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

Sint itaque ſemicirculi A B C, A D E, F G C, vti diſpoſuimus, &
duæ lineæ N G, N D tangentes illos duos ſemicirculos in G, D, & æ-
quales, ſibique occurrentes in N, & linea B N tranſiens per punctum
N perpendiculariter erecta ſuper A C, & tangat illam circulus M N I
in I, & idem tangat circulum A B C in H, & circulum A D E in L,

501[Figure 501]& educamus diametrum I M parallelam ipſi A C, & iungamus C H,
quæ tranſibit per I, & iungamus M E tranſibit per L, & iungamus A I
11Prop. I.
huius.
Ibidem,
Scholium
præc.
Almoc. tranſibit per L, & producamus eam ad P, & iungamus C O tranſibit
per P, eritque parallela ipſi E M, & erit proportio A O ad O M, nem-
pe proportio A N ad M I vt proportio A C ad C E, & rectangulum A
N in C E æquale rectangulo A C in I M. Et eodem modo oſtendetur,
quod rectangulum C N in F A ſit æquale rectangulo A C in diametrum
circuli, qui eſt ex altera parte; & quia rectangulum C N in N F æqua-
le eſt quadrato G N, & eſt æquale quadrato D N, quod eſt æquale re-
ctangulo A N in N E erit rectangulum C N in N F æquale rectangulo
A N in N E, & proportio C N ad A N vt E N ad N F, & vt propor-
tio totius C E ad totum A F, ergo rectangulum A N in C E æquale eſt
rectangulo C N in F A, & iam oſtenſum eſt, quod A N in C E æqua-
le eſt rectangulo A C in I M, & quod rectangulum C N in F A ſit æqua-
le rectangulo A C in diametrum alterius circuli: ergo duæ diametri ſunt
æquales, & duo circuli æquales, & hoc eſt quæſitum.

Notæ in Propoſit. V.

HAEc propoſitio parum quidem differt à poſtrema parte propoſit. 14, 16.
& 17. lib. 4. Pappi Alex. , ſi figuram, conſtructionem, &

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