Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica
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ET HYPERBOLÆ QUADRATURA.
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F D M K, P L M D. </
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">dico triangulum A F L eſſe medium arith-
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meticum inter parallelogramma F D M K, P L M D. </
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rius à S. </
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<
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">de Hyperbola demonſtrat triangu-
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lum A F L eſſe æquale trapezio D F L M, ſed manifeſtum eſt
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trapezium D F L M eſſe medium arithmeticum inter paral-
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lelogramma F D M K, P L M D; </
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<
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ſitum.</
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">Iisdem poſitis: </
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">ducatur A I rectam F L bifariam dividens in
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XLVIII.
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fig. 4.</
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I & </
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">hyperbolam interſecans in puncto G, fiatque trape-
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zium ſectori circumſcriptum A F G L, quod dico eſſe me-
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dium geometricum inter parallellogramma F D M K, P L M D.
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</
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<
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zium A F G L æquale eſſe rectilineo D F G L M. </
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<
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A G I recta ſecat rectam F L bifariam in I, ex ejuſdem Gre-
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gorii à S. </
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">de hyperbola, manifeſtum eſt rectas
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L M, G H, FD, eſſe continuè proportionales in eadem ratione
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cum tribus continuè proportionalibus A D, A H, A M. </
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<
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ptoto A O per punctum G ducatur parallela recta R G S
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rectis F D, M K, occurrens in punctis R, S. </
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F D, G H, L M, ſunt continuè proportionales, erit dividen-
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do & </
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<
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rectæ M A, H A, D A, ſunt continuè proportionales, erit
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etiam dividendo & </
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G R ut H A ad D A, vel ut G H ad L M; </
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<
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eſt ad S L ut S G ad G R, cumque anguli F R G, G S L, ſint
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æquales ob parallelas F R, S L, erunt triangula F R G, G L S,
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æqualia; </
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<
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rectilineo D F G L M ſeu trapezio A F G L; </
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grammum R D M S eſt medium geometricum inter parale-
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logramma P D M L, F D M K, quoniam eandem habentia alti-
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tudinem eorum baſes nempe L M, S M, K M, ſunt continuè
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proportionales; </
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