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-s1976" xml:space="preserve">
              <pb o="387" file="0101" n="108" rhead="DE CIRCULI MAGNIT. INVENTA."/>
            31415926538, major autem quam 31415926533 ad
              <lb/>
            10000000000.</s>
            <s xml:id="echoid-s1977" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1978" xml:space="preserve">Quos terminos ſi ex additis inſcriptorum & </s>
            <s xml:id="echoid-s1979" xml:space="preserve">circumſcripto-
              <lb/>
            rum polygonorum lateribus inquirendum eſſet ferè ad late-
              <lb/>
            rum quadringenta millia deveniendum. </s>
            <s xml:id="echoid-s1980" xml:space="preserve">Nam ex ſexagintan-
              <lb/>
            gulo inſcripto circumſcriptoque hoc tantum probatur, mi-
              <lb/>
            norem eſſe rationem peripheriæ ad diametrum quam 3145 ad
              <lb/>
            1000, majorem autem quam 3140. </s>
            <s xml:id="echoid-s1981" xml:space="preserve">Adeo ut triplum & </s>
            <s xml:id="echoid-s1982" xml:space="preserve">am-
              <lb/>
            plius verarum notarum numerum noſtro ratiocinio produ-
              <lb/>
            ctum appareat. </s>
            <s xml:id="echoid-s1983" xml:space="preserve">Idem vero in ulterioribus polygonis ſi quis
              <lb/>
            experiatur ſemper evenire cernet: </s>
            <s xml:id="echoid-s1984" xml:space="preserve">non ignota nobis ratione,
              <lb/>
            ſed quæ longiori explicatione indigeret.</s>
            <s xml:id="echoid-s1985" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1986" xml:space="preserve">Porro autem quomodo, datis quibuſcunque aliis inſcriptis,
              <lb/>
            arcuum quibus ſubtenduntur longitudo per hæc inveniri que-
              <lb/>
            at ſatis puto manifeſtum. </s>
            <s xml:id="echoid-s1987" xml:space="preserve">Si enim quadrati inſcripti latere
              <lb/>
            majores ſunt, longitudo arcus ad ſemicircumferentiam reli-
              <lb/>
            qui inquirenda eſt, cujus tum quoque ſubtenſa datur. </s>
            <s xml:id="echoid-s1988" xml:space="preserve">Sci-
              <lb/>
            endum autem & </s>
            <s xml:id="echoid-s1989" xml:space="preserve">dimidiorum arcuum ſubtenſas inveniri cum
              <lb/>
            totius arcus ſubtenſa data eſt. </s>
            <s xml:id="echoid-s1990" xml:space="preserve">Atque hâc ratione ſi biſectioni-
              <lb/>
            bus uti placebit, poterimus ad omnem ſubtenſam, arcus i-
              <lb/>
            pſius longitudinem quamlibet veræ propinquam non difficul-
              <lb/>
            ter cognoſcere. </s>
            <s xml:id="echoid-s1991" xml:space="preserve">Utile hoc ad ſinuum tabulas examinandas.
              <lb/>
            </s>
            <s xml:id="echoid-s1992" xml:space="preserve">Imo ad componendas quoque: </s>
            <s xml:id="echoid-s1993" xml:space="preserve">quia cognitâ arcus alicujus
              <lb/>
            ſubtenſâ, etiam ejus qui paulò major minorve ſit ſatis accu-
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            ratè definiri poteſt.</s>
            <s xml:id="echoid-s1994" xml:space="preserve"/>
          </p>
          <figure number="53">
            <image file="0101-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0101-01"/>
          </figure>
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