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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12486Apollonij Pergæi

Quod autem infimus ramus breuiſecans D C non ſit neceſſario minimus om-
nium ramorum cadentium ad peripheriam ſectionis A B, modò oſtendetur.

In coniſectione duos ramos hreuiſecantes, ducere, quorum infimus
11PROB.6.
Addit. maior ſit ramo ſecante poſito in peripheria à vertice, & ſuprema bre-
uiſecante compræhenſa: oportet autem in ellipſi, vt rami ſecantes ad
vnum eius quadrantem ducantur à concurſu, inter axim minorem, &
verticem collocato.

In coniſectione A B C, cuius ver-

106[Figure 106] tex A axis A D, & in hyperbola,
& ellipſi centrum E ducatur quæli-
228. 9. 10.
huius. bet breuiſsima F B: poſtea ſecetur
F G ex axi, ita vt punctum G non
cadat ſupra verticem A, ſeceturque
F H non maior, quam F G, ducan-
turque rectæ H C, G G parallelæ ipſi
F B occurrentes ſectioni in C, &
G, coniungaturque recta C G ſecans
F B in I: patet, C I maiorem non
eſſe, quàm I G; propterea quod G C,
G H à parallelis ſecantur proportio-
naliter; Deinde ex C ducatur alia
338. 9. 10.
26. 27. 28.
huius. breuiſsima C K, occurrens B F vl-
tra axim in L, iungaturque ramus
G L: oſtendendum eſt L C maiorem
eſſe, quàm L G. Secetur C G bifa-
riam in M, atque per M ducatur ſe-
ctionis diameter M N parallela axi
in parabola, & per centrum exſten-
ſa in reliquis ſectionibus, occurrens
ſectioni in N, ducaturque O N ſe-
ctionem contingens in N, iungantur-
4433. 34.
lib. 1. que L M, & L N, quæ ſecet G C in
P. Quoniam G I æqualis, aut ma-
ior eſt, quàm I C, cadet punctum
M bipartitæ diuiſionis totius C G,
vel in I, vel inter I, G, & in vtro-
que caſu punctum N cadet inter G,
& B (eoquod diameter M N paral-
lela axi in parabola, aut ex centro
E educta in reliquis ſectionibus effi-
cit angulum N M L ad partes ver-
ticis A) & ideo ramus L N cadens
ſupra duos breuiſecantes L C, L B
ad partes verticis efficit cum

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