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

507[Figure 507] A B, & iungamus D B, D G: & quia duo
anguli D E G, D G E ſunt æquales, erit
angulus G D C duplus anguli D E G,
& quia angulus B D C æqualis eſt angu-
lo B C D, & angulus C E G æqualis eſt
angulo A C E, erit angulus G D C du-
plus anguli C D B, & totus angulus B
D G triplus anguli B D C, & arcus B G
æqualis arcui A E, triplus eſt arcus B F,
& hoc eſt, quod voluimus.

SCHOLIVM ALMOCHTASSO.

DIcit Doctor Almoch-

508[Figure 508] taſſo. Cum dicit ar-
cum B G æqualem eſſe ar-
cui A E, id ex eo eſt pro-
pter æquidiſtantiam duarum
cordarum. Sint itaque in
circulo A B C cordæ A C,
B D parallelæ; Dico quod
duo arcus A B, C D ſunt
æquales,

Iungamus A D, ergo duo anguli C A D, A D B ſunt æquales; &
propterea duo arcus ſunt æquales, & conuerſum eodem modo demon-
ſtratur.

Notæ in Propoſit. VIII.

HAEc quidem propoſitio elegantiſſima eſt, quæ ſi problematicè reſolui poſ-
ſet via plana, reperta iam eßet tripartitio cuiuſlibet anguli.

Breuius tamen demonſtratio

509[Figure 509] perfici poteſt hac ratione. Iuncta
recta E B, quia in triangulo Iſo-
ſcele B D C duo anguli C, & C
D B æquales ſunt, eſtque pariter
externus angulus B D C duplus an-
guli D E B in triangulo Iſoſcelio
D E B, ergo angulus C duplus eſt
anguli B E C, & propterea illi an-
guli ſimul ſumpti, ſeu externus an-
gulus A B E triplus erit anguli B
E F, & circunferentia A E tripla ipſius B F.

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