Huygens, Christiaan, Christiani Hugenii opera varia; Bd. 1: Opera mechanica

Table of handwritten notes

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              <pb o="225" file="0303" n="330" rhead="CONTROVERSIA."/>
            in quodam magni ſui Curſus Mathematici loco, memorando
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            experimentum cum Pendulo compoſito ex duobus ponderi-
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            bus inſtitutum, in quo computans rationem non habuit
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            (ut debebat) ponderis baculi, cui pondera erant applicata,
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            immerito regulas noſtras de determinando centro gravitatis
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            culpare, quaſi non convenirent cum iis quæ ille revera obſer-
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            varat.</s>
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        <div xml:id="echoid-div429" type="section" level="1" n="173">
          <head xml:id="echoid-head211" xml:space="preserve">IV.</head>
          <head xml:id="echoid-head212" style="it" xml:space="preserve">Exceptio Abbatis Catelani ad reſponſionem
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          Hugenii.</head>
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            <s xml:id="echoid-s4959" xml:space="preserve">NOn debebat Hugenius a ſuo principio ſeparare conſe-
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            quentiam, ut hanc aliter intelligat, quam ego in ſcri-
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            ptis meis. </s>
            <s xml:id="echoid-s4960" xml:space="preserve">Prorſus deberem oblitus eſſe Arithmetices, ſi ab-
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            ſolute negarem, ut me facere contendit, quod 4 magnitudi-
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            nes inæquales poſſint efficere 2 ſummas æquales, quum nil a-
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            liud concludo in ſcriptis, præterquam quod propoſitio Hu-
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            genii vera eſſe nequeat, niſi pars ſit æqualis toti. </s>
            <s xml:id="echoid-s4961" xml:space="preserve">Ut hoc
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            melius pateat, debemus hic proferre propoſitionem illam ge-
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            neralem propriis terminis.</s>
            <s xml:id="echoid-s4962" xml:space="preserve"/>
          </p>
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            <s xml:id="echoid-s4963" xml:space="preserve">Si Pendulum e pluribus ponderibus compoſitum, at que e quie-
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            te demiſſum, partem quamcunque Oſcillationis integræ confece-
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            rit, atque inde porro intelligantur pondera ejus ſingula, reli-
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            cto communi vinculo, celeritates acquiſitas ſurſum convertere,
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            ac quousque poſſunt aſcendere; </s>
            <s xml:id="echoid-s4964" xml:space="preserve">hoc facto, centrum gravitatis
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            ex omnibus compoſitæ, ad eandem altitudinem reverſum erit,
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            quam ante inceptam Oſcillationem obtinebat.</s>
            <s xml:id="echoid-s4965" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4966" xml:space="preserve">Cum hæc propoſitio terminis generaliſſimis concepta ſit,
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            ita ut numerus ponderum, ſitus eorum, duratio Vibrationis,
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            ipſam non mutent, pono, Exempli cauſâ, Pendulum compoſi-
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            tum e ponderibus duo bus æqualibus, & </s>
            <s xml:id="echoid-s4967" xml:space="preserve">inter ſe ad quam li-
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            buerit a ſe invicem diſtantiam junctis. </s>
            <s xml:id="echoid-s4968" xml:space="preserve">Conſidero porro al-
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            titudines, quæ ſunt proportionales quadratis velocitatum in
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            duobus Pendulis ſimplicibus, eſſe inter ſe ut velocitates </s>
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