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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169131Conicor. Lib. V. breuiſsimæ B D, GI, quarum B D per centrũ

167[Figure 167] tranſit, quæ productæ concurrunt in puncto E
axis minoris, & concluditur, quodrami E F,
portio F H, nedũ breuiſsima non eſt, ſed ſupra
ipſam breuiſsimã ex puncto F eductam cadit.

Sed duo hic notanda ſunt. Primo, quod hæc
prop. 35. non poterat poſtponi, nã vſum habet
in 57. huius vbi malè citatur prop. 52. loco hu-
ius 35. , vt ibidem inſinuatum eſt. Secundo,
quod hæc demonſtratio non videtur omnino
perſecta nam pendet ex prop. 34. , & ex eius
conuerſa, quæ demonſtrata non reperitur qua-
re ſuperuacanea non fuit noua demonſtratio in
Lemmat. 8. appoſita.

Notæ in Prop. XXXVI.

SI verò nulla earum tranſit per centrũ,
11a educamus D O, & c. Si enim fuerint
quatuor lineæ breuiſſimæ G K, F I, H L, M
N, quarum nulla per centrum D tranſit, ſi-
militer oſtendetur, quod non conueniunt in
vno puncto E; nam ducto ſemiaxe minori
D O neceſſe eſt, vt punctum E concurſus duorũ
breuiſecantiũ E G, E F cadat intra angulũ A
D O; pariterque idem punctum E concurſus
2234. huius.
Ibidem. duorum breuiſec antium E H, E M, cadet ne-
ceſſario intra angulum C D O, ſed idem pun-
ctum E nequit duobus in locis reperiri, ni-
mirũ intra angulum A D O, & intra angu-
lum C D O, igitur non poſſunt ab eodẽ puncto
educi ad ellipſim quatuor rami breuiſecantes.

Notæ in Prop. XXXVIII.

NAm ſi educamus B G tangentem erit
33a4432. huius. B D minor quàm D H, & c. Quo-
niam C B eſt linea breuiſſima, aut ſi maxima
5529. 30.
huius. eſt, eius portio erit breuiſſima, & G B cõtin-
gens ſectionem in eius termino B perpendicu-
laris ad B C; propterea in triangulo B D H
latus H D, ſubtendens angulum rectum B,
maius erit latere D B; eſt verò D E maior,
quàm D H, eo quod punctum H contingentis
B G cadit extra ſectionem; igitur linea B D
minor eſt, quàm D E, & propterea angulus
D E B acutus erit, quare eſt minor

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