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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13092Apollonij Pergæi

Si vero ex illo educatur alius bre-

114[Figure 114] uiſecans erit æqualis vni breuiſecan-
ti ex altera parte recti poſito, &
omnium reliquorum erit maximus.

11b

Quia breuiſſimæ egredientes ab ex-
tremitatibus reliquorum ramorum ab-
ſcindunt cum C, vel A lineas maiores,
quàm ſecent rami (illi 44. ex 5.) de-
monſtrabitur ductis tangentibus, per
extremitates illorum (quemadmodum,
antea oſtenſum eſt) quod E B ſit maximus ramorum egredientium ad
duos quadrantes C B, B A, & hoc erat oſtendendum.

PROPOSITIO LXXVII.

POſtea educatur alius breuiſe-

115[Figure 115]22a cans E F; Dico, quod eſt æ-
qualis vni breuiſecanti E G æque
remoto à recto D B, & eſt maxi-
mus reliquorum omnium.

Quia B D, F H ſunt duæ breuiſſimæ,
33b ergo rami egredientes ad ſectionem B
F abſcindunt cum A maiores lineas,
quàm ſecent breuiſſimæ, egredientes ab
eorum extremitatibus: idem dicendum eſt de ramis educti ad ſectionis
peripheriam B G, & rami educti ad peripherias C G, A F abſcindunt
cum C, vel A lineas minores (45. ex 5.) conſtat itaque adhibitis li-
44c neis tangentibus, vt dictum eſt, quod E F ſit maximus ramorum ſecan-
tium ex E ad C B A egredientium, excepto vno E G, cui eſt æqualis,
quod erat oſtendendum.

Notæ in Propoſit. LXXIII.

PR O clariori intelligentia propoſitionum huius ſectionis hæc præmitto.

LEMMA XII.

Si in ellipſi A B C à concurſu E ductus fuerit ramus E G ſecans
vtrumque axim in H, & 1, cuius portio G 1, inter axim maiorem
A C, & ſectionem intercepta, ſit linea breuiſsima; dico, quod quili-
bet alius ramus E K inter breuiſecantem G E, & axim minorem in-
terceptus, efficit cum ſectionem tangente K P angulum E K P

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