Full text: Pergaeus, Apollonius: Apollonii Pergaei Conicorvm Lib. V. VI. VII. paraphraste Abalphato Asphahanensi

Apollonij Pergæi tis potius, quàm demonſtrantis
eſſet dicere. Eo quod H F, ad
F b poſita fuit vt C B ad B a; vbi nam, aut quando hoc ſuppo-
ſitum eſt, ſi in definitione non
continetur? Nec ſuspicari po-
teſt caſu hæc verba in textu ir-
repſiß, cum in alijs locis repe-
tantur, & ab eis pendeat tota
demonſtratio; igitur in defini-
tione vulgata addenda eſt illa
particula, abſciſſæ fint in ea-
dem ratione ad erecta;

202.1.

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Rurſus in propoſ. II. & I. parte 12. quando concluſio demonſtrationis eſt quod ſectiones A B, E F ſimi-
les ſint: tunc quidem quia tenetur oſtendere Apollonius definitionem traditam,
conuenire ſectionibus A B, E F, non aßumit incautè abſciſſas homologas C B,
H F, ſed ait in II. propoſitionc ponamus C B ad B D vt H F ad F I, & in 12. inquit, nam pofuimus H F ad F b vt C B ad B a & c. Poſtea in pro-
poſitione 16. litera a: ergo M A ad A P, ideſt abſciſſa ad erectum eſt vt O
C ad C Q, ſeu vt homologa abſcißa ad latus rectum, & angulus O æqualis
eſt M: patet igitur, vt diximus in II. ex 6. quod ſi, & c. Ex quibus locis
ſatis apertè colligitur ( ni fallor ) id quod ſupra rationibus non leuibus inſi-
nuaui, quod abſciſſæ proportionales eſſe debent erectis in ſectionibus ſimilibus.

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Sed hic animaduertendum eſt, eandem definitionem non poſſe æquè aptari ſe-
ctionibus conicis, atque ſegmentis conicis ſimilibus, vt perperam cenſuit Mydor-
gius: nam in ſegmentis conicis ſimilibus A B C, & D E F diametrorum æquè
ad baſes inclinatarum abſciſſæ homologæ ex ſui natura determinatæ ſunt, quan-
doquidem non poßunt eße maiores, neque minores quàm G B, & H E, quæ inter
baſes A C, & D F ſegmentorum conicorum, & vertices B, E intercipiuntur; at ſi in conicis ſectionibus A B S, & K F G ſint axes tranſuerſis a B, & b F
ad ſua latera recta B D, & F I in eadem proportione, tunc quidem ſimiles e-
runt curuæ lineæ A B S, & K F G, quæ poßunt habere indeterminatas, & mul-
tiplices longitudines, immo poßunt in inſinitum prolongari, ſi fuerint parabolæ

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