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

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        <div xml:id="echoid-div244" type="section" level="1" n="93">
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            <s xml:id="echoid-s2955" xml:space="preserve">
              <pb o="130" file="0190" n="208" rhead="CHRISTIANI HUGENII"/>
            titudinibus iſtis in ſua pondera, erit ſumma productorum
              <lb/>
              <note position="left" xlink:label="note-0190-01" xlink:href="note-0190-01a" xml:space="preserve">
                <emph style="sc">De centro</emph>
                <lb/>
                <emph style="sc">OSCILLA-</emph>
                <lb/>
                <emph style="sc">TIONIS.</emph>
              </note>
            major quam {a e e y + b f f y + c g g y/x x}. </s>
            <s xml:id="echoid-s2956" xml:space="preserve">quæ proinde major quoque
              <lb/>
            probatur quam {a d y + b d y + c d y/x}. </s>
            <s xml:id="echoid-s2957" xml:space="preserve">Nam quia poſita eſt longitudo
              <lb/>
            x æqualis {a e e + b f f + g g/a d + b d + c d}; </s>
            <s xml:id="echoid-s2958" xml:space="preserve">erit a d x + b d x + c d x æquale
              <lb/>
            a e e + b f f + c g g. </s>
            <s xml:id="echoid-s2959" xml:space="preserve">Et ductis omnibus in y, & </s>
            <s xml:id="echoid-s2960" xml:space="preserve">dividen-
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            do per x x, erit {a d y + b d y + c d y/x} æquale {a e e y + b f f y + c g g y/x x}. </s>
            <s xml:id="echoid-s2961" xml:space="preserve">Unde
              <lb/>
            quod dictum eſt conſequitur. </s>
            <s xml:id="echoid-s2962" xml:space="preserve">Eſt autem ſumma iſta produ-
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            ctorum æqualis ei, quod fit ducendo altitudinem, ad quam
              <lb/>
            aſcendit centrum gravitatis commune ponderum A, B, C, in
              <lb/>
            ſummam ipſorum ponderum, a + b + c; </s>
            <s xml:id="echoid-s2963" xml:space="preserve">ſi nempe ſingu-
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            la, uti dictum, ſeorſim quousque poſſunt moveantur. </s>
            <s xml:id="echoid-s2964" xml:space="preserve">Quan-
              <lb/>
            titas vero {a d y + b d y + c d y/x} producitur ex deſcenſu centri gravi-
              <lb/>
            tatis eorundem ponderum, (qui deſcenſus eſt R Q, ſive {d y/x},
              <lb/>
            ut ſupra inventum fuit,) in eandem quoque ponderum ſum-
              <lb/>
            mam a + b + c. </s>
            <s xml:id="echoid-s2965" xml:space="preserve">Ergo quum prius productum altero hoc
              <lb/>
            majus oſtenſum fuerit, ſequitur aſcenſum centri gravitatis
              <lb/>
            ponderum A, B, C, ſi, relicto pendulo ubi pervenere in
              <lb/>
            T, V, X, ſingula celeritates acquiſitas ſurſum convertant,
              <lb/>
            majorem fore ejusdem centri gravitatis deſcenſu, dum ex
              <lb/>
            A, B, C, moventur in T, V, X. </s>
            <s xml:id="echoid-s2966" xml:space="preserve">quod eſt abſurdum, cum
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            dictus aſcenſus deſcenſui æqualis eſſe debeat, per anteceden-
              <lb/>
            tem.</s>
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          <p>
            <s xml:id="echoid-s2968" xml:space="preserve">Eodem modo, ſi dicatur celeritatem puncti L, ubi per-
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            venerit in P, minorem eſſe celeritate ponderis G quum in O
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            pervenerit; </s>
            <s xml:id="echoid-s2969" xml:space="preserve">oſtendemus aſcenſum poſſibilem centri gravitatis
              <lb/>
            ponderum A, B, C, minorem eſſe quam deſcenſum, quod
              <lb/>
            eidem propoſitioni antecedenti repugnat. </s>
            <s xml:id="echoid-s2970" xml:space="preserve">Quare relinquitur
              <lb/>
            ut eadem ſit celeritas puncti L, ad P tranſlati, quæ ponde-
              <lb/>
            ris G in O. </s>
            <s xml:id="echoid-s2971" xml:space="preserve">Unde, ut ſuperius dictum, ſequitur pendulum
              <lb/>
            ſimplex F G compoſito ex A, B, C, iſochronum eſſe.</s>
            <s xml:id="echoid-s2972" xml:space="preserve"/>
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        <div xml:id="echoid-div250" type="section" level="1" n="94">
          <head xml:id="echoid-head120" xml:space="preserve">PROPOSITIO VI.</head>
          <p style="it">
            <s xml:id="echoid-s2973" xml:space="preserve">DAto pendulo ex quotcunque ponderibus æqua-
              <lb/>
            libus compoſito; </s>
            <s xml:id="echoid-s2974" xml:space="preserve">ſi ſumma quadratorum </s>
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