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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8244Apollonij Pergæi in G, & non bifariam in M, ergo (ex lemmate ſexto huius libri) G O ad O M, ſeu
G B ad P M (propter ſimilitudinem triangulorum B G O, & P M O) & multo magis
G B ad illius portionem K M habebit maiorem proportionem, quàm M F, ad F G;
ideoque rectangulum K M F ſub intermedĳs contentum minus erit rectangulo B G F
11Lem. 5.
pręmiſ. contento ſub extremis nõ proportionalium; ſed rectangulum B G F æquale eſt rectan-
gulo E D F (propterea quod D F, ad F G erat, vt B G ad H, ſeu ad ei æqualæm E D)
22Lem. 5.
pręmiſ. igitur rectangulum K M F minus erit rectangulo E D F, & propterea E D ad K M,
ſeu D R ad R M (propter ſimilitudinem triangulorum E D R, K M R) maiorem ra-
tionem habebit, quàm M F ad F D, & componendo, eadem D M maiorem rationem
habebit ad R M, quàm ad F D, & propterea R M minor erit, quàm F D, ſeu quàm
A C; igitur minimus ramorum ex K ad axim cadentium fertur infra K R; Quapro-
33ex 8. 13.
huius. pter ramus E K ſupra, vel infra breuiſecantem E B ad ſectionem ductus non eſt bre-
uiſecans, & abſcindit ex axi ſegmentum A R minus, quàm abſcindat breuiſsima ex
K ad axim ducta, quod erat oſtendendum.

Tertio loco ſit E D minor, quàm H, & oſtendetur, & c. Quia H ad B G eſt,
44h vt G F ad F D, eſtque E D minor, quàm H; ergo E D ad B G minorem proportionem
habet, quàm G F ad F D; & ideo rectangulum E D F ſub extremis contentum minus
55Lem. 5.
pręmiſ. eſt rectangulo B G F, quod ſub intermedĳs continetur; ponatur iam rectangulum T
G F æquale rectangulo E D F, & per F ducatur F V perpendicularis ſuper axim
A D.

59[Figure 59]

Et componendo, patet, quod D F eſt æqualis R M, & c. Nam D Rad R M
66i eſt, vt M F ad F D, & componendo, eadem D M ad R M, atque ad D F, ſeuad ſemi-
erectum A C eandem proportionem habebit, & ideo D F eſt æqualis R M.

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