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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[201.] COROLLARIVM I.
[202.] COROLLARIVM II.
[203.] Notæ in Propoſit. XI.
[204.] Notæ in Propoſit. XII.
[205.] Notæ in Propoſit. XIII.
[206.] Notæ in Propoſit. XIV.
[207.] SECTIO QVINTA Continens ſex Propoſitiones Præmiſſas, PROPOSITIO I. II. III. IV. & V.
[208.] PROPOSITIO Præmiſſa VI.
[209.] Notæ in Propoſit. Præmiſſas I. II. III. IV. & V.
[210.] Notæ in Propoſit. Præmiſſ. VI.
[211.] SECTIO SEXTA Continens Propoſit. XV. XVI. & XVII. PROPOSITIO XV.
[212.] PROPOSITIO XVI.
[213.] PROPOSITIO XVII.
[214.] Notæ in Propoſit. XV.
[215.] MONITVM.
[216.] LEMMA VI.
[217.] LEMMA VII.
[218.] LEMMA VIII.
[219.] Notæ in Propoſit. XVI.
[220.] Notæ in Propoſit. XVII.
[221.] SECTIO SEPTIMA Continens Propoſit. XVIII. & XIX.
[222.] Notæ in Propoſit. XVIII. & XIX.
[223.] SECTIO OCTAVA Continens Propoſit. XX. & XXI. Apollonij. PROPOSITIO XX.
[224.] PROPOSITIO XXI.
[225.] PROPOSITIO XXII.
[226.] PROPOSITIO XXIII.
[227.] PROPOSITIO XXIV.
[228.] Notæ in Propoſit. XX.
[229.] Notæ in Propoſit. XXI.
[230.] Notæ in Propoſit. XXII.
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310272Apollonij Pergæi reliquæ verò lineæ referuntur ad hoc latus.
VII.
Inſuper vocabo duas diametros coniugatas, & æquales in elli-
pſi, ÆQVALES.
Et ſi quidem ad vtraſque partes axis ſectionis duæ diame-
tri educantur, quæ ad ſua erecta eandem proportionem ha-
beant, vtique vocabo cas ÆQVALES.
VIII.
Diametros verò æquales ad vtraſque partes duarum axium elli-
pſis cadentes, voco Homologas illius axis:
ſuntque homo-
logæ diametri in ellipſi tranſuerſa ad tranſuerſam, &
recta
ad rectam.
NOTÆ.
I. P Rima definitio breuiſſimè exponi poteſt hac ratione. Si axis tranſuerſus
interius in hyperbola diuidatur, aut exterius in ellipſi, ſecundum pro-
portionem figuræ, ſegmentum homologum axis tranſuerſi vocabo Præſectum, vt
ſi fuerit hyperbole, vel ellipſis A B, cuius axis tranſuerſus A C, centrum D,
latus rectũ A F, &
in hyperbola ſecetur C A inter vertices A, & C; in ellipſi
verò ſecetur exterius in puncto G, ita vt ſumma, vel differentia ipſarum G A,
&
axis C A, ideſt C G ad G A habeat proportionem figuræ ſcilicet eandem,
quàm habet latus tranſuerſum C A ad latus rectum A F;
tunc quidem vocatur
recta linea C G Præſecta.
II. Atque G A vocatur Intercepta.
III. Punctum verò A extremum
357[Figure 357] interceptæ G A, &
diametri C A
vocabitur terminus communis dua-
rum linearum, ſcilicet axis C A, &

additæ, vel ablatæ A G.
IV. Punctum verò G, in quo axis
A C interius, vel exterius diuiditur
ſecundum proportionem figuræ voca-
tur terminus diuidens;
Si verò ſece-
tur C H æqualis A G vocabitur etiã
C H intercepta, &
A H præſecta,
atque C terminus communis, &
H
terminus diuidens.
V. Si diameter I L ſecuerit biſa-
riam ſubtenſam A B à ſectionis ver
tice A eductam, atque à termino

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