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

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        <div xml:id="echoid-div294" type="section" level="1" n="107">
          <pb o="150" file="0214" n="234" rhead="CHRISTIANI HUGENII"/>
          <p>
            <s xml:id="echoid-s3385" xml:space="preserve">Sit figura A B C, cujus centrum gravitatis E, ſuſpenſa
              <lb/>
              <note position="left" xlink:label="note-0214-01" xlink:href="note-0214-01a" xml:space="preserve">
                <emph style="sc">De centro</emph>
                <lb/>
                <emph style="sc">OSCILLA-</emph>
                <lb/>
                <emph style="sc">TIONIS</emph>
              .</note>
            ab axe qui, per F punctum ad planum quod conſpicitur,
              <lb/>
            erectus ſit. </s>
            <s xml:id="echoid-s3386" xml:space="preserve">Ponendoque diviſam figuram in particulas mini-
              <lb/>
              <note position="left" xlink:label="note-0214-02" xlink:href="note-0214-02a" xml:space="preserve">TAB. XXII.
                <lb/>
              Fig. 1.</note>
            mas æquales, à quibus omnibus, in dictum axem, perpen-
              <lb/>
            diculares cadere intelligantur: </s>
            <s xml:id="echoid-s3387" xml:space="preserve">eſto, per ſuperius oſtenſa,
              <lb/>
            inventum planum H, cujus multiplex per numerum dicta-
              <lb/>
            rum particularum, æquetur quadratis omnibus dictarum
              <lb/>
            perpendicularium. </s>
            <s xml:id="echoid-s3388" xml:space="preserve">Applicatoque plano H ad rectam F E,
              <lb/>
            fiat longitudo F G. </s>
            <s xml:id="echoid-s3389" xml:space="preserve">Dico hanc eſſe longitudinem penduli
              <lb/>
            ſimplicis, iſochronas oſcillationes habentis magnitudini
              <lb/>
            A B C, agitatæ circa axem per F.</s>
            <s xml:id="echoid-s3390" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3391" xml:space="preserve">Quia enim ſumma quadratorum, à diſtantiis ab axe F,
              <lb/>
            applicata ad diſtantiam F E, multiplicem ſecundum par-
              <lb/>
            tium numerum, facit longitudinem penduli ſimplicis iſo-
              <lb/>
            chroni . </s>
            <s xml:id="echoid-s3392" xml:space="preserve">Iſti vero quadratorum ſummæ æquale ponitur
              <note symbol="*" position="left" xlink:label="note-0214-03" xlink:href="note-0214-03a" xml:space="preserve">Prop. 6.
                <lb/>
              huj.</note>
            num H, multiplex per eundem particularum numerum. </s>
            <s xml:id="echoid-s3393" xml:space="preserve">Er-
              <lb/>
            go & </s>
            <s xml:id="echoid-s3394" xml:space="preserve">planum H, multiplex per eundem particularum nu-
              <lb/>
            merum, ſi applicetur ad diſtantiam F E, multiplicem ſe-
              <lb/>
            cundum particularum numerum; </s>
            <s xml:id="echoid-s3395" xml:space="preserve">ſive, omiſſa communi mul-
              <lb/>
            tiplicitate, ſi planum H applicetur ad diſtantiam F E; </s>
            <s xml:id="echoid-s3396" xml:space="preserve">o-
              <lb/>
            rietur quoque longitudo penduli ſimplicis iſochroni. </s>
            <s xml:id="echoid-s3397" xml:space="preserve">Quam
              <lb/>
            proinde ipſam longitudinem F G eſſe conſtat. </s>
            <s xml:id="echoid-s3398" xml:space="preserve">quod erat de-
              <lb/>
            monſtrandum.</s>
            <s xml:id="echoid-s3399" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div297" type="section" level="1" n="108">
          <head xml:id="echoid-head134" xml:space="preserve">PROPOSITIO XVIII.</head>
          <p style="it">
            <s xml:id="echoid-s3400" xml:space="preserve">SI ſpatium planum, cujus multiplex ſecundum
              <lb/>
            numerum particularum ſuſpenſæ magnitudinis,
              <lb/>
            æquetur quadratis diſtantiarum ab axe gravitatis,
              <lb/>
            axi oſcillationis parallelo; </s>
            <s xml:id="echoid-s3401" xml:space="preserve">id, inquam, ſpatium
              <lb/>
            ſi applicetur ad rectam, æqualem diſtantiæ inter
              <lb/>
            utrumque dictorum axium, orietur recta æqualis
              <lb/>
            intervallo, quo centrum oſcillationis inferius eſt
              <lb/>
            centro gravitatis ejusdem magnitudinis.</s>
            <s xml:id="echoid-s3402" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3403" xml:space="preserve">Eſto magnitudo A B C D, cujus centrum gravitatis E;
              <lb/>
            </s>
            <s xml:id="echoid-s3404" xml:space="preserve">
              <note position="left" xlink:label="note-0214-04" xlink:href="note-0214-04a" xml:space="preserve">TAB. XXII.
                <lb/>
              Fig. 2.</note>
            </s>
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