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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[181.] Notæ in Propoſit. III.
Page: 187 (149)
[182.] Notæ in Propoſit. VI.
Page: 187 (149)
[183.] Notæ in Propoſit. VII.
Page: 187 (149)
[184.] Notæ in Propoſit. IX.
Page: 188 (150)
[185.] LEMMAI.
Page: 188 (150)
[186.] SECTIO TERTIA Continens Propoſit. V. & VIII. PROPOSITIO V.
Page: 190 (152)
[187.] PROPOSITIO VIII.
Page: 191 (153)
[188.] Notæ in Propoſit. V.
Page: 192 (154)
[189.] Notæ in Propoſit. VIII.
Page: 192 (154)
[190.] SECTIO QVARTA Continens Propoſit. XI. XII. XIII. & XIV. PROPOSITIO XI.
Page: 192 (154)
[191.] PROPOSITIO XII.
Page: 193 (155)
[192.] PROPOSITIO XIII.
Page: 194 (156)
[193.] PROPOSITIO XIV.
Page: 195 (157)
[194.] MONITVM.
Page: 196 (158)
[195.] LEMMA II.
Page: 196 (158)
[196.] COROLLARIVM.
Page: 197 (159)
[197.] LEMMA III.
Page: 197 (159)
[198.] LEMMA IV.
Page: 198 (160)
[199.] COROLLARIVM.
Page: 198 (160)
[200.] LEMMAV.
Page: 199 (161)
[201.] COROLLARIVM I.
Page: 199 (161)
[202.] COROLLARIVM II.
Page: 199 (161)
[203.] Notæ in Propoſit. XI.
Page: 203 (165)
[204.] Notæ in Propoſit. XII.
Page: 204 (166)
[205.] Notæ in Propoſit. XIII.
Page: 205 (167)
[206.] Notæ in Propoſit. XIV.
Page: 206 (168)
[207.] SECTIO QVINTA Continens ſex Propoſitiones Præmiſſas, PROPOSITIO I. II. III. IV. & V.
Page: 206 (168)
[208.] PROPOSITIO Præmiſſa VI.
Page: 209 (171)
[209.] Notæ in Propoſit. Præmiſſas I. II. III. IV. & V.
Page: 209 (171)
[210.] Notæ in Propoſit. Præmiſſ. VI.
Page: 212 (174)
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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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