Huygens, Christiaan - Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica

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172445ET HYPERBOLÆ QUADRATURA. F D M K, P L M D. dico triangulum A F L eſſe medium arith-
meticum inter parallelogramma F D M K, P L M D. Grego-
rius à S. Vincentio in Lib. de Hyperbola demonſtrat triangu-
lum A F L eſſe æquale trapezio D F L M, ſed manifeſtum eſt
trapezium D F L M eſſe medium arithmeticum inter paral-
lelogramma F D M K, P L M D; & ideo patet propo-
ſitum.

PROP. XXVII. THEOREMA.

Iisdem poſitis: ducatur A I rectam F L bifariam dividens in
11TAB.
XLVIII.
fig. 4. I & hyperbolam interſecans in puncto G, fiatque trape-
zium ſectori circumſcriptum A F G L, quod dico eſſe me-
dium geometricum inter parallellogramma F D M K, P L M D.
ex demonſtratis Gregorii à S. Vincentio evidens eſt trape-
zium A F G L æquale eſſe rectilineo D F G L M. & quoniam
A G I recta ſecat rectam F L bifariam in I, ex ejuſdem Gre-
gorii à S. Vincentio Lib. de hyperbola, manifeſtum eſt rectas
L M, G H, FD, eſſe continuè proportionales in eadem ratione
cum tribus continuè proportionalibus A D, A H, A M. aſym-
ptoto A O per punctum G ducatur parallela recta R G S
rectis F D, M K, occurrens in punctis R, S. quoniam rectæ
F D, G H, L M, ſunt continuè proportionales, erit dividen-
do & permutando F R ad S L ut G H ad L M: & quoniam
rectæ M A, H A, D A, ſunt continuè proportionales, erit
etiam dividendo & permutando M H ad H D hoc eſt S G ad
G R ut H A ad D A, vel ut G H ad L M; & proinde F R
eſt ad S L ut S G ad G R, cumque anguli F R G, G S L, ſint
æquales ob parallelas F R, S L, erunt triangula F R G, G L S,
æqualia; & proinde parallelogrammum R D M S æquale eſt
rectilineo D F G L M ſeu trapezio A F G L; ſed parallelo-
grammum R D M S eſt medium geometricum inter parale-
logramma P D M L, F D M K, quoniam eandem habentia alti-
tudinem eorum baſes nempe L M, S M, K M, ſunt continuè
proportionales; & ideo trapezium A F G L eſt medium

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61	349
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71	359
72	360
73	361
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83	368
84	369
85	370
86	371
87	372
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89	374
90	375

Scan	Original
61	349
62	350
63
64
65
66
67
68
69
70	358
71	359
72	360
73	361
74	362
75	363
76	364
77	365
78	366
79
80
81
82	367
83	368
84	369
85	370
86	371
87	372
88	373
89	374
90	375