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

Conicor. Lib. V. dente in hyperbola, & deficiente in ellipſi rectangulo F K H ſimile ei, quod la-
teribus recto, & tranſuerſo continetur, ſcilicet G A E, & eſt A F ſemiſsis la-
teris recti, igitur quadratum B G æquale eſt ſummæ in hyperbole, & differen-
tiæ in ellipſi rectanguli G A F bis ſumpti, & rectanguli F K H, quod eſt æqua-
le duplo trianguli F K H: ſed quadrilaterum A G H F æquale eſt aggregato in
hyperbola, & differentiæ in ellipſi rectanguli G A F, & trianguli F K H, ergò
quadratum B G æquale eſt duplo quadrilateri A G H F, ſeù diſſerentiæ triangu-
lorum D A F, & D G H.

33.1.

b
Ibidem.
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34. Notæ in Propoſitionem
ſecundam.

SEcunda propoſitio facilè ex prima deducitur; nam, quando ordinata B G H I tranſit per cen-
trum D ellipſis; tunc tria puncta G, D, H conue-
niunt, & triangulum D G H euaneſcit, & ideò
differentia trianguli D A F, & trianguli D G H
nullum ſpatium habentis, erit triangulum ipſum
D A F.

35. Notæ in Propoſitionem
tertiam.

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IN tertia propoſitione ſimilitèr, quandò ordinata
B H G I cadit infrà centrum D ellipſis, tunc
ducta C L parallela ipſi A E, erunt duo triangula
D A F, & D C L æqualia inter ſe, cum ſint ſimi-
lia, & latera homologa D A, D C ſint æqualia,
quia ſunt ſemiaxes; proptereà differentia triangu-
lorum D G H, & D A F, ſeù D C L erit trapezium
C G H L, quod ſubduplum eſt quadrati ordinatæ
B G.

36. SECTIO SECVNDA
Continens propoſitiones IV. V. VI. Apollonij.

COmparata eſt minima ramorum egredientium ex ſua origine
(4) in parabola (5) & hyperbola (6) pariterque in ellipſi (ſi
comparata fuerit portio maioris duorum axium, & tunc maxi-
mus eſt reſiduum tranſuerſi axis.) Reliquorum verò propinquior

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