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

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427388Archimedis quas confecimus de rectangulis. Et quia

490[Figure 490] in triangulo G A C linea B E educta eſt
parallela baſi, & iam educta eſt ex D
ſemipartitione baſis linea D A ſeca ns
parallelam in F, erit B F æqualis ipſi F
E, & hoc eſt quod voluimus.

SCHOLIVM ALMOCHTASSO.

DIcit Doctor: Quod autem C D ſit æqualis ipſi D G, vti remittit ad
ſuum librum de propoſitionibus rectangulorum, eo quod duo angu-
li D C B, D B C æquales ſunt propter æqualitatem D B, D C, & an-
gulus D B C cum augulo D B G eſt rectus, & ſimiliter angulus D C B
cum angulo C G B: neceſſe eſt, vt ſint duo anguli D G B, D B G æqua-
les etiam, ergo duo latera D B, D G ſunt æqualia.

Rurſus ſi dicatur quod proportio C D ad D B ſit vt proportio D B ad
D G, & D C æqualis ipſi D B, ergo D B æqualis eſt D G, eſſet para-
bola. Dicit, quod vero B F ſit æqualis F E, hoc conſtat ex eo quod
caſus A D ſuper duas lineas B E, G C parallelas in triangulo A G C,
exigit eorum ſectio in eadem proportione, & id quidem, quia A D ad
A F eandem proportionem habet, quam G D ad B F, & quam D C ad
E F, ergo G D ad B F eſt vt D C ad E F, & permutando G D ad ei æ-
qualem D C, eſt vt B F ad E F, & propterea ipſæ etiam ſunt æquales.

Notæ in Propoſ. II.

HVius ſecundæ propoſitionis expoſitio, & demonſtratio inſigniter deformata
eſt; in propoſitione enim ſupponuntur duæ rectæ D C, D B tangere cir-
culum tantummodo, non autem conſtituere angulum rectum, & ſolummodo re-
cta linea B E perpendicularis ducitur ad diametrum A C, quare male in de-
monſtratione pronunciatur quadrilaterum B D C E parallelogrammum rectan-
gulum, cum ferè ſemper ſit Trapetium: pariterque errat, quando ait rectam
B D perpendicularem eſſe ſuper C G, quæ nunquam vera ſunt, niſi in vnico caſu,
quando ſcilicet B E cadit perpendiculariter ſuper centrum circuli.

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