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-s3793" xml:space="preserve">
              <pb o="450" file="0168" n="177" rhead="VERA CIRCULI."/>
            pezium L I K M eſſe medium arithmeticum inter prædicta re-
              <lb/>
            ctangula, hoc eſt 49500000000000000000000000. </s>
            <s xml:id="echoid-s3794" xml:space="preserve">invenia-
              <lb/>
            tur inter rectangula L N K M, Q I K M, medium geometri-
              <lb/>
            cum 28460498941515413987990042 quod erit pentagonum
              <lb/>
            ſpatio hyperbolico L I K M regulariter circumſcriptum. </s>
            <s xml:id="echoid-s3795" xml:space="preserve">Sit-
              <lb/>
            que ut trapezium LIKM unà cum dicto pentagono circumſcri-
              <lb/>
            pto ad dictum pentagonum, ita duplum dicti pentagoni ad
              <lb/>
            hexagonum ſpatio hyperbolico L I K M regulariter inſcriptum,
              <lb/>
            nempe 20779754131836628160009835; </s>
            <s xml:id="echoid-s3796" xml:space="preserve">quod hexagonum
              <lb/>
            erit polygonum complicatum cum prædicto pentagono; </s>
            <s xml:id="echoid-s3797" xml:space="preserve">quæ
              <lb/>
            duo rectilinea efficiant primos ſeriei terminos convergentes:
              <lb/>
            </s>
            <s xml:id="echoid-s3798" xml:space="preserve">inter quæ ſit medium geometricum cujus quadrati duplum di-
              <lb/>
            vidatur per idem medium geometricum unà cum majori ter-
              <lb/>
            mino ſeu pentagono circumſcripto; </s>
            <s xml:id="echoid-s3799" xml:space="preserve">eruntque medium geo-
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            metricum & </s>
            <s xml:id="echoid-s3800" xml:space="preserve">quotus, ſecundi terminiconvergentes: </s>
            <s xml:id="echoid-s3801" xml:space="preserve">atque ita
              <lb/>
            continuetur ſeries hæc convergens polygonorum complica-
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            torum, donec medietas prima notarum eadem ſit in utroque
              <lb/>
            termino convergente, nempe ad terminum vigeſimum; </s>
            <s xml:id="echoid-s3802" xml:space="preserve">po-
              <lb/>
            lygonum enim circumſcriptum eſt 23025850929958961534-
              <lb/>
            173864, & </s>
            <s xml:id="echoid-s3803" xml:space="preserve">inſcriptum 23025850929931203593181124: </s>
            <s xml:id="echoid-s3804" xml:space="preserve">ad-
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            hibeatur deinde approximatio in hujus 23 & </s>
            <s xml:id="echoid-s3805" xml:space="preserve">24 demonſtra-
              <lb/>
            ta, & </s>
            <s xml:id="echoid-s3806" xml:space="preserve">invenientur termini intra quos conſiſtit vera ſpatii
              <lb/>
            hyperbolici L I K M menſura, nempe 230258509299404562-
              <lb/>
            40178681, minor ſpatio, & </s>
            <s xml:id="echoid-s3807" xml:space="preserve">23025850929940456240178704
              <lb/>
            eodem major, & </s>
            <s xml:id="echoid-s3808" xml:space="preserve">ideo non latet ſpatii menſura, quam in-
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            venire oportuit: </s>
            <s xml:id="echoid-s3809" xml:space="preserve">totam polygonorum ſeriem hic appono unà
              <lb/>
            cum numero rectarum curvam hyperbolicam ſubtendentium
              <lb/>
            in unoquoque polygono circumſcripto.</s>
            <s xml:id="echoid-s3810" xml:space="preserve"/>
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