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

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        <div xml:id="echoid-div78" type="section" level="1" n="36">
          <pb o="370" file="0080" n="85" rhead="CHRISTIANI HUGENII"/>
          <p>
            <s xml:id="echoid-s1484" xml:space="preserve">Vel potius ſex ſe midiameſtris addatur {1/5} dicti lateris qua-
              <lb/>
            drati inſcripti ut habeatur recta æqualis peripheriæ toti.</s>
            <s xml:id="echoid-s1485" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div79" type="section" level="1" n="37">
          <head xml:id="echoid-head59" xml:space="preserve">
            <emph style="sc">Problbma</emph>
          III.
            <emph style="sc">Prop</emph>
          . XII.</head>
          <head xml:id="echoid-head60" style="it" xml:space="preserve">Dato arcui cuicunque rectam æqualem
            <lb/>
          ſumere.</head>
          <p>
            <s xml:id="echoid-s1486" xml:space="preserve">Eſto datus circumferentiæ arcus C D, primum quadrante mi-
              <lb/>
              <note position="left" xlink:label="note-0080-01" xlink:href="note-0080-01a" xml:space="preserve">TAB. XXXIX.
                <lb/>
              Fig. 3.</note>
            nor, cui rectam æqualem ſumere oporteat. </s>
            <s xml:id="echoid-s1487" xml:space="preserve">Dividatur ar-
              <lb/>
            cus C D bifariam in E, ſitque ſubtenſæ C D æqualis recta F G.
              <lb/>
            </s>
            <s xml:id="echoid-s1488" xml:space="preserve">Duabus vero C E, E D, quæ ſubtendunt arcus dimidios,
              <lb/>
            æqualis F H. </s>
            <s xml:id="echoid-s1489" xml:space="preserve">Et ipſi F H jungatur H I triens exceſſus G H. </s>
            <s xml:id="echoid-s1490" xml:space="preserve">
              <lb/>
            Erit tota F I arcui C D æqualis ferè: </s>
            <s xml:id="echoid-s1491" xml:space="preserve">adeo ut unâ ſui particulâ,
              <lb/>
            qualium 1200 continet, aucta, major futura ſit, etiamſi arcus
              <lb/>
            C D quadranti æqualis detur. </s>
            <s xml:id="echoid-s1492" xml:space="preserve">In minoribus autem arcubus
              <lb/>
            minor erit differentia. </s>
            <s xml:id="echoid-s1493" xml:space="preserve">Nam ſi fuerit datus non major peri-
              <lb/>
            pheriæ ſextante, linea inventa minus quam {1/6000} ſui parte à ve-
              <lb/>
            ra arcus longitudine deficiet. </s>
            <s xml:id="echoid-s1494" xml:space="preserve">Et minores quidem eſſe arcu-
              <lb/>
            bus rectas eo modo inventas conſtat ex Theoremate 7. </s>
            <s xml:id="echoid-s1495" xml:space="preserve">huj. </s>
            <s xml:id="echoid-s1496" xml:space="preserve">
              <lb/>
            De quantitate autem differentiæ eſt oſtendendum.</s>
            <s xml:id="echoid-s1497" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1498" xml:space="preserve">Primum itaque ponendo arcum C D quadranti peripheriæ
              <lb/>
            æqualem, erit C D recta, hoc eſt, F G, latus quadrati
              <lb/>
            circulo inſcripti, & </s>
            <s xml:id="echoid-s1499" xml:space="preserve">minor proinde quam partium 141422,
              <lb/>
            qualium radius circuli 100000. </s>
            <s xml:id="echoid-s1500" xml:space="preserve">C E autem vel E D latus in-
              <lb/>
            ſcripti octogoni, ideoque major quam 76536. </s>
            <s xml:id="echoid-s1501" xml:space="preserve">Eſt autem du-
              <lb/>
            plæ E D æqualis F H. </s>
            <s xml:id="echoid-s1502" xml:space="preserve">Ergo hæc major quam 153072. </s>
            <s xml:id="echoid-s1503" xml:space="preserve">Qua-
              <lb/>
            re exceſſus G H major quam 11650: </s>
            <s xml:id="echoid-s1504" xml:space="preserve">Et hujus triens H I
              <lb/>
            major quam 3883. </s>
            <s xml:id="echoid-s1505" xml:space="preserve">Ideoque tota F I major quam 156955.
              <lb/>
            </s>
            <s xml:id="echoid-s1506" xml:space="preserve">Arcus autem C D cum quadranti æqualis ponitur, minor eſt
              <lb/>
            quam 157080. </s>
            <s xml:id="echoid-s1507" xml:space="preserve">Itaque minus ab hoc diſcrepat recta F I quam
              <lb/>
            partibus 125, qualium ipſa eſt 156955. </s>
            <s xml:id="echoid-s1508" xml:space="preserve">Quæ utique minus
              <lb/>
            efficiunt quam {1/1200} ipſius F I.</s>
            <s xml:id="echoid-s1509" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1510" xml:space="preserve">Si vero ſextans peripheriæ ſit arcus C D, erit recta C D,
              <lb/>
            hoc eſt, F G, latus hexagoni inſcripti, ideoque partium
              <lb/>
            10000, & </s>
            <s xml:id="echoid-s1511" xml:space="preserve">C E vel E D latus dodecagoni, ac proinde </s>
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