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

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              <pb file="0062" n="66" rhead="PRÆFATIO."/>
            ro polygonum eâdem proportione circuli are-
              <lb/>
            am exuperat. </s>
            <s xml:id="echoid-s1108" xml:space="preserve">Et hoc quidem ut inter ea quæ de-
              <lb/>
            monſtraturi ſumus & </s>
            <s xml:id="echoid-s1109" xml:space="preserve">difficillimum & </s>
            <s xml:id="echoid-s1110" xml:space="preserve">contempla-
              <lb/>
            tione præcipue dignum videatur, alia tamen ſunt
              <lb/>
            non accuratiora modò, ſed quæ & </s>
            <s xml:id="echoid-s1111" xml:space="preserve">uſu magis pro-
              <lb/>
            bentur; </s>
            <s xml:id="echoid-s1112" xml:space="preserve">quæ ſane hic in anteceſſum non recenſebi-
              <lb/>
            mus, quippe in ſequentibus rectius percipienda. </s>
            <s xml:id="echoid-s1113" xml:space="preserve">Bre-
              <lb/>
            viter tamen quid ſtudiis Geometriæ conferant ex-
              <lb/>
            poſuiſſe proderit, cum non minimam habeant utili-
              <lb/>
            tatis commendationem. </s>
            <s xml:id="echoid-s1114" xml:space="preserve">Cum igitur duplicem propo-
              <lb/>
            ſiti tractationem inſtituerimus, primum eatraden-
              <lb/>
            do quorum demonſtratio conſuetis Geometriæ ele-
              <lb/>
            mentis contenta eſt, deinde centrorum gravitatis
              <lb/>
            quoque conſiderationem adhibendo: </s>
            <s xml:id="echoid-s1115" xml:space="preserve">in prioribus
              <lb/>
            quidem illud explicatum reperietur, quomodo non
              <lb/>
            tantum circumferentiæ toti, ſed & </s>
            <s xml:id="echoid-s1116" xml:space="preserve">arcui cuilibet
              <lb/>
            dato recta linea æqualis invenienda ſit; </s>
            <s xml:id="echoid-s1117" xml:space="preserve">expeditâ
              <lb/>
            ratione ad Mechanicas conſtructiones, quæque vel
              <lb/>
            ſubtiliſſimas earum minime fruſtretur. </s>
            <s xml:id="echoid-s1118" xml:space="preserve">Quomodo
              <lb/>
            item numeros exercentibus peripheriæ ad diametrum
              <lb/>
            ratio, quam Archimedes ex polygonis laterum 96
              <lb/>
            eruit, per dodecagona ſola comprobari queat. </s>
            <s xml:id="echoid-s1119" xml:space="preserve">Ex
              <lb/>
            polygonis autem laterum 10800, cum iis qui vete-
              <lb/>
            rem inſiſtunt viam vix hi peripheriæ termini exi-
              <lb/>
            ſtant 62831852 & </s>
            <s xml:id="echoid-s1120" xml:space="preserve">62831855, ad diametrum par-
              <lb/>
            tium 20000000, noſtrâ Methodo iſti prodiiſſe cer-
              <lb/>
            nentur, 6283185307179584, 6283185307179589;
              <lb/>
            </s>
            <s xml:id="echoid-s1121" xml:space="preserve">ſemperque duplicem obtineri verorum characterum
              <lb/>
            numerum, quacunque laterum multitudine </s>
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