Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 1: Opera mechanica
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CHRISTIANI HUGENII
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ut quadratum B D ad quadratum D G ita eſt H K ad K G.
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<
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<
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Ut autem H K ad K G, ita eſt quadratum F K ad quadra-
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tum K G. </
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<
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xml:space
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">Ergo ſicut quadratum B D ad quadratum D G,
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ita quadratum F K ad quadratum K G. </
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<
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xml:space
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">Et proinde ſicut
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B D ad D G longitudine, ita F K ad K G. </
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<
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xml:space
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">Unde ſequitur
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B G F eſſe lineam rectam. </
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<
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">Sed G F occurrit parabolæ E F ad
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angulos rectos. </
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<
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xml:space
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">Ergo apparet B G, tangentem paraboloidis,
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productam occurrere eidem parabolæ ad angulos rectos. </
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<
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ſimiliter de quavis illius tangente demonſtrabitur. </
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<
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xml:space
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">Ergo con-
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ſtat ex evolutione lineæ E A B, à termino E incepta, de-
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ſcribi parabolam E F . </
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<
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xml:space
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">quod erat demonſtrandum.</
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huj.</
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">REctam lineam invenire æqualem datæ portioni
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curvæ paraboloidis, ejus nempe in qua qua-
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drata ordinatim applicatarum ad axem, ſunt in-
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ter ſe ſicut cubi abſciſſarum ad verticem.</
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<
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">Quomodo hoc fiat ex prop. </
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<
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">præcedenti manifeſtum eſt.
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">TAB. XIII.
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Fig. 2.</
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Parabola vero E F ad conſtructionem non requiritur, quæ
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ſic peragetur. </
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<
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">Data quavis parte paraboloidis hujus A B, cui
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rectam æqualem invenire oporteat, ducatur B G tangens in
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puncto B, quæ occurrat axi A G in G. </
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<
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A G fuerit tertia pars A D, inter verticem & </
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<
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">ordinatim ap-
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plicatam B D interceptæ. </
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<
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">Porro ſumpta A E æquali {8/27} lineæ
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M, quæ latus rectum eſt paraboloidis A B, ducatur E F
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parallela B G, occurratque lineæ A F, quæ parallela eſt
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B D, in F. </
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">Jam ſi ad rectam B G addatur N F, exceſſus
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rectæ E F ſupra E A, habebitur recta æqualis curvæ A B.
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</
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<
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<
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">Semper ergo curva A B tantum ſuperat tangentem B G,
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quantum recta E F rectam E A.</
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<
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">Rurſus autem hic in lineam incidimus, cujus longitudi-
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nem alii jam ante dimenſi ſunt. </
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<
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Joh. </
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">Heuratius Harlemenſis rectæ æqualem oſtendit, cujus
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demonſtratio poſt commentarios Joh. </
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