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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429390Archimedis ipſius A B, eſtque nota A D medietas differentiæ inter diametrum A C, & chor-
dam differentiæ F C;
at propoſitio Archimedea verificatur in quolibet circuli
ſegmento ſiue maiori, ſiue minori;
ex datis enim circumferentijs A C, A B,
493[Figure 493] A F, &
F C vna cum cordis A C, & F C, haberi quidem poteſt chorda A B
paulo difficilius, ſi nimirum ex chorda A C tollatur chorda F C, &
differen-
tia A E bifariam ſecetur in D, &
ex arcu cognito B C datur angulus A, atque
angulus D rectus eſt, ergo triangulum A B D ſpecie notum erit, &
propterea
proportio D A ad A B cognita erit, eſtque D A longitudine data, igitur A B
longitudine innoteſcet.
Notandum eſt quod figura appoſita in hac propoſ. non exprimit omnes caſus
propoſitionis, quandoquidem ſemicirculus eſt A B C, &
propterea ex præceden-
tibus erroribus Arabici expoſitoris ſuſpicari licet non ritè eum percepiſſe Archi-
medis mentem.
PROPOSITIO IV.
A B C ſemicirculus, & fiant ſuper
494[Figure 494] A C diametrum duo ſemicirculi, quo-
rum vnus A D, alter vero D C, &

D B perpendicularis, vtique figura pro-
ueniens, quam vocat Archimedes AR-
BELON, eſt ſuperficies comprehenſa ab
arcu ſemicirculi maioris, &
duabus cir-
cumferentijs ſemicirculorum minorum, eſt æqualis circulo, cuius
diameter eſt perpendicularis D B.
Demonſtratio. Quia linea D B media proportionalis eſt inter duas li-
neas D A, D C, erit planum A D in D C æquale quadrato D B, &

ponamus A D in D C cum duobus quadratis A D, D C communiter,
fiet planum A D in D C bis cum duobus quadratis A D, D C, nempe
quadratum A C, æquale duplo quadrati D B cum duobus quadratis A
D, D C, &
proportio circulorum eadem eſt, ac proportio

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