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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G H, nempe X; </
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G H, nempe X, æqualis eſt minori duarum mediarum arith-
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meticè continuè proportionalium inter A & </
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dem minor eſt, quod demonſtrare oportuit.</
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A B # A B
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C D # G H
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E F # M N
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K L # O P
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Z # X
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hyperbolæ minorem eſſe quam mi-
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nor duarum mediarum geometricè con-
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tinuè proportionalium inter A & </
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</
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& </
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Item inter G & </
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geometriea N; </
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<
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MN, OP, &</
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ex prædictis C & </
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quam D; </
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& </
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N media geometrica inter M & </
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inter eaſdem; </
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media harmonica inter M & </
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nica inter E & </
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major eritquam F. </
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">eadem methodo utramque ſeriem in in-
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finitum continuando, ſemper demonſtratur terminum quem-
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libet ſeriei A B, C D, minorem eſſe quam idem numero ter-
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minus ſeriei A B, G H; </
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">igitur terminatio ſeriei A B, C D,
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nempe Z minor erit quam terminatio ſeriei A B, G H, nem-
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pe X; </
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lis eſt minori duarum mediarum geometricè continuè propor-
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tionalium inter A & </
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demonſtrare oportuit.</
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<
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rem eſſe illa, in antecedenti propoſitione, demonſtrata, et-
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iamſi hæc ſit paulò laborioſior. </
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eſt duas poſſe eſſe ſeries æquales terminationes habentes, </
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