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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11173Conicor. Lib. V.

Notæ in Propoſit. XXIX. XXX.
& XXXI.

A Lioquin producatur perpendicularis C E, & c. Exiſtente C A lineæ
11a breuiſsima, & A D tangente, ſi C A non eſt perpendicularis ad tangen-
tem ducatur ex origine C recta C E perpendicularis ad tangentem A D, ſecans
eam in E, & ſectionem in F, erit in triangulo A C E angulus C A E acutus,
& minor angulo recto E, & propterea C A ſubtendens maiorem angulum re-
ctum, maior erit quàm C E, quæ acutum ſubtendit: cumque punctum E tan-
gentis cadat extra ſectionem, erit C F minor, quàm C E; ideoque C A multo
maior eſt, quàm C F, quapropter C A non erit breuiſsima, quod eſt contra,
hypotheſin.

Si vero fuerit D A C rectus, & c. Quia C A ſupponitur breuiſsima,
22b3333. 34.
lib. 2.& angulus D A C rectus, erit A D tangens; nam ſi hoc verum non eſt,
ducatur ex puncto A recta linea A G, contingens ſectionem in
A; ſecabit vtique tangens A G ipſam D A, & erit an-
gulus C A G rectus nimirum contentus à breuiſsima
C A, & tangente A G, ex proxime demon-
ſtrata propoſitione; ergo duo anguli recti
C A D, & C A G æquales ſunt
inter ſe, pars, & totum, quod
eſt abſurdum.

93[Figure 93]

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