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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[91.] Notæ in Propoſ. XLV.
[92.] SECTIO VNDECIMA Continens Propoſ. LXVIII. LXIX. LXX. & LXXI. Apollonij. PROPOSITIO LXVIII. LXIX.
[93.] PROPOSITIO LXX.
[94.] PROPOSITIO LXXI.
[95.] Notæ in Propoſit. LXVIII. LXIX. LXX. & LXXI.
[96.] SECTIO DVODECIMA Continens XXIX. XXX. XXXI. Propoſ. Appollonij.
[97.] Notæ in Propoſit. XXIX. XXX. & XXXI.
[98.] SECTIO DECIMATERTIA Continens Propoſ. LXIV. LXV. LXVI. LXVII. & LXXII. Apollonij. PROPOSITIO LXIV. LXV.
[99.] PROPOSITIO LXVI.
[100.] PROPOSITIO LXVII.
[101.] PROPOSITIO LXXII.
[102.] MONITVM.
[103.] LEMMA IX.
[104.] LEMMA X.
[105.] LEMMA XI.
[106.] Notæ in Propoſ. LXIV. & LXV.
[107.] Notæ in Propoſ. LXVI.
[108.] Ex demonſtratione præmiſſa propoſitionum 64. & 65. deduci poteſt conſectarium, à quo notæ ſubſe-quentes breuiores reddantur. COROLLARIVM PROPOSIT. LXIV. & LXV.
[109.] Notæ in Propoſ. LXVII.
[110.] COROLLARIVM PROPOSIT. LXVII.
[111.] Notæ in Propoſit. LXXII.
[112.] SECTIO DECIMAQVARTA Continens Propoſ. LXXIII. LXXIV. LXXV. LXXVI. & LXXVII. PROPOSITIO LXXIII.
[113.] PROPOSITO LXXIV.
[114.] PROPOSITO LXXV.
[115.] PROPOSITIO LXXVI.
[116.] PROPOSITIO LXXVII.
[117.] Notæ in Propoſit. LXXIII.
[118.] LEMMA XII.
[119.] Notæ in Propoſ. LXXIV.
[120.] Notæ in Propoſit. LXXV.
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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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