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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162124Apollonij Pergæi

Erit angulus BHE ma-

155[Figure 155]11b ior, iquàm E B H, & c. Eo
quod ramorum omnium ab
origine E ad ellipſim C B H
cadentium maximus ſuppo-
nitur E B; ergo maior erit,
quàm E H, & propterea
angulus E B H minori late-
ri oppoſitus minor erit angu-
lo E H B: cadit vero recta
H F infra H E; propterea
quod punctum F infra pun-
ctum E exiſtit; igitur angu-
lus F H B maior eſt angulo
E H B; & ideo angulus F H B multo maior erit angulo F B H; igitur ramus
F B, maiorem angulum ſubtendens, maior erit, quàm F H, & c.

SECTIO DECIMAOCTAVA

Continens XXXII. XXXIII. XXXIV. XXXV.
XXXVI. XXXVII. XXXVIII. XXXIX.
XXXX. XXXXVII. XXXXVIII.

Propoſit. Apollonij.

PROPOSITIO XXXII.

IN ellipſi A B C rami cuiuslibet

156[Figure 156]22a maximi G H vtrumque axim ſe-
cantis portio N H inter axim maio-
rem, & ſectionem intercepta, eſt li-
nea breuiſsima.

Producatur rectus axis minor A D vl-
tra centrum D ad I, G, & ex I, G ad ſe-
ctionem ducantur duo rami maximi G H,
I K, qui ſecent tranſuerſum B D in N,
M, & ſit B E dimidium erecti axis B D,
& A F dimidium erecti axis A G; & edu-
cantur perpendiculares ad axes H O, H
P, K Q, K R. Dico, N H breuiſsimum
eſſe ramorum egredientium ex H. Quia
G H eſt linea maxima, erit D A ad A F,
nempe B E ad B D, vt D O ad O G (22.
33b ex 5.) nempe N H ad H G, ſeu N P

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