Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 1: Opera mechanica
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CHRISTIANI HUGENII
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E A G, quia omnes F L æquales totidem G A . </
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<
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.</
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que quadrata L F æquantur totidem rectangulis H A G , hoc eſt, totidem quadratis A G cum totidem rectangulis
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xml:space
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huj.</
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A G H. </
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xml:space
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xml:space
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præced.</
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quadratis E A, cum totidem duplis rectangulis E A G, at-
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que inſuper totidem quadratis A G cum totidem rectangulis
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A G H. </
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<
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rectangulo E A G & </
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<
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">quadrato A G; </
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<
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">faciunt quadratum E G.
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</
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<
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xml:space
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">Ergo apparet quadrata omnia F K æquari totidem quadratis
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E G, una cum totidem rectangulis A G H. </
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<
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xml:space
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dendum.</
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<
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">Porro in reliquis omnibus caſibus, quadrata omnia F K
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Fig. 1. 2.</
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æquantur totidem quadratis K L, minus bis totidem rectan-
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gulis K L F, plus totidem quadratis L F; </
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<
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xml:space
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dem quadratis E A, minus totidem duplis rectangulis E A G,
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plus totidem quadratis A G, cum totidem rectangulis A G H.
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</
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<
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drato A G, minus duplo rectangulo E A G, æquale qua-
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drato E G. </
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<
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xml:space
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">Ergo rurſus quadrata omnia F K æqualia erunt
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totidem quadratis E G, una cum totidem rectangulis A G H. </
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Quare conſtat propoſitum.</
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<
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">Hinc ſequitur, rectangulum A G H eadem magnitudine
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eſſe, utriusvis cunei ſubcentrica fuerit A H; </
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per hanc, ſive per illam tangentium parallelarum A L ab-
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ſciſſi. </
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<
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xml:space
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">Itaque A G unius caſus ad A G alterius, ut H G hu-
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jus ad H G illius. </
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<
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">Sicut autem rectæ A G inter ſe, ita in
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utroque caſu cunei per A L abſciſſi, ut colligitur ex prop. </
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</
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<
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<
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xml:space
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<
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ſubcene
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rica cunei, per alterutram tangentium parallelarum
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A L abſciſſi, dari quoque cunei, pertangentem alteram A L
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abſciſſi, ſubcentricam.</
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Fig. 3.</
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recta E D transeat per G, centrum </
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