Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 1: Opera mechanica
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CHRISTIANI HUGENII
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<
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<
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.</
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xml:space
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">SPatium peractum certo tempore, à gravi è quie-
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te caſum inchoante, dimidium eſſe ejus ſpatii
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quod pari tempore transiret motu æquabili, cum
<
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celeritate quam acquiſivit ultimo caſus momento.</
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<
s
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xml:space
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">Sit tempus deſcenſus totius A H, quo tempore mobile
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xml:space
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">TAB. V.
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Fig. 3.</
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peregerit ſpatium quoddam cujus quantitas deſignetur plano P.
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</
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<
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xml:space
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">ductaque H L perpendiculari ad A H, longitudinis cujus-
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libet, referat illa celeritatem in fine caſus acquiſitam. </
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<
s
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xml:space
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de completo rectangulo A H L M, intelligatur eo notari
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quantitas ſpatii quod percurreretur tempore A H, cum ce-
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leritate H L. </
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<
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xml:space
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">Oſtendendum eſt igitur planum P dimidium
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eſſe rectanguli M H, hoc eſt, ducta diagonali A L, æqua-
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le triangulo A H L.</
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<
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<
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xml:space
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">Si planum P non eſt æquale triangulo A H L, ergo aut
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minus eo erit, aut majus. </
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<
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xml:space
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">Sit primo, ſi fieri poteſt, pla-
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num P minus triangulo A H L. </
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<
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xml:space
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">dividatur autem A H in tot
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partes æquales A C, C E, E G &</
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<
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xml:space
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<
s
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xml:space
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">ut, circumſcriptâ tri-
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angulo A H L figurâ è rectangulis quorum altitudo ſingulis
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diviſionum ipſius A H partibus æquetur, ut ſunt rectangula
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B C, D E, F G, alterâque eidem triangulo inſcriptâ, ex
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rectangulis ejusdem altitudinis, ut ſunt K E, O G &</
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<
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<
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">ut,
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inquam, exceſſus illius figuræ ſupra hanc, minor ſit exceſ-
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ſu trianguli A H L ſupra planum P. </
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>
<
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xml:space
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">hoc enim fieri poſſe
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perſpicuum eſt, cum totus exceſſus figuræ circumſcriptæ ſu-
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per inſcriptam æquetur rectangulo infimo, baſin habenti H L.
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</
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>
<
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xml:space
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">Erit itaque omnino exceſſus ipſius trianguli A H L ſupra
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figuram inſcriptam minor quam ſupra planum P, ac proin-
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de figura triangulo inſcripta major plano P. </
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>
<
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xml:space
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">Porro autem,
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quum recta A H tempus totius deſcenſus referat, ejus par-
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tes æquales A C, C E, E G, æquales temporis illius par-
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tes referent. </
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>
<
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xml:space
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">Cumque celeritates mobilis cadentis creſcant
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<
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*
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xml:space
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">Prop. I.
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huj.</
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eadem proportione qua tempora deſcenſus ; </
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