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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240202Apollonij Pergæi

Sed tangens in V perueniens ad L O, & c. Si enim ex punctis γ, V du-
11f cantur V e, & γ f tangentes parabolas, & producantur quouſque ſecent axes
in e, & f eſſicientur duo parallelogramma V e O R, & γ f Q S, in quibus tã-
gentes V e, & γ f efficientur æquales ipſis O R, & Q S: & propterea inuer-
tendo R V abſciſſa ad contingentem V e æqualem ipſi R O eandem proportionem
habebit, quàm abſcißa S γ ad contingentem γ f æqualem ipſi S Q, atque effi-
ciunt prædictæ contingentes cum axibus angulos e, f æquales ipſis O, & Q æ-
qualibus propter parallelas; igitur ſegmenta N V A, & P γ D ſimilia ſunt in-
22Prop. 16.
huius. ter ſe.

273[Figure 273]

Et pariter duo ſegmenta A B C, D E F, atque duo ſegmenta N B, P
33g E ſunt ſimilia inter ſe, & ſimiliter poſita, & c. Hoc manifeſtum eſt, ſi enim
coniungantur rectæ lineæ N C, & P F, & bifariam diuidantur, atque ducan-
tur diametri, & c, vti fecimus in ſectione N A, oſtendetur ſimiliter (ex ea-
dem 16. propoſitione) ſegmenta N C, P F ſimilia eſſe inter ſe. Non ſecus ſi
coniungantur rectæ lineæ N B, & P E, & bifariam diuidantur, atque ducan-
tur diametri, & reliqua perficiantur, vt prius, oſtendentur codem modo, ſegmẽ-
ta N B, & P E ſimilia inter ſe.

Deinde ponamus ſegmentũ P d; quia non abſcindunt illa duæ ordina-
44h tiones vnius axis (18. ex 6.) , & hoc erat, & c. Sed legendum puto vt in
textu apparet. & horum verborũ ſenſus erit; fieri non poteſt, vt ſegmentũ p d ſit
ſimile ipſi N A, vel N B, propterea quod in ſectione P F ſegmenta P d vni tan-
tummodo portioni ſimile eſt (præter quàm in ellipſi), & ambo intercipi debent à
duabus ordinatim applicatis ad axim E Q: & propterea ſegmenta P D, vel P E
non erunt ſimilia ipſi P d, & quia N A oſtenſum eſt ſimile P D, pariterque N
B oſtenſum eſt ſimile P E; igitur ſegmentum P d ſimile non eſt, neque N A,
neque ſegmento N B; quod erat oſtendundum.

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