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

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        <div xml:id="echoid-div102" type="section" level="1" n="46">
          <pb o="385" file="0097" n="103" rhead="DE CIRCULI MAGNIT. INVENTA."/>
          <p style="it">
            <s xml:id="echoid-s1919" xml:space="preserve">Inventorum terminorum differentia ſeſquitertia jungatur du-
              <lb/>
            plæ ſubtenſæ & </s>
            <s xml:id="echoid-s1920" xml:space="preserve">ſinui triplo, & </s>
            <s xml:id="echoid-s1921" xml:space="preserve">quam rationem habet ex his
              <lb/>
            compoſita ad triplam ſeſquitertiam ſeu {10/3} utriuſque ſimul, ſi-
              <lb/>
            nus, ſubtenſæque, eandem habeat ſubtenſæ ſupra ſinum exceſ-
              <lb/>
            ſus ad aliam quandam; </s>
            <s xml:id="echoid-s1922" xml:space="preserve">Hæc ad ſinum addita rectam conſtituet
              <lb/>
            arcu minorem.</s>
            <s xml:id="echoid-s1923" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1924" xml:space="preserve">Minor terminus erat 104465 {2/3}. </s>
            <s xml:id="echoid-s1925" xml:space="preserve">Major 104727. </s>
            <s xml:id="echoid-s1926" xml:space="preserve">differentia
              <lb/>
            horum eſt 261 {1/3}. </s>
            <s xml:id="echoid-s1927" xml:space="preserve">Eſtque rurſus tribus numeris inveniendus
              <lb/>
            quartus proportionalis. </s>
            <s xml:id="echoid-s1928" xml:space="preserve">Primus eſt partium duplæ A B & </s>
            <s xml:id="echoid-s1929" xml:space="preserve">
              <lb/>
            triplæ A M & </s>
            <s xml:id="echoid-s1930" xml:space="preserve">ſeſquitertiæ terminorum differentiæ, 460158
              <lb/>
            vero major. </s>
            <s xml:id="echoid-s1931" xml:space="preserve">Secundus {10/3} utriuſque ſimul A B, A M, 622008
              <lb/>
            vero minor. </s>
            <s xml:id="echoid-s1932" xml:space="preserve">Tertius denique exceſſus A B ſupra A M, 13397
              <lb/>
            vero min. </s>
            <s xml:id="echoid-s1933" xml:space="preserve">Quibus quartus proportionalis eſt 18109 vero min.
              <lb/>
            </s>
            <s xml:id="echoid-s1934" xml:space="preserve">Hic igitur additus numero partium A M 86602 {1/2} vero min. </s>
            <s xml:id="echoid-s1935" xml:space="preserve">
              <lb/>
            fiunt 104711 {1/2} minores arcu A B. </s>
            <s xml:id="echoid-s1936" xml:space="preserve">Quare ſexcuplum earum,
              <lb/>
            628269 minus erit circumferentiâ totâ. </s>
            <s xml:id="echoid-s1937" xml:space="preserve">At quoniam 104727
              <lb/>
            majores inventæ ſunt arcu A B, earum ſexcuplum 628362
              <lb/>
            circumferentiâ majus erit. </s>
            <s xml:id="echoid-s1938" xml:space="preserve">Itaque circumferentiæ ad diame-
              <lb/>
            trum ratio minor eſt quam 628362, major autem quam 628269
              <lb/>
            ad 200000. </s>
            <s xml:id="echoid-s1939" xml:space="preserve">Sive minor quam 314181, major autem quam
              <lb/>
            314135 ad 100000. </s>
            <s xml:id="echoid-s1940" xml:space="preserve">Unde conſtat minorem utique eſſe quam
              <lb/>
            triplam ſeſquiſeptimam, & </s>
            <s xml:id="echoid-s1941" xml:space="preserve">majorem quam 3 {10/@}. </s>
            <s xml:id="echoid-s1942" xml:space="preserve">Quin etiam
              <lb/>
            Longomontani error per hæc refutatur, qui ſcripſit peri-
              <lb/>
            pheriam majorem eſſe partibus 314185 qualium rad. </s>
            <s xml:id="echoid-s1943" xml:space="preserve">
              <lb/>
            100000.</s>
            <s xml:id="echoid-s1944" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1945" xml:space="preserve">Eſto nunc arcus A B {1/@} circumferentiæ, & </s>
            <s xml:id="echoid-s1946" xml:space="preserve">erit A M, ſe-
              <lb/>
            miſſis lateris quadrati circulo inſcripti, partium 7071068,
              <lb/>
            non unâ minus, qualium radius D B 10000000. </s>
            <s xml:id="echoid-s1947" xml:space="preserve">A B vero
              <lb/>
            latus octanguli partium 7653668 non unâ majus. </s>
            <s xml:id="echoid-s1948" xml:space="preserve">Quibus da-
              <lb/>
            tis ad ſimilitudinem præcedentium invenietur primus minor
              <lb/>
            terminus longitudinis arcus A B 7847868. </s>
            <s xml:id="echoid-s1949" xml:space="preserve">Deinde major
              <lb/>
            terminus 7854066. </s>
            <s xml:id="echoid-s1950" xml:space="preserve">Et ex utroque rurſus terminus minor ac-
              <lb/>
            curatior 7853885. </s>
            <s xml:id="echoid-s1951" xml:space="preserve">Unde conſtat peripheriæ ad diametrum
              <lb/>
            rationem minorem haberi quam 31416 {1/3}, majorem autem quam
              <lb/>
            31415 ad 10000.</s>
            <s xml:id="echoid-s1952" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1953" xml:space="preserve">Et quum terminus major 7854066 à vera arcus A B </s>
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