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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[281.] Notæ in Propoſit. XII.
Page: 332 (293)
[282.] Notæ in Propoſit. XIII.
Page: 333 (294)
[283.] Notæ in Propoſit. XXIX.
Page: 334 (295)
[284.] Notæ in Propoſit. XXX.
Page: 334 (295)
[285.] Notæ in Propoſit. XIV. & XXV.
Page: 335 (296)
[286.] Notæ in Propoſit. XXVII.
Page: 335 (296)
[287.] SECTIO QVINTA Continens Propoſit. XXI. XXVIII. XXXXII. XXXXIII. XXIV. & XXXVII.
Page: 337 (298)
[288.] PROPOSITIO XXI. & XXVIII.
Page: 338 (299)
[289.] PROPOSITIO XXVI
Page: 339 (300)
[290.] PROPOSITIO XXXXII.
Page: 340 (301)
[291.] PROPOSITIO XXXXIII.
Page: 341 (302)
[292.] PROPOSITIO XXIV.
Page: 342 (303)
[293.] PROPOSITIO XXXVII.
Page: 343 (304)
[294.] Notę in Propoſit. XXVIII.
Page: 344 (305)
[295.] LEMMA. I.
Page: 345 (306)
[296.] Notę in Propoſit. XXI.
Page: 347 (308)
[297.] Notę in Propoſit. XXXXII.
Page: 349 (310)
[298.] Notæ in Propoſit. XXXXIII.
Page: 350 (311)
[299.] Notæ in Propoſit. XXIV.
Page: 352 (313)
[300.] SECTIO SEXTA Continens Propoſit. XXXIII. XXXIV. XXXV. & XXXVI. PROPOSITIO XXXIII.
Page: 353 (314)
[301.] PROPOSITIO XXXIV.
Page: 354 (315)
[302.] PROPOSITIO XXXV. & XXXVI.
Page: 355 (316)
[303.] In Sectionem VI.
Page: 356 (317)
[304.] LEMMA II.
Page: 357 (318)
[305.] LEMMA III.
Page: 357 (318)
[306.] LEMMA IV.
Page: 357 (318)
[307.] LEMMA V.
Page: 358 (319)
[308.] Notæ in Propof. XXXIII. & XXXIV.
Page: 359 (320)
[309.] Notæ in Propoſit. XXXV.
Page: 360 (321)
[310.] SECTIO SEPTIMA Continens Propoſit. XXXVIII. XXXIX. & XXXX. PROPOSITIO XXXVIII.
Page: 362 (323)
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page |< < (208) of 458 > >|
246208Apollonij Pergæi
Efficiant duo plana parallela D
11b282[Figure 282] E N F, G H P I in baſim coni A C
duas rectas lineas D F, G I, & pla-
num per axim coniductum efficiat
triangulum A B C perpendiculare
ad duo illa plana parallela; quæ ab
illo ſecentur in E K, H L. Erunt
D F, I G perpendiculares ad A C,
& educamus B M parallelam ipſis
E K, H L; & vt quadratum B M ad
A M in M C; ita ponatur N E ad
E O, & ita P H ſiat ad H Q, erunt
2212. 13.
lib. 1. N E, P H inclinata duarũ ſectionũ
F E D, I H G, aut eorum tranſuer-
ſæ; igitur O E, H Q erunt eorum
erecta, & propterea figuræ duarum ſectionũ ſunt ſimiles; igitur duæ ſectio-
3312. huius.283[Figure 283] nes ſimiles ſunt. Et ſi quidem fuerint N E, P H æquales; ipſæ quoque
442. & 10.
huius. æquales erunt, alias non; Et hoc erat propoſitum.
Notæ in Propoſit. XXV.
SI abſcindant conum aliquem duo plana parallela prouenient duæ ſe-
55a ctiones hyperbolicæ, vel quia duæ ſectiones ſunt ſimiles, & c. Quæ,
immutanda cenſui vt in textu videre eſt.
Sint abſciſſiones duorum planorum æquidiſtantium cum baſi I G, F D,
66b& ſecet conum planum tranſiens per eius axim, & c. Addidi verba, quæ
in textu d ſiderantur, quæ expoſitionem perſiciunt. Animaduertendum eſt, hanc
propoſitionem conuertibilem non eſſe; licet enim plana parallela in eodem cono
eſſiciant ſectiones ſimiles, verum non eſt, quod quotieſcunque in eodem cono

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