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

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        <div xml:id="echoid-div99" type="section" level="1" n="45">
          <pb o="384" file="0096" n="102" rhead="CHRISTIANI HUGENII"/>
        </div>
        <div xml:id="echoid-div102" type="section" level="1" n="46">
          <head xml:id="echoid-head69" xml:space="preserve">
            <emph style="sc">Problema</emph>
          IV.
            <emph style="sc">Propos</emph>
          . XX.</head>
          <p style="it">
            <s xml:id="echoid-s1893" xml:space="preserve">CIrcumferentiæ ad diametrum rationem inve-
              <lb/>
            ſtigare; </s>
            <s xml:id="echoid-s1894" xml:space="preserve">& </s>
            <s xml:id="echoid-s1895" xml:space="preserve">ex datis inſcriptis in dato circulo
              <lb/>
            invenire longitudinem arcuum quibus illæ ſubtendun-
              <lb/>
            tur.</s>
            <s xml:id="echoid-s1896" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1897" xml:space="preserve">Eſto circulus centro D, cujus diameter C B, & </s>
            <s xml:id="echoid-s1898" xml:space="preserve">ſit arcus
              <lb/>
              <note position="left" xlink:label="note-0096-01" xlink:href="note-0096-01a" xml:space="preserve">TAB. XL.
                <lb/>
              Fig. 6.</note>
            B A ſextans circumferentiæ, cui ſubtenſa ducatur A B,
              <lb/>
            itemque ſinus A M. </s>
            <s xml:id="echoid-s1899" xml:space="preserve">Poſitâ igitur D B ſemidiametro par-
              <lb/>
            tium 100000, totidem quoque erit ſubtenſa B A. </s>
            <s xml:id="echoid-s1900" xml:space="preserve">A M ve-
              <lb/>
            rò partium 86603 non unâ minus, hoc eſt, ſi una pars ſi-
              <lb/>
            ve unitas auferatur ab 86603 fiet minor debito. </s>
            <s xml:id="echoid-s1901" xml:space="preserve">quippe ſe-
              <lb/>
            miſſis lateris trianguli æquilateri circulo inſcripti.</s>
            <s xml:id="echoid-s1902" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1903" xml:space="preserve">Hinc exceſſus A B ſupra A M fit 13397 vero minor.
              <lb/>
            </s>
            <s xml:id="echoid-s1904" xml:space="preserve">Cujus triens 4465 {2/3} additus ipſi A B 100000, fiunt partes
              <lb/>
            104465 {2/3} minores arcu A B. </s>
            <s xml:id="echoid-s1905" xml:space="preserve">Et hic primus eſt minor termi-
              <lb/>
            nus, quo poſtea alium vero propiorem inveniemus. </s>
            <s xml:id="echoid-s1906" xml:space="preserve">Prius
              <lb/>
            autem major quoque terminus ſecundum Theorema præce-
              <lb/>
            dens inquirendus eſt.</s>
            <s xml:id="echoid-s1907" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1908" xml:space="preserve">Tres nimirum ſunt numeri quibus quartum proportiona-
              <lb/>
            lem invenire oportet. </s>
            <s xml:id="echoid-s1909" xml:space="preserve">Primus eſt partium duplæ A B & </s>
            <s xml:id="echoid-s1910" xml:space="preserve">tri-
              <lb/>
            plæ A M qui erit 459807, vero minor, (nam hoc quoque
              <lb/>
            obſervandum ut minor ſit, idemque in cæteris prout dicetur)
              <lb/>
            ſecundus quadruplæ A B & </s>
            <s xml:id="echoid-s1911" xml:space="preserve">ſimplæ A M qui 486603 vero
              <lb/>
            maj. </s>
            <s xml:id="echoid-s1912" xml:space="preserve">Et tertius triens exceſſus A B ſupra A M, 4466 vero
              <lb/>
            major. </s>
            <s xml:id="echoid-s1913" xml:space="preserve">Itaque quartus proportionalis erit 4727 vero maj.
              <lb/>
            </s>
            <s xml:id="echoid-s1914" xml:space="preserve">quo addito ad A B 100000 fit 104727, major numero par-
              <lb/>
            tium, quas continet arcus A B, peripheriæ ſextans. </s>
            <s xml:id="echoid-s1915" xml:space="preserve">
              <note symbol="*" position="left" xlink:label="note-0096-02" xlink:href="note-0096-02a" xml:space="preserve">per præced.</note>
            igitur invenimus longitudinem arcus A B ſecundum mino-
              <lb/>
            rem majoremque terminum, quorum hic quidem longe pro-
              <lb/>
            pior vero eſt, cum vero proximus ſit 104719.</s>
            <s xml:id="echoid-s1916" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1917" xml:space="preserve">Sed ex utroque iſtorum alius minor terminus habebi-
              <lb/>
            tur priore accuratior ſi@ utamur præcepto ſequenti, quod
              <lb/>
            à diligentiori centrorum gravitatis inſpectione dependet.</s>
            <s xml:id="echoid-s1918" xml:space="preserve"/>
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