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

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            <s xml:id="echoid-s1370" xml:space="preserve">
              <pb o="366" file="0074" n="78" rhead="CHRISTIANI HUGENII"/>
            ad B H, ita K G ad C H. </s>
            <s xml:id="echoid-s1371" xml:space="preserve">Ergo major erit ratio E G ad
              <lb/>
            C H, quam duplicata ejus, quam habet K G ad C H. </s>
            <s xml:id="echoid-s1372" xml:space="preserve">Qua-
              <lb/>
            re major ratio E G ad K G, quam K G ad C H. </s>
            <s xml:id="echoid-s1373" xml:space="preserve">Ideoque
              <lb/>
            duæ ſimul E G, C H omnino majores duplâ K G. </s>
            <s xml:id="echoid-s1374" xml:space="preserve">Et ſumptis
              <lb/>
            omnium trientibus, erunt trientes utriuſque E G & </s>
            <s xml:id="echoid-s1375" xml:space="preserve">C H ſi-
              <lb/>
            mul majores duabus tertiis K G. </s>
            <s xml:id="echoid-s1376" xml:space="preserve">Quamobrem addito utrim-
              <lb/>
            que ipſius C H triente, erit triens E G cum duabus tertiis
              <lb/>
            C H, major duabus tertiis K G cum triente C H. </s>
            <s xml:id="echoid-s1377" xml:space="preserve">Hiſce
              <lb/>
            vero minor etiam eſt arcus C G . </s>
            <s xml:id="echoid-s1378" xml:space="preserve">Igitur duæ tertiæ C
              <note symbol="*" position="left" xlink:label="note-0074-01" xlink:href="note-0074-01a" xml:space="preserve">per pra
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              ced.</note>
            ſimul cum triente ipſius E G majores omnino ſunt eodem ar-
              <lb/>
            cu C G. </s>
            <s xml:id="echoid-s1379" xml:space="preserve">Unde ſumptis omnibus toties quoties arcus C G
              <lb/>
            circumferentiâ totâ continetur, erunt quoque duæ tertiæ pe-
              <lb/>
            rimetri polygoni C D, cum triente perimetri polygoni E F,
              <lb/>
            majores circuli totius circumferentiâ. </s>
            <s xml:id="echoid-s1380" xml:space="preserve">Quod fuerat oſtenden-
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            dum.</s>
            <s xml:id="echoid-s1381" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s1382" xml:space="preserve">Omnis igitur circumferentiæ arcus quadrante minor, mi-
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            nor eſt ſinus ſui beſſe & </s>
            <s xml:id="echoid-s1383" xml:space="preserve">tangentis triente.</s>
            <s xml:id="echoid-s1384" xml:space="preserve"/>
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        <div xml:id="echoid-div72" type="section" level="1" n="33">
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            <emph style="sc">Problema</emph>
          I.
            <emph style="sc">Prop</emph>
          . X.</head>
          <head xml:id="echoid-head55" style="it" xml:space="preserve">Peripheriæ ad diametrum rationem invenire
            <lb/>
          quamlibet veræ propinquam.</head>
          <p>
            <s xml:id="echoid-s1385" xml:space="preserve">MInorem eſſe peripheriæ ad diametrum rationem quam tri-
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            plam ſeſquiſeptimam: </s>
            <s xml:id="echoid-s1386" xml:space="preserve">majorem vero quam 3 {10/71}, Archi-
              <lb/>
            medes oſtendit inſcripto circumſcriptoque 96 laterum po-
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            lygono. </s>
            <s xml:id="echoid-s1387" xml:space="preserve">Idem verò hic per dodecagona demonſtrabimus.</s>
            <s xml:id="echoid-s1388" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1389" xml:space="preserve">Quia enim latus inſcripti circulo dodecagoni majus eſt par-
              <lb/>
            tibus 5176 {3/8}, qualium radius continet 10000: </s>
            <s xml:id="echoid-s1390" xml:space="preserve">duodecim la-
              <lb/>
            tera proinde, hoc eſt, perimeter inſcripti dodecagoni major
              <lb/>
            erit quam 62116 {1/2}: </s>
            <s xml:id="echoid-s1391" xml:space="preserve">perimeter autem hexagoni inſcripti eſt
              <lb/>
            radii ſextupla, ideoque partium 60000. </s>
            <s xml:id="echoid-s1392" xml:space="preserve">Igitur dodecagoni
              <lb/>
            perimeter perimetrum hexagoni excedit amplius quam par-
              <lb/>
            tibus 2116 {1/2}. </s>
            <s xml:id="echoid-s1393" xml:space="preserve">Quare triens exceſſus major erit quam 705 {1/2}. </s>
            <s xml:id="echoid-s1394" xml:space="preserve">Igi-
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            tur dodecagoni perimeter unà cum triente exceſſus, quo pe-
              <lb/>
            rimetrum hexagoni ſuperat, major erit aggregato </s>
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