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

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        <div xml:id="echoid-div320" type="section" level="1" n="116">
          <p>
            <s xml:id="echoid-s3605" xml:space="preserve">
              <pb o="160" file="0228" n="250" rhead="CHRISTIANI HUGENII"/>
            numerum particularum ſecctoris B C D, æquale erit quadra-
              <lb/>
              <note position="left" xlink:label="note-0228-01" xlink:href="note-0228-01a" xml:space="preserve">
                <emph style="sc">De centro</emph>
                <lb/>
                <emph style="sc">OSCILLA-</emph>
                <lb/>
                <emph style="sc">TIONIS</emph>
              .</note>
            tis diſtantiarum particularum ejus à puncto B. </s>
            <s xml:id="echoid-s3606" xml:space="preserve">Ideoque re-
              <lb/>
            ctangulum N B O, applicatum ad B A, diſtantiam inter
              <lb/>
            ſuſpenſionem & </s>
            <s xml:id="echoid-s3607" xml:space="preserve">centrum gravitatis ſectoris, dabit longitudi-
              <lb/>
            nem penduli iſochroni, cum ſector ex B ſuſpenditur . </s>
            <s xml:id="echoid-s3608" xml:space="preserve">
              <note symbol="*" position="left" xlink:label="note-0228-02" xlink:href="note-0228-02a" xml:space="preserve">Prop. 17.
                <lb/>
              huj.</note>
            autem rectangulum N B O = {1/2} r r: </s>
            <s xml:id="echoid-s3609" xml:space="preserve">diſtantia autem B A, ut
              <lb/>
            jam ante diximus, = {2 br/3 p}. </s>
            <s xml:id="echoid-s3610" xml:space="preserve">Unde, facta applicatione, oritur {3 p r/4 b},
              <lb/>
            longitudo penduli iſochroni, ut ante quoque inventa fuit.</s>
            <s xml:id="echoid-s3611" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div324" type="section" level="1" n="117">
          <head xml:id="echoid-head143" style="it" xml:space="preserve">Centrum oſcillationis Circuli, aliter quam ſupra.</head>
          <p>
            <s xml:id="echoid-s3612" xml:space="preserve">Eodem modo etiam ſimpliciſſime, in circulo, centrum
              <lb/>
              <note position="left" xlink:label="note-0228-03" xlink:href="note-0228-03a" xml:space="preserve">TAB.XXIV.
                <lb/>
              Fig. 1.</note>
            oſcillationis invenire licet. </s>
            <s xml:id="echoid-s3613" xml:space="preserve">Sit enim circulus G C F, cujus
              <lb/>
            centrum B; </s>
            <s xml:id="echoid-s3614" xml:space="preserve">ſectorque in eo minimus intelligatur B C P,
              <lb/>
            ſicut ante in ſectore B C D.</s>
            <s xml:id="echoid-s3615" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3616" xml:space="preserve">Cum igitur, ſecundum modo expoſita, quadrata, à di-
              <lb/>
            ſtantiis particularum ſectoris B C P ad centrum B, æquen-
              <lb/>
            tur rectangulo N B O, hoc eſt, dimidio quadrato radii,
              <lb/>
            multiplici ſecundum ſectoris ipſius particularum numerum;
              <lb/>
            </s>
            <s xml:id="echoid-s3617" xml:space="preserve">circulus autem ex ejusmodi ſectoribus componatur; </s>
            <s xml:id="echoid-s3618" xml:space="preserve">erunt
              <lb/>
            proinde quadrata, à diſtantiis particularum circuli totius ad
              <lb/>
            centrum B, æqualia dimidio quadrato radii, multiplici ſe-
              <lb/>
            cundum numerum earundem circuli particularum.</s>
            <s xml:id="echoid-s3619" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3620" xml:space="preserve">Eſt autem B centrum gravitatis circuli. </s>
            <s xml:id="echoid-s3621" xml:space="preserve">Ergo dictum di-
              <lb/>
            midium quadratum radii, hic erit ſpatium applicandum di-
              <lb/>
            ſtantiæ inter ſuſpenſionem & </s>
            <s xml:id="echoid-s3622" xml:space="preserve">centrum B, ut habeatur inter-
              <lb/>
            vallum, quo centrum oſcillationis inferius eſt ipſo centro B .</s>
            <s xml:id="echoid-s3623" xml:space="preserve">
              <note symbol="*" position="left" xlink:label="note-0228-04" xlink:href="note-0228-04a" xml:space="preserve">Prop. 18.
                <lb/>
              @uj.</note>
            quod & </s>
            <s xml:id="echoid-s3624" xml:space="preserve">ſupra ita ſe habere oſtendimus.</s>
            <s xml:id="echoid-s3625" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div327" type="section" level="1" n="118">
          <head xml:id="echoid-head144" style="it" xml:space="preserve">Centrum oſcillationis Peripheriæ circuli.</head>
          <p>
            <s xml:id="echoid-s3626" xml:space="preserve">Facilius etiam, centrum oſcillationis circumferentiæ cir-
              <lb/>
              <note position="left" xlink:label="note-0228-05" xlink:href="note-0228-05a" xml:space="preserve">TAB.XXIV.
                <lb/>
              Fig. 2.</note>
            culi, hoc pacto reperitur. </s>
            <s xml:id="echoid-s3627" xml:space="preserve">Eſto enim circumferentia deſcri-
              <lb/>
            pta centro B, radio B R. </s>
            <s xml:id="echoid-s3628" xml:space="preserve">Quadratum igitur B R, multi-
              <lb/>
            plex ſecundum numerum particularum in quas circumferen-
              <lb/>
            tia diviſa intelligitur, æquatur quadratis à diſtantiis </s>
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