuiſsima, (octaua ex quinto) & hoc erat probandum.

PROPOSITIO LIX. LXII. & LXIII.

D Einde fit ſectio hyperbole, aut ellipſis, cuius centrum D, & lineis,
66a atque ſignis in eodem ſtatu manentibus, ponamus D F ad F E, &

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