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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[111.] Notæ in Propoſit. LXXII.
Page: 123 (85)
[112.] SECTIO DECIMAQVARTA Continens Propoſ. LXXIII. LXXIV. LXXV. LXXVI. & LXXVII. PROPOSITIO LXXIII.
Page: 126 (88)
[113.] PROPOSITO LXXIV.
Page: 128 (90)
[114.] PROPOSITO LXXV.
Page: 128 (90)
[115.] PROPOSITIO LXXVI.
Page: 129 (91)
[116.] PROPOSITIO LXXVII.
Page: 130 (92)
[117.] Notæ in Propoſit. LXXIII.
Page: 130 (92)
[118.] LEMMA XII.
Page: 130 (92)
[119.] Notæ in Propoſ. LXXIV.
Page: 134 (96)
[120.] Notæ in Propoſit. LXXV.
Page: 135 (97)
[121.] Notæ in Propoſ. LXXVI.
Page: 137 (99)
[122.] Notæ in Propoſit. LXXVII.
Page: 138 (100)
[123.] COROLLARIVM.
Page: 143 (105)
[124.] SECTIO DECIMAQVINTA Continens Propoſ. XXXXI. XXXXII. XXXXIII. Apollonij. PROPOSITIO XXXXI.
Page: 147 (109)
[125.] PROPOSITO XXXXII.
Page: 147 (109)
[126.] PROPOSITIO XXXXIII.
Page: 148 (110)
[127.] Notæ in Propoſ. XXXXI.
Page: 148 (110)
[128.] Notæ in Propoſ. XXXXII.
Page: 149 (111)
[129.] Notæ in Propoſit. XXXXIII.
Page: 149 (111)
[130.] SECTIO DECIMASEXTA Continens XVI. XVII. XVIII. Propoſ. Apollonij.
Page: 150 (112)
[131.] Notæ in Propoſit. XVI. XVII. XVIII.
Page: 152 (114)
[132.] SECTIO DECIMASEPTIMA Continens XIX. XX. XXI. XXII. XXIII. XXIV. & XXV. Propoſ. Apollonij. PROPOSITIO XIX.
Page: 154 (116)
[133.] PROPOSITIO XX. XXI. & XXII.
Page: 155 (117)
[134.] PROPOSITIO XXIII. & XXIV.
Page: 156 (118)
[135.] PROPOSITIO XXV.
Page: 157 (119)
[136.] Notæ in Propoſit. XIX.
Page: 157 (119)
[137.] Notæ in Propoſit. XX. XXI. XXII.
Page: 158 (120)
[138.] Notæ in Propoſ. XXIII. XXIV.
Page: 161 (123)
[139.] Notæ in Propoſ. XXXV.
Page: 161 (123)
[140.] SECTIO DECIMAOCTAVA Continens XXXII. XXXIII. XXXIV. XXXV. XXXVI. XXXVII. XXXVIII. XXXIX. XXXX. XXXXVII. XXXXVIII. Propoſit. Apollonij. PROPOSITIO XXXII.
Page: 162 (124)
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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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