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

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        <div xml:id="echoid-div237" type="section" level="1" n="91">
          <pb o="126" file="0184" n="201" rhead="CHRISTIANI HUGENII"/>
          <p>
            <s xml:id="echoid-s2863" xml:space="preserve">Intelligatur enim planum horizontale cujus ſectio recta
              <lb/>
              <note position="left" xlink:label="note-0184-01" xlink:href="note-0184-01a" xml:space="preserve">
                <emph style="sc">De centro</emph>
                <lb/>
                <emph style="sc">OSCILLA-</emph>
                <lb/>
                <emph style="sc">TIONIS.</emph>
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            M P, atque in ipſum incidant productæ A D, B E, C F
              <lb/>
            & </s>
            <s xml:id="echoid-s2864" xml:space="preserve">G H, in M, N, O, P.</s>
            <s xml:id="echoid-s2865" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2866" xml:space="preserve">Quia igitur ſumma productorum ex A M in A, B N in B,
              <lb/>
            C O in C, æqualis eſt facto ex G P in omnes A, B, C .</s>
            <s xml:id="echoid-s2867" xml:space="preserve">
              <note symbol="*" position="left" xlink:label="note-0184-02" xlink:href="note-0184-02a" xml:space="preserve">Prop. 1.
                <lb/>
              huj.</note>
            Similiterque ſumma productorum ex D M in A, E N in B,
              <lb/>
            F O in C, æqualis facto ex H P in omnes A, B, C; </s>
            <s xml:id="echoid-s2868" xml:space="preserve">ſe-
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            quitur & </s>
            <s xml:id="echoid-s2869" xml:space="preserve">exceſſum priorum productorum ſupra poſteriora,
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            æquari facto ex G H in omnes magnitudines A, B, C. </s>
            <s xml:id="echoid-s2870" xml:space="preserve">Di-
              <lb/>
            ctum vero exceſſum æquari manifeſtum eſt productis ex A D
              <lb/>
            in A, B E in B, C F in C. </s>
            <s xml:id="echoid-s2871" xml:space="preserve">Ergo hæc ſimul etiam æqua-
              <lb/>
            lia erunt producto ex G H in omnes A, B, C. </s>
            <s xml:id="echoid-s2872" xml:space="preserve">quod erat
              <lb/>
            demonſtrandum.</s>
            <s xml:id="echoid-s2873" xml:space="preserve"/>
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        <div xml:id="echoid-div241" type="section" level="1" n="92">
          <head xml:id="echoid-head118" xml:space="preserve">PROPOSITIO IV.</head>
          <p style="it">
            <s xml:id="echoid-s2874" xml:space="preserve">SI pendulum è pluribus ponderibus compoſitum,
              <lb/>
            atque è quiete dimiſſum, partem quamcunque
              <lb/>
            oſcillationis integræ confecerit, atque inde porro
              <lb/>
            intelligantur pondera ejus ſingula, relicto communi
              <lb/>
            vinculo, celeritates acquiſitas ſurſum convertere,
              <lb/>
            ac quousque poſſunt aſcendere; </s>
            <s xml:id="echoid-s2875" xml:space="preserve">hoc facto, centrum
              <lb/>
            gravitatis ex omnibus compoſitæ, ad eandem alti-
              <lb/>
            tudinem reverſum erit, quam ante inceptam oſcil-
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            lationem obtinebat.</s>
            <s xml:id="echoid-s2876" xml:space="preserve"/>
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            <s xml:id="echoid-s2877" xml:space="preserve">Sit pendulum compoſitum ex ponderibus quotlibet
              <lb/>
              <note position="left" xlink:label="note-0184-03" xlink:href="note-0184-03a" xml:space="preserve">TAB. XVIII.
                <lb/>
              Fig. 3. 4.</note>
            A, B, C, virgæ, vel ſuperficiei pondere carenti, inhæren-
              <lb/>
            tibus. </s>
            <s xml:id="echoid-s2878" xml:space="preserve">Sitque ſuſpenſum ab axe per D punctum ducto, qui
              <lb/>
            ad planum, quod hic conſpicitur, perpendicularis intelliga-
              <lb/>
            tur. </s>
            <s xml:id="echoid-s2879" xml:space="preserve">In quo eodem plano etiam centrum gravitatis E, pon-
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            derum A, B, C, poſitum ſit; </s>
            <s xml:id="echoid-s2880" xml:space="preserve">lineaque centri D E, incli-
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            netur ad lineam perpendiculi D F, angulo E D F: </s>
            <s xml:id="echoid-s2881" xml:space="preserve">attra-
              <lb/>
            cto, nimirum, eo uſque pendulo. </s>
            <s xml:id="echoid-s2882" xml:space="preserve">Hinc vero dimitti jam
              <lb/>
            ponatur, ac partem quamlibet oſcillationis conficere, ita ut
              <lb/>
            pondera A, B, C, perveniant in G, H, K. </s>
            <s xml:id="echoid-s2883" xml:space="preserve">Unde, </s>
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