Full text: Pergaeus, Apollonius: Apollonii Pergaei Conicorvm Lib. V. VI. VII. paraphraste Abalphato Asphahanensi

Archimedis & circulus I H L tangat circulum A B C in H, & circulum A D E in
L, & perpendicularem in I. Dico eſſe æqualem circulo, qui eſt in al-
tera parte. Hoc modo, Educamus I M parallelam ipſi A C, & iungamus
A H, quæ tranſibit per M, quemadmodum demonſtrauit Archimedes,
& producamus eam quouſque occurrat perpendiculari N G in N, & iungamus I A, quæ tranſibit per L, & producamus illam ad O, & iun-
gamus C O, O N, quæ erit linea recta, & iungamus M E, quæ tranſi-
bit per L, & iungamus C H, quæ tranſibit per I; & linea C O N pa-
[...] a eſt lineæ E M, & proportio A N ad N M, nempe proportio A
G ad I M eſt vt C A ad C E, ergo rectangulum A G in C E æquale
eſt rectangulo C A in I M; & quia G D eſt perpendicularis in duobus
circulis C D F, E D A ſuper duas diametros C F, E A, erit rectangu-
lum C G in G F æquale quadrato G D, & rectangulum A G in G E
æquale etiam eſt illi, ergo rectangulum C G in G F æquale eſt rectan-
lo A G in G E, & proportio C G ad G A eſt vt proportio E G ad G
F, immo vt proportio C E ad F A reſiduam; ergo rectangulum C G in
F A, eſt æquale rectangulo C A in I M cui æquale eſt rectangulum G
A in C E. Et ſi fuerit in altera parte circulus modo præfato eadem ra-
tione oſtendemus, quod reſtangulum C A in diametrum illius circuli
æquale ſit rectangulo C G in A F, & oſtendetur quod duæ diametri duo-
rum circulorum ſint æquales.

361.1.

0431-03
Prop. I.
huius.
0432-01

362. SCHOLIVM SECVNDVM ALKAVHI.

POrrò ſecunda eſt hæc. Dicit quod ſi duo ſemicirculi non
ſint tangentes, nec ſe mutuo ſecantes, ſed ſeparati, & perpendicularis tranſeat per concurſum duarum linearum tangen-

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