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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451412Archimedis pleantur parallelogramma rectangula A L, A K, L B, B K, atque axe
11Prop. 52.
lib. 1.
F G, latere recto F N deſcribatur parabole F M ſecans H G in M;
erit
igitur in parabola quadratum M G æquale rectangulo G F N ſub abſciſ-
22Prop. 11.
lib. 1.
ſa, &
latere recto contento, ideoque idem quadratum F G ad rectangu-
lum N F G, atque ad quadratum M G eandem proportionem habebit:
eſt vero quadratum F G ad rectangulum N F G, vt F G ad F N, cum
525[Figure 525] F G ſit illorum altitudo communis, nec non vt C F G ad C F N ſum-
pta nimirum C F communi altitudine, ergo rectangulum C F G ad C
F N eandem proportionem habebit, quam quadratum F G ad quadra-
tum M G, &
permutando rectangulum C F G ad quadratum F G erit
vt rectangulum C F N ad quadratum G M, ſed vt rectangulum C F G
ad quadratum F G, ita eſt C F ad F G, &
E A ad A C, igitur E A ad
A C erit vt rectangulum C F N ad quadratum G M, ſeu vt quadratum
E B, vel K G ad quadratum G M:
eſt vero A C minor, quàm A E,
quæ triens eſt totius A B, igitur M G minor eſt, quàm G K.
Poſtea
per B circa aſymptotos A C F deſcribatur hyperbole B K, quæ tran-
33Prop. 4. &
12. lib. 2.
ſibit per punctum K, cum parallelogramma A F, &
C K æqualia
ſint propter diagonalem C E G, quare punctum M paraboles cadet
intra hyperbolem B K, ſed parabole F M occurrit aſymptoto C F in ver-
tice F, &
occurrit etiam aſymptoto C A in aliquo alio puncto, cum C
A ſit parallela axi F G paraboles, &
hyperbole ſemper intra aſymptotos
44Prop. 26.
lib. 1.
incedat, igitur parabola F M bis hyperbolæ occurrit ſupra, &
inſra pun-
55ex 1. & 2.
lib. 2.
ctum M:
ſint occurſus X, à quibus ductis parallelis ad aſymptotos com-
pleantur parallelogramma R P, &
A F, quæ erunt æqualia inter aſym-
ptotos, &
hyperbolen conſtituta, & propterea C O S parallelogrammo-
66Prop. 12.
lib. 2.
rum diameter erit, &
vna linca recta: & quia O A ad A C eſt vt C F
ad F S, ſiue vt rectangulum C F N ad rectangulum S F N:
erat autem
quadratum E B æquale rectangulo C F N ex conſtructione, &

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