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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243205Conicor. Lib. VI.

Sed B T ad B I erat vt X E ad E K propter ſimilitudinem duarum ſe-
11e ctionum, & c. Quoniam ex hypotheſi abſcißa axis I B ad latus rectum B G
erat vt abſciſſa K E ad latus rectum E H; & propter ſimilitudinem ſectionum
2212. huius. latera erecta G B, & H E ad axes tranſuerſos, & ideo ad eorum ſemißes T B
& E X eandem proportionem habebunt; ergo ex æquali I B ad B T erit vt K
E ad E X, & inuertendo T B

277[Figure 277] ad B I erit vt X E ad E K.
Sed libet aliam expoſitionem
afferre Apollonĳ principĳs cõue-
nientiorẽ. Quia ex definitione
2. huius libri legitime inter pre-
tata, & ſicuticõſtat ex 12. prop.
huius. In ſectionibus ſimilibus
non quælibet axium abſcißæ ad
conterminas potentiales habent
eandem rationem; ſed illæ tan-
tummodo, quæ figuræ lateribus
proportionales ſunt: itaq; in ſe-
ctionibus ſimilibus A B, D E
vt quælibet axium, abſcißæ B
I, E K ad conterminas poten-
tiales I A, K D ſint proportio-
nales, neceße eſt, vt eædem I B,
& E K lateribus figurarum B
T, E X proportionales ſint.

Et quadratum V Z ad quadratum Z e eſt, vt quadratum a Y ad qua-
33f dratum a f, & c. oſtenſa enim fuerunt duo trìangula V Z e, & γ a f ſimilia
inter ſe; & ideo latera circa angulos rectos Z, & a proportionalia erunt; &
pariter eorum quadrata.

Inſuper dico non eſſe ſimilia alicui alteri ſegmento, & c. Sicutì in præ-
44g cedenti propoſitione factum eſt oſtendetur, quod ſegmentum N C non eſt ſimile
alicui alio ſegmento in altera ſectione P E, quando non compræhenduntur ab
ordinatim ad axes applicatis, & in ellipſibus æqualiter à centris diſtant.

Notæ in Propoſit. XXII.

ET propterea duo ſectiones A B C, D E F ſimiles erunt, & c. Quo-
55Lem. 8.
huius. niam ſegmenta G B C, & H E F poſita ſunt ſimilia, erunt diamctrorum

278[Figure 278]

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