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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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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