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

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        <div xml:id="echoid-div350" type="section" level="1" n="124">
          <p>
            <s xml:id="echoid-s3811" xml:space="preserve">
              <pb o="168" file="0242" n="267" rhead="CHRISTIANI HUGENII"/>
            horizonti parallelum, A D vero verticale: </s>
            <s xml:id="echoid-s3812" xml:space="preserve">ut inveniatur
              <lb/>
              <note position="left" xlink:label="note-0242-01" xlink:href="note-0242-01a" xml:space="preserve">
                <emph style="sc">De centro</emph>
                <lb/>
                <emph style="sc">OSCILLA</emph>
                <lb/>
                <emph style="sc">TIONIS</emph>
              .</note>
            ſumma quadratorum à diſtantiis à plano A D, noſcenda eſt
              <lb/>
            diſtantia centri gr. </s>
            <s xml:id="echoid-s3813" xml:space="preserve">parabolæ O V H ab O H, quæ ſit Φ P,
              <lb/>
            eſtque {2/5} V P. </s>
            <s xml:id="echoid-s3814" xml:space="preserve">Deinde, diviſâ P V bifariam in Δ, conſtat
              <lb/>
            rectangulum Δ Ρ Φ, multiplex per numerum particularum
              <lb/>
            ſphæræ A B C, æquari quadratis diſtantiarum à plano A D .</s>
            <s xml:id="echoid-s3815" xml:space="preserve">
              <note symbol="*" position="left" xlink:label="note-0242-02" xlink:href="note-0242-02a" xml:space="preserve">Prop. 15.
                <lb/>
              @n fine.</note>
            Eſt autem rectangulum Δ Ρ Φ æquale {1/5} quadrati P V, vel
              <lb/>
            quadrati B E.</s>
            <s xml:id="echoid-s3816" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3817" xml:space="preserve">Atqui, quadrata diſtantiarum à plano B C, æqualia eſſe
              <lb/>
            liquet quadratis diſtantiarum à plano A D, ac proinde ei-
              <lb/>
            dem rectangulo Δ Ρ Φ, multiplici per dictum particularum
              <lb/>
            numerum. </s>
            <s xml:id="echoid-s3818" xml:space="preserve">Ergo ſpatium applicandum, in ſphæra A B C,
              <lb/>
            erit duplum rectanguli Δ Ρ Φ; </s>
            <s xml:id="echoid-s3819" xml:space="preserve">ideoque æquale {2/5} quadrati à
              <lb/>
            radio E B.</s>
            <s xml:id="echoid-s3820" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3821" xml:space="preserve">Itaque, ſi ſphæra ſuſpenſa ſit ex puncto in ſuperficie ſua
              <lb/>
            A, erit E S, à centro ſphæræ E ad centrum agitationis S,
              <lb/>
            æqualis {2/5} ſemidiametri A E. </s>
            <s xml:id="echoid-s3822" xml:space="preserve">Totaque A S æqualis {7/10} dia-
              <lb/>
            metri A D. </s>
            <s xml:id="echoid-s3823" xml:space="preserve">Si vero ex puncto alio, ut L, ſphæra ſuſpenſa
              <lb/>
            ſit; </s>
            <s xml:id="echoid-s3824" xml:space="preserve">erit E S æqualis {2/5} tertiæ proportionalis duabus L E, E B.</s>
            <s xml:id="echoid-s3825" xml:space="preserve"/>
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        <div xml:id="echoid-div352" type="section" level="1" n="125">
          <head xml:id="echoid-head151" style="it" xml:space="preserve">Centrum oſcillationis Cylindri.</head>
          <p>
            <s xml:id="echoid-s3826" xml:space="preserve">In cylindro, invenimus ſpatium applicandum æquari {@/12}
              <lb/>
            quadrati altitudinis, una cum {1/4} quadrati à ſemidiametro ba-
              <lb/>
            ſis. </s>
            <s xml:id="echoid-s3827" xml:space="preserve">Unde, ſi cylindrus à centro baſis ſuperioris ſuſpendatur,
              <lb/>
            fit longitudo penduli iſochroni æqualis {2/3} altitudinis, una cum
              <lb/>
            ſemiſſe ejus, quæ ſit ad ſemidiametrum baſis ut hæc ad alti-
              <lb/>
            tudinem.</s>
            <s xml:id="echoid-s3828" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div353" type="section" level="1" n="126">
          <head xml:id="echoid-head152" style="it" xml:space="preserve">Centrum oſcillationis Conoidis Parabolici.</head>
          <p>
            <s xml:id="echoid-s3829" xml:space="preserve">In conoide parabolico, rectangulum oſcillationis eſt {@/18}
              <lb/>
            quadrati altitudinis, cum {1/6} quadrati à ſemidiametro baſis.
              <lb/>
            </s>
            <s xml:id="echoid-s3830" xml:space="preserve">Unde, ſi à puncto verticis fuerit ſuſpenſum, fit longitudo
              <lb/>
            penduli iſochroni {3/4} axis, cum {1/4} ejus quæ ſit ad ſemidiame-
              <lb/>
            trum baſis, ſicut hæc ad axem, id eſt, una cum {1/4} lateris re-
              <lb/>
            cti parabolæ genitricis.</s>
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