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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236198Apollonij Pergæi

268[Figure 268] tione figuræ diametri A L (40. ex 1.) erit vt quadratum E Q ad M Q
1137. lib. 1. in O Q, nempe in eadem proportione figuræ diametri D M (40. ex 1.)
22Ibidem. quapropter duæ proportiones figurarum earundem ſectionum ſunt eædem
inter ſe; & propterea duæ ſectiones ſunt ſimiles (12. ex 6.) at ſuppoſitæ
fuerunt non ſimiles. Quod eſt abſurdum.

PROPOSITIO XXIII.

SI autem ſectio A B C fuerit parabola, & ſectio D E F hy-
perbola, aut ellipſis: manifeſtum eſt, ſectiones non eſſe in-
3313. huius. ter ſe ſimiles. Et dico quod duo ſegmenta G C, H F non ſunt
ſimilia.

Si enim ſimilia eſſent haberent conditiones ſimilitudinis, quod eſt im-
44a poſſibile, quemadmodum oſtenſum eſt in omnibus ſectionibus ad propo-
ſitionem 13. ſi vero vna earum fuerit hyperbole, altera verò ellipſis,
idipſum oſtenſum eſt ad propoſitionem 14. Et hoc erat propoſitum.

PROPOSITIO XXIV.

CViuslibet coniſectionis A C D portio B A C D non erit
arcus circuli.

Si enim hoc verum non eſt educamus in illa chordas A B, C D, A C,
quarum nulla alteri ſit parallela: & educamus E F parallelam A B, & E
G parallelam A C, atque G H parallelam C D, & per ſingularum dua-
rum æquidiſtantium ſemipartitiones iungamus K I, L M, N O, quæ

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