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

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        <div xml:id="echoid-div302" type="section" level="1" n="109">
          <p>
            <s xml:id="echoid-s3468" xml:space="preserve">
              <pb o="154" file="0218" n="238" rhead="CHRISTIANI HUGENII"/>
            mum atque agitata ab axe in B, deinde vero ab axe in C;
              <lb/>
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            <s xml:id="echoid-s3469" xml:space="preserve">
              <note position="left" xlink:label="note-0218-01" xlink:href="note-0218-01a" xml:space="preserve">
                <emph style="sc">De centro</emph>
                <lb/>
                <emph style="sc">OSCILLA-</emph>
                <lb/>
                <emph style="sc">TIONIS</emph>
              .</note>
            ſitque in prima ſuſpenſione centrum oſcillationis D, in po-
              <lb/>
            ſteriori vero centrum oſcillationis E. </s>
            <s xml:id="echoid-s3470" xml:space="preserve">Dico eſſe ut B A ad
              <lb/>
            C A ita E A ad D A.</s>
            <s xml:id="echoid-s3471" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3472" xml:space="preserve">Quum enim, in ſuſpenſione ex B, efficiatur diſtantia A D,
              <lb/>
            qua nempe centrum oſcillationis inferius eſt centro gravita-
              <lb/>
            tis, applicando ad diſtantiam B A ſpatium quoddam, cujus
              <lb/>
            multiplex ſecundum numerum particularum minimarum æ-
              <lb/>
            qualium, in quas magnitudo diviſa intelligitur, æquatur
              <lb/>
            quadratis diſtantiarum ab axe per A, parallelo axi in B ;</s>
            <s xml:id="echoid-s3473" xml:space="preserve">
              <note symbol="*" position="left" xlink:label="note-0218-02" xlink:href="note-0218-02a" xml:space="preserve">Prop.
                <lb/>
              præced.</note>
            erit proinde rectangulum B A D dicto ſpatio æquale. </s>
            <s xml:id="echoid-s3474" xml:space="preserve">Item,
              <lb/>
            in ſuſpenſione ex C, quum fiat diſtantia A E, applicando
              <lb/>
            idem dictum ſpatium ad diſtantiam C A; </s>
            <s xml:id="echoid-s3475" xml:space="preserve">erit & </s>
            <s xml:id="echoid-s3476" xml:space="preserve">rectangu-
              <lb/>
            lum C A E eidem ſpatio æquale. </s>
            <s xml:id="echoid-s3477" xml:space="preserve">Itaque æqualia inter ſe re-
              <lb/>
            ctangula B A D, C A E; </s>
            <s xml:id="echoid-s3478" xml:space="preserve">ac proinde ratio B A ad C A
              <lb/>
            eadem quæ A E ad A D. </s>
            <s xml:id="echoid-s3479" xml:space="preserve">quod erat demonſtrandum.</s>
            <s xml:id="echoid-s3480" xml:space="preserve"/>
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            <s xml:id="echoid-s3481" xml:space="preserve">Hinc patet, dato pendulo ſimplici, quod magnitudini
              <lb/>
            ſuſpenſæ iſochronum ſit in una ſuſpenſione, datoque ejus
              <lb/>
            centro gravitatis; </s>
            <s xml:id="echoid-s3482" xml:space="preserve">etiam in alia omni ſuſpenſione, longiori
              <lb/>
            vel breviori, dummodo idem maneat planum oſcillationis,
              <lb/>
            longitudinem penduli iſochroni datam eſſe.</s>
            <s xml:id="echoid-s3483" xml:space="preserve"/>
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        <div xml:id="echoid-div305" type="section" level="1" n="110">
          <head xml:id="echoid-head136" xml:space="preserve">PROPOSITIO XX.</head>
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            <s xml:id="echoid-s3484" xml:space="preserve">CEntrum Oſcillationis & </s>
            <s xml:id="echoid-s3485" xml:space="preserve">punctum ſuſpenſionis
              <lb/>
            inter ſe convertuntur.</s>
            <s xml:id="echoid-s3486" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3487" xml:space="preserve">In figura ſuperiori, quia, poſita ſuſpenſione ex B, cen-
              <lb/>
              <note position="left" xlink:label="note-0218-03" xlink:href="note-0218-03a" xml:space="preserve">TAB. XXII.
                <lb/>
              Fig. 3.</note>
            trum oſcillationis eſt D; </s>
            <s xml:id="echoid-s3488" xml:space="preserve">etiam invertendo omnia, ponendo-
              <lb/>
            que ſuſpenſionem ex D, erit tunc centrum oſcillationis B.
              <lb/>
            </s>
            <s xml:id="echoid-s3489" xml:space="preserve">Hoc enim ex ipſa propoſitione præcedenti manifeſtum eſt.</s>
            <s xml:id="echoid-s3490" xml:space="preserve"/>
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        <div xml:id="echoid-div307" type="section" level="1" n="111">
          <head xml:id="echoid-head137" xml:space="preserve">PROPOSITIO XXI.</head>
          <p style="it">
            <s xml:id="echoid-s3491" xml:space="preserve">QUomodo in figuris planis centra oſcillationis in-
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            veniantur.</s>
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          <p>
            <s xml:id="echoid-s3493" xml:space="preserve">Intellectis quæ hactenus demonſtrata ſunt, facile jam </s>
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