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

Table of handwritten notes

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        <div xml:id="echoid-div102" type="section" level="1" n="46">
          <p>
            <s xml:id="echoid-s1953" xml:space="preserve">
              <pb o="386" file="0098" n="104" rhead="CHRISTIANI HUGENII"/>
            gitudine minus diſtet quam partibus 85; </s>
            <s xml:id="echoid-s1954" xml:space="preserve">(Eſt enim arcus
              <lb/>
            A B, per ea quæ ſupra oſtendimus, major quam 7853981)
              <lb/>
            partes autem 85 efficiant minus quam duos ſcrupulos ſecun-
              <lb/>
            dos, hoc eſt, quam {2/1296600} circumferentiæ, nam tota earun-
              <lb/>
            dem plures habet quam 60000000: </s>
            <s xml:id="echoid-s1955" xml:space="preserve">Hinc manifeſtum eſt, ſi
              <lb/>
            trianguli rectanguli angulos quæramus ex datis lateribus, eo
              <lb/>
            modo quo majorem iſtum terminum paulò antè, nunquam
              <lb/>
            duobus ſcrupulis ſecundis aberraturos; </s>
            <s xml:id="echoid-s1956" xml:space="preserve">etiamſi æqualia inter
              <lb/>
            ſe fuerint latera circa angulum rectum, veluti hic erant in
              <lb/>
            triangulo D A M.</s>
            <s xml:id="echoid-s1957" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1958" xml:space="preserve">Si vero ea ſit ratio lateris D M ad M A, ut angulus A D M
              <lb/>
            non excedat {1/4} recti; </s>
            <s xml:id="echoid-s1959" xml:space="preserve">non unius tertii ſcrupuli error erit. </s>
            <s xml:id="echoid-s1960" xml:space="preserve">Po-
              <lb/>
            ſito enim arcu A B {1/16} circumferentiæ, erit A M ſemiſſis la-
              <lb/>
            teris octanguli æquilateri circulo inſcripti partium 382683433,
              <lb/>
            non unâ minus. </s>
            <s xml:id="echoid-s1961" xml:space="preserve">A B vero latus ſexdecanguli 390180644
              <lb/>
            non unâ amplius, qualium radius D B 1000000000. </s>
            <s xml:id="echoid-s1962" xml:space="preserve">Unde
              <lb/>
            primus minor terminus longitudinis arcus A B invenitur par-
              <lb/>
            tium 392679714. </s>
            <s xml:id="echoid-s1963" xml:space="preserve">Terminus autem major 392699148. </s>
            <s xml:id="echoid-s1964" xml:space="preserve">Et ex
              <lb/>
            his minor rurſus 392699010. </s>
            <s xml:id="echoid-s1965" xml:space="preserve">Conſtat autem ex ſupra demon-
              <lb/>
            ſtratis arcum A B {1/16} peripheriæ, majorem eſſe quam
              <lb/>
            392699081, quas terminus major ſuperat partibus 67. </s>
            <s xml:id="echoid-s1966" xml:space="preserve">Hæ
              <lb/>
            autem minus efficiunt uno ſcrupulo tertio, hoc eſt, {1/77760000} to-
              <lb/>
            tius circumferentiæ, quoniam ea major eſt utique quam
              <lb/>
            6000000000.</s>
            <s xml:id="echoid-s1967" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1968" xml:space="preserve">Porro ex noviſſimis terminis inventis orietur ratio circum-
              <lb/>
            ferentiæ ad diametrum minor quam 3141593 {1/5}, major autem
              <lb/>
            quam 3141592 ad 1000000.</s>
            <s xml:id="echoid-s1969" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1970" xml:space="preserve">Quod ſi {1/60} circumferentiæ ponatur arcus A B, ſeu par-
              <lb/>
            tium 6 qualium tota 360: </s>
            <s xml:id="echoid-s1971" xml:space="preserve">Erit A M ſemiſſis lateris trigin-
              <lb/>
            tanguli inſcripti partium 10452846326766, non unâ minus,
              <lb/>
            qualium radius 100000000000000. </s>
            <s xml:id="echoid-s1972" xml:space="preserve">Et A B latus ſexagintan-
              <lb/>
            guli inſcripti 10467191248588 non unâ amplius. </s>
            <s xml:id="echoid-s1973" xml:space="preserve">Invenietur-
              <lb/>
            que ex his arcus A B ſecundum primum minorem terminum
              <lb/>
            10471972889195. </s>
            <s xml:id="echoid-s1974" xml:space="preserve">Secundum majorem 10471975512584.
              <lb/>
            </s>
            <s xml:id="echoid-s1975" xml:space="preserve">Et ex his minor alter terminus 10471975511302. </s>
            <s xml:id="echoid-s1976" xml:space="preserve">Unde
              <lb/>
            efficitur peripheriæ ad diametrum ratio minor </s>
          </p>
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      </text>
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