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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10163Conicor. Lib. V.

Notæ in Propoſit. LVIII.

I Am poſſumus producere ex puncto aſſignato C extra datam ſectionem
11a A B, aut intra (ſi punctum non fuerit ad axim I A) lineam diuiden-
tem ex illo inter ſectionem, & axim lineam breuiſſimam, & c. Sic legen-
dum puto. Ex punto dato C extra, vel intra ſectionem A B, quod in axi non
ſit, lineam rectam ducere, cuius portio incercepta inter ſectionem, & axim ſit
linea breuiſsima.

80[Figure 80]

Et per C ducamus ſectionem H C B circa duas continentes illam G F,
22b I F, quæ occurrat ſectioni A B (16. ex 5.) in B, & c. Scilicet ducamus per
C hyperbolen H C B circa aſymptots G F, F I, & quia aſymptoti, & hyperbo-
334. lib. 2. le H C B productæ ad ſe ipſas ſemper proprius accedunt, atque parabole A B
4414. 2.
Ex 8. 1. producta ſemper magis ab axi A I remouetur; igitur hyperbole H C B, & para-
bola A B ſe mutuo ſecabunt; ſecent ſe ſe in puncto B. Animaduertendum eſt,
quod in textu Arabico aſſumitur hæc concluſio, vt demonſtrata in propoſitione
16. huius quinti libri; & ſiquidem numeri huius citationis mendoſi non ſunt,
hæc propoſitio ſexta decima deſideratur in hoc libro.

Producatur perpendicularis B K. Quoniam C I, & c. Ex puncto B ad
55c axim ducatur perpendicularis B K, ſecans eum in K; quoniam quando punctum
C ponitur intra parabolen, tunc B G æqualis eſt I C; quando vero cadit extra,
668. lib. 2. tunc C G eſt æqualis B I, & addita communi B C erit I C æqualis B G, cumq;
duæ rectæ lineæ I G, I F conuenientes in I ſecentur à rectis lineis K B, E C,
F G inter ſe parallelis, eo quod ſunt perpendiculares ad eundem axim; ergo I G,
& I F ſecantur in ĳſdem rationibus, & propterea E I æqualis erit K F; ſicuti
I C æqualis erat B g, pariterque I K æqualis erit E F, ſicuti I B æqualis erat
C G; poſita autem fuit E F æqualis ſemierecto; igitur K I ſemiſsi lateris recti
pariter æqualis erit.

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