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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8446Apollonij Pergæi

Et ponamus quamlibet duarum proportionum C F ad F D, & I S ad S C,
11b vt proportio figuræ, & educamus ex E, S, & c. Ideſt fiat diſtantia ex centro
vſque ad perpendicularem E D ad eius portionem D F in hyperbola, vt ſumma late-
ris tranſuerſi, & recti ad latus rectum, & vt eorum differentia in ellipſi ad latus
rectum ita fiat C D ad eius productionem D F; tunc enim C F ad F D diuidendo in
hyperbola, & compo-

61[Figure 61] nendo in ellipſi habe-
bit eandem propor-
tionem, quàm latus
tranſuerſum ad re-
ctum; pariterq; fiat
E K ad K D in eadẽ
proportione figuræ,
& ex E, K educamus
rectas E I, K S pa-
rallelas axi A C D,
ſecantes I C, & L F
parallelas ipſi E D
in I, S, L, & M.
Immutaui poſtremã
partem conſtructio-
nis, vt manifeſte er-
roneã in textu Ara-
bico; Si enim I C ad
libitum ſumpta ſeca-
tur in S in ratione
C F ad F D non ca-
det neceſſariò E L
parallela C D ſuper
punctum I.

Et interponamus
22c inter F C, C A du-
as C N, C O pro-
portionales illis duabus, & c. Textum corruptum ſic reſtituo: Interponamus in-
ter F C, & A C duas medias proportionales, itaut F C, N C, C O, C A ſint continuè
proportionales, quod fieri poſſe conſtat ex lemmate 7. huius librt.

Et ponamus proportionem lineæ alicuius, vt eſt Q compoſitam, & c. Vo-
33d catur Trutina in hyperbola, & ellipſi linea recta Q, quæ ad B O compoſitam propor-
tionem habet ex C D ad D F, & ex ratione F O ad O C.

Producatur priùs E B ſecans axim in H, & c. Producatur priùs E B ſecans
44e axim in H, & rectam S K in R, nec non rectam I C in puncto T.

Ergo E D ad B O, quæ componitur ex E D ad D K, & c. Nam poſita inter-
55f media D K, proportio E D ad B O compoſita erit ex ratione E D ad D K, & ex ra-
tione D K ad B O; eſt verò I C ad C S, vt E D ad D K (propter parallelas I E, S K,
C D) atque D K eſt æqualis G O in parallelogrammo G D; ergo proportio E D ad B O
componitur ex ratione I C ad C S, & ex ratione G O ad O B.

Sed E D ad D K eſt, vt CD ad DF, quia quælibet earum vt proportio
66g

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