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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12991Conicor. Lib. V.

112[Figure 112]

Quoniam I K, H M ſunt duæ breuiſſimæ conſtat, quod E I maximus
11b ſit ramorum cadentium ad illam ſectionem (72. ex 5.) & propinquior
illi maior eſt remotiore: nec non; quia H M, G N ſunt duæ breuiſſimæ
22c3374. huius. conſtat, vt dictum eſt, quod G E ſit maximus ramorum cadentium vtrin-
que ad ſectionẽ A H. Dico etiam, E G maiorem eſſe, quàm E I; nam
44d ſi producatur I O parallela ipſi A C, & iungatur E O, ducanturque per-
5515, huius. pendiculares I P, O Q, G R, E F S, quia G N, I K ſunt breuiſſimæ er it
D P ad P K, quæ eſt, vt proportio figuræ, vt D R ad R N; ergo F P
ad P K minorem proportionem habet, quàm F R ad R N, & diuidendo
F K ad K P, nempe F E ad I P, minorem proportionem habet, quàm,
F N ad N R, nempe F E ad G R: ergo F E ad I P minorem proportio-
nem habet, quàm ad G R, & propterea G R minor eſt, quàm I P, quæ
eſt æqualis O Q, cuius punctum O remotior eſt à vertice, quàm G,
& ideo E G maior eſt, quàm E O. (74. ex 5.) Et quia O T æqualis
eſt T I erit O S maior quàm S I, & S E perpendicularis ad O I eſt com-
munis; igitur O E maior eſt, quàm E I; & oſtenſa eſt E G maior, quàm
O E; Ergo E G maior eſt, quàm E I, quod erat oſtendendum.

PROPOSITIO LXXVI.

SI ex concurſu E in recto E B

113[Figure 113]66a poſito ellipſis A B C nõ edu-
catur breuiſecans præter E B, qui
tranſeat per centrum; erit E B ma-
ximus ramorum ſecantium ex con-
curſu ad ſectionem egredientium.

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