Huygens, Christiaan, Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica

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        <div xml:id="echoid-div75" type="section" level="1" n="34">
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            <s xml:id="echoid-s1455" xml:space="preserve">
              <pb o="369" file="0079" n="84" rhead="DE CIRCULI MAGNIT. INVENTA."/>
            tem dodecagoni inſcripti facile invenitur, quia radius pe-
              <lb/>
            ripheriæ ſextantem ſubtendit. </s>
            <s xml:id="echoid-s1456" xml:space="preserve">Eſtque hæc ratio accuratior
              <lb/>
            quam ſi triplâ ſeſquiſeptimâ utamur. </s>
            <s xml:id="echoid-s1457" xml:space="preserve">Nam ſecundum eam
              <lb/>
            excedetur {1/2} peripheriæ longitudo amplius quam {1/100} diame-
              <lb/>
            tri.</s>
            <s xml:id="echoid-s1458" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div76" type="section" level="1" n="35">
          <head xml:id="echoid-head57" xml:space="preserve">
            <emph style="sc">Aliter</emph>
          .</head>
          <p>
            <s xml:id="echoid-s1459" xml:space="preserve">Eſto datus circulus cujus B C diameter. </s>
            <s xml:id="echoid-s1460" xml:space="preserve">Dividatur ſemi-
              <lb/>
              <note position="right" xlink:label="note-0079-01" xlink:href="note-0079-01a" xml:space="preserve">TAB. XXXIX.
                <lb/>
              Fig. 2.</note>
            circumferentia B C bifariam in D. </s>
            <s xml:id="echoid-s1461" xml:space="preserve">reliqua vero trifariam
              <lb/>
            in E & </s>
            <s xml:id="echoid-s1462" xml:space="preserve">F. </s>
            <s xml:id="echoid-s1463" xml:space="preserve">Et jungantur D E, D F, quæ ſecent diametrum
              <lb/>
            in G & </s>
            <s xml:id="echoid-s1464" xml:space="preserve">H. </s>
            <s xml:id="echoid-s1465" xml:space="preserve">Erit trianguli G D H latus alterum una cum
              <lb/>
            baſi G H quadrante B D exiguo majus, neque enim exce-
              <lb/>
            det {1/5000} diametri B C. </s>
            <s xml:id="echoid-s1466" xml:space="preserve">Sciendum eſt enim fieri D G vel D H
              <lb/>
            duobus inſcripti dodecagoni lateribus æquales. </s>
            <s xml:id="echoid-s1467" xml:space="preserve">G H autem
              <lb/>
            lateri dodecagoni circumſcripti. </s>
            <s xml:id="echoid-s1468" xml:space="preserve">Unde quidem junctas D G
              <lb/>
            & </s>
            <s xml:id="echoid-s1469" xml:space="preserve">G H majores eſſe conſtat quadrante B D. </s>
            <s xml:id="echoid-s1470" xml:space="preserve">Nam quia per
              <lb/>
            8. </s>
            <s xml:id="echoid-s1471" xml:space="preserve">huj. </s>
            <s xml:id="echoid-s1472" xml:space="preserve">octo latera dodecagoni circulo inſcripti cum quatuor
              <lb/>
            lateribus circumſcripti majora ſunt peripheriâ totâ, ideo ſum-
              <lb/>
            ptâ omnium quartâ parte erunt quoque duo latera inſcripti
              <lb/>
            cum latere uno circumſcripti majora peripheriæ quadrante.
              <lb/>
            </s>
            <s xml:id="echoid-s1473" xml:space="preserve">Porro quoniam latus inſcripti dodecagoni minus eſt quam
              <lb/>
            partium 51764 qualium B C 200000: </s>
            <s xml:id="echoid-s1474" xml:space="preserve">erunt latera duo, hoc
              <lb/>
            eſt, G D, minor quam 103528. </s>
            <s xml:id="echoid-s1475" xml:space="preserve">Circumſcripti autem dode-
              <lb/>
            cagoni latus minus eſt partibus 53590, ipſa nimirum G H. </s>
            <s xml:id="echoid-s1476" xml:space="preserve">
              <lb/>
            Itaque junctæ una D G, G H efficiunt minus quam 157118. </s>
            <s xml:id="echoid-s1477" xml:space="preserve">
              <lb/>
            At quadrantem B D conſtat ex præcedentibus majorem
              <lb/>
            eſſe quam 157079. </s>
            <s xml:id="echoid-s1478" xml:space="preserve">Ergo differentia minor eſt quam partium
              <lb/>
            39, cum 40 demum efficiant {1/3000} diametri B C.</s>
            <s xml:id="echoid-s1479" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div78" type="section" level="1" n="36">
          <head xml:id="echoid-head58" xml:space="preserve">
            <emph style="sc">Aliter</emph>
          .</head>
          <p>
            <s xml:id="echoid-s1480" xml:space="preserve">Tribus ſemidiametris addatur {1/10} lateris inſcripti quadrati;
              <lb/>
            </s>
            <s xml:id="echoid-s1481" xml:space="preserve">compoſita ſemicircumferentiæ æquabitur tam propè, ut
              <lb/>
            non {1/18000} diametri brevior ſit. </s>
            <s xml:id="echoid-s1482" xml:space="preserve">Latus quadrati eſt majus quam
              <lb/>
            partium 141421 qualium radius 100000, unde quod dictum eſt
              <lb/>
            facile demonſtratur.</s>
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