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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