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

Table of contents

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[31.] PROPOS. II.
Page: 43 (5)
[32.] PROPOS. III.
Page: 44 (6)
[33.] Notæ in Propoſitionem primam.
Page: 44 (6)
[34.] Notæ in Propoſitionem ſecundam.
Page: 45 (7)
[35.] Notæ in Propoſitionem tertiam.
Page: 45 (7)
[36.] SECTIO SECVNDA Continens propoſitiones IV. V. VI. Apollonij.
Page: 45 (7)
[37.] PROPOSITIO IV.
Page: 46 (8)
[38.] PROPOSITIO V. & VI.
Page: 46 (8)
[39.] Notæ in pro poſitionem quartam.
Page: 47 (9)
[40.] Notæ in propoſitionem quintam.
Page: 48 (10)
[41.] MONITVM.
Page: 50 (12)
[42.] LEMMA I.
Page: 51 (13)
[43.] LEMMA II.
Page: 52 (14)
[44.] LEMMA III.
Page: 53 (15)
[45.] LEMMA IV.
Page: 53 (15)
[46.] SECTIO TERTIA Continens VIII. IX. X. Propoſ. Apollonij.
Page: 54 (16)
[47.] PROPOSITIO IX. & X.
Page: 56 (18)
[48.] Notæ in Propoſitionem VIII.
Page: 57 (19)
[49.] Notæ in Propoſitionem IX. & X.
Page: 59 (21)
[50.] SECTIO IV. Continens Propoſit. VII. & XII. Apollonij.
Page: 62 (24)
[51.] NOTÆ.
Page: 63 (25)
[52.] SECTIO QVINTA Continens XI. Propoſit. Apollonij.
Page: 64 (26)
[53.] NOTÆ.
Page: 64 (26)
[54.] SECTIO SEXTA Continens Propoſit. XIII. XIV. XV. Apollonij.
Page: 65 (27)
[55.] NOTÆ.
Page: 66 (28)
[56.] SECTIO SEPTIMA Continens XXVI. XXVII. XXVIII. Propoſ. Apollonij. PROPOSITIO XXVI. & XXVII.
Page: 67 (29)
[57.] PROPOSITIO XXVIII.
Page: 67 (29)
[58.] NOTÆ.
Page: 68 (30)
[59.] LEMMA V.
Page: 68 (30)
[60.] LEMMA. VI.
Page: 69 (31)
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page |< < (124) of 458 > >|
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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