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

Table of handwritten notes

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            <s xml:id="echoid-s3731" xml:space="preserve">
              <pb o="447" file="0165" n="174" rhead="ET HYPERBOLÆ QUADRATURA."/>
            convergente, nimirum uſque ad polygona laterum 16384;
              <lb/>
            </s>
            <s xml:id="echoid-s3732" xml:space="preserve">inſcriptum enim eſt 3141592576586860 & </s>
            <s xml:id="echoid-s3733" xml:space="preserve">circumſcriptum
              <lb/>
            3141592692091258; </s>
            <s xml:id="echoid-s3734" xml:space="preserve">non conſideratur nota ultima, quoniam
              <lb/>
            in diviſionibus & </s>
            <s xml:id="echoid-s3735" xml:space="preserve">radicum extractionibus ſemper à vera quan-
              <lb/>
            titate paululum aberramus, quod ultimam notam imperfectam
              <lb/>
            plerumque reddit. </s>
            <s xml:id="echoid-s3736" xml:space="preserve">adhibeatur deinde approximatio in hujus
              <lb/>
            20 & </s>
            <s xml:id="echoid-s3737" xml:space="preserve">21 demonſtrata, & </s>
            <s xml:id="echoid-s3738" xml:space="preserve">invenientur termini intra quos eſt vera
              <lb/>
            circuli menſura, poſito diametri quadrato 4000000000000000,
              <lb/>
            3141592653589789 minor circulo & </s>
            <s xml:id="echoid-s3739" xml:space="preserve">3141592653589792 eo-
              <lb/>
            dem major, & </s>
            <s xml:id="echoid-s3740" xml:space="preserve">proinde non latet circuli menſura, quam
              <lb/>
            invenire oportuit. </s>
            <s xml:id="echoid-s3741" xml:space="preserve">polygonorum ſeriem hic appono.</s>
            <s xml:id="echoid-s3742" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">
            <lb/>
          # Intra circulum # extra circulum
            <lb/>
          4 # 2000000000000000 # 4000000000000000
            <lb/>
          8 # 2828427124746190 # 3313708498984760
            <lb/>
          16 # 3061467458920718 # 3182597878074527
            <lb/>
          32 # 3121445152258051 # 3151724907429255
            <lb/>
          64 # 3136548490545938 # 3144118385245904
            <lb/>
          128 # 3140331156954752 # 3142223629942456
            <lb/>
          256 # 3141277250932772 # 3141750369168965
            <lb/>
          512 # 3141513801144299 # 3141632080703181
            <lb/>
          1024 # 3141572940367090 # 3141602510256808
            <lb/>
          2048 # 3141587725277158 # 3141595117749588
            <lb/>
          4096 # 3141591421543029 # 3141593269613390
            <lb/>
          8192 # 3141592345578073 # 3141592807595664
            <lb/>
          16384 # 3141592576586860 # 3141592692091258
            <lb/>
          ### Circulus intra ſequentes terminos conſiſtit
            <lb/>
          # 3141592653589789 # 3141592653589792
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s3743" xml:space="preserve">@odem omnino modo reperitur rectilineum æquale cuicun-
              <lb/>
            que ſectori circulari vel elliptico ex cognito triangulo inſcri-
              <lb/>
            pr
              <unsure/>
            o & </s>
            <s xml:id="echoid-s3744" xml:space="preserve">trapezio circumſcripto.</s>
            <s xml:id="echoid-s3745" xml:space="preserve"/>
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