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

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        <div xml:id="echoid-div234" type="section" level="1" n="89">
          <pb o="125" file="0183" n="200" rhead="HOROLOG. OSCILLATOR."/>
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        <div xml:id="echoid-div236" type="section" level="1" n="90">
          <head xml:id="echoid-head116" xml:space="preserve">PROPOSITIO II.</head>
          <note position="right" xml:space="preserve">
            <emph style="sc">De centro</emph>
            <lb/>
            <emph style="sc">OSCILLA-</emph>
            <lb/>
            <emph style="sc">TIONIS.</emph>
            <lb/>
          TAB. XVIII.
            <lb/>
          Fig. 1.</note>
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            <s xml:id="echoid-s2845" xml:space="preserve">POſitis quæ prius, ſi pondera omnia A, B, C,
              <lb/>
            ſint æqualia; </s>
            <s xml:id="echoid-s2846" xml:space="preserve">dico ſummam omnium perpendi-
              <lb/>
            cularium A D, B E, C F, æquari perpendicula-
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            ri, à centro gravitatis ductæ, G H, multiplici
              <lb/>
            ſecundum ponderum numerum.</s>
            <s xml:id="echoid-s2847" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s2848" xml:space="preserve">Quum enim ſumma productorum, à ponderibus ſingulis
              <lb/>
            in ſuas perpendiculares, æquetur producto ex G H in pon-
              <lb/>
            dera omnia; </s>
            <s xml:id="echoid-s2849" xml:space="preserve">ſitque hìc, propter ponderum æqualitatem,
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            ſumma illa productorum æqualis producto ex uno pondere
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            in ſummam omnium perpendicularium; </s>
            <s xml:id="echoid-s2850" xml:space="preserve">itemque productum
              <lb/>
            ex G H in pondera omnia, idem quod productum ex pon-
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            dere uno in G H, multiplicem ſecundum ponderum nume-
              <lb/>
            rum: </s>
            <s xml:id="echoid-s2851" xml:space="preserve">patet ſummam perpendicularium neceſſario jam æquari
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            ipſi G H, multiplici ſecundum ponderum numerum. </s>
            <s xml:id="echoid-s2852" xml:space="preserve">quod
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            erat demonſtrandum.</s>
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        <div xml:id="echoid-div237" type="section" level="1" n="91">
          <head xml:id="echoid-head117" xml:space="preserve">PROPOSITIO III.</head>
          <p style="it">
            <s xml:id="echoid-s2854" xml:space="preserve">SI magnitudines quædam deſcendant omnes, vel
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            aſcendant, licet inæqualibus intervallis; </s>
            <s xml:id="echoid-s2855" xml:space="preserve">alti-
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            tudines deſcenſus vel aſcenſus cujusque, in ipſam
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            magnitudinem ductæ, efficient ſummam producto-
              <lb/>
            rum æqualem ei, quæ fit ex altitudine deſcenſus
              <lb/>
            vel aſcenſus centri gravitatis omnium magnitudi-
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            num, ducta in omnes magnitudines.</s>
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          </p>
          <p>
            <s xml:id="echoid-s2857" xml:space="preserve">Sunto magnitudines A, B, C, quæ ex A, B, C, deſcen-
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              <note position="right" xlink:label="note-0183-02" xlink:href="note-0183-02a" xml:space="preserve">TAB. XVIII.
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              Fig. 2.</note>
            dant in D, E, F; </s>
            <s xml:id="echoid-s2858" xml:space="preserve">vel ex D, E, F, aſcendant in A, B, C.
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            </s>
            <s xml:id="echoid-s2859" xml:space="preserve">Sitque earum centrum gravitatis omnium, dum ſunt in
              <lb/>
            A, B, C, eadem altitudine cum puncto G; </s>
            <s xml:id="echoid-s2860" xml:space="preserve">cum vero ſunt in
              <lb/>
            D, E, F, eadem altitudine cum puncto H. </s>
            <s xml:id="echoid-s2861" xml:space="preserve">Dico ſummam
              <lb/>
            productorum ex altitudine A D in A, B E in B, C F in C,
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            æquari producto ex G H in omnes A, B, C.</s>
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