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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203165Conicor. Lib. VI.

221[Figure 221] vel hyperbolæ, nec habent baſes, à quibus circumſcribantur, igitur in ſectionibus
ſimilibus A B, & G F homolegæ axium abſciſſæ B C, F H non ſupponuntur iam
dißectæ, & determinatæ; quare poßunt eße cuiuſcunque menſuræ, & habere poſ-
ſunt eandem, & non eandem proportionem ad conterminas potentiales; & ideo
ad vitandam incertitudinem adiungi debet determinatio, quod prædictæ homo-
logæ abſcißæ B C, F H proportionales ſint lateribus rectis B D, F I, at in ſeg-
mentis, ſeu portionibus ſectionum conicarum ſimilium inutilis omnino eßet illa
determinatio. An verò hæc mea ſententia omninò reĳci debeat alĳs iudicandũ
relinquo.

Notæ in Propoſit. XI.

CVmque B C ad B L poſita ſit vt H F ad F N, & c. Quia inuertendo
11a D B ad B C eandem proportionem habet quàm I F ad F H, & C B ad B
L eſt vt H F ad F N; ergo ex æquali ordinata D B ad B L eandem proportio-
nem habebit, quàm I F ad F N; eſtque ordinatim applicata Q L media pro.

222[Figure 222] portionatis inter abſciſſam B L, & latus rectum B D ( cum in parabola quadra-
tum Q L æquale ſit rectangulo L B D ) pariterque X N media proportionalis eſt
2211. lib. I. inter F N, & I F; ergo Q L ad L B eſt vt X N ad N F, & antecedentium,
duplæ, ſcilicet Q R ad L B, atque X r ad N F in eadem ratione erunt. Non
ſecus oſtendetur O P ad K B vt T V ad M F.

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