Huygens, Christiaan, Christiani Hugenii opera varia; Bd. 1: Opera mechanica

Table of Notes

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            O L ſuper regula L D; </s>
            <s xml:id="echoid-s1509" xml:space="preserve">deſcribente nempe puncto N, in cir-
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                <emph style="sc">De de-</emph>
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                <emph style="sc">SCENSU</emph>
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                <emph style="sc">GRAVIUM</emph>
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            cumferentia figuræ O L ſumpto. </s>
            <s xml:id="echoid-s1510" xml:space="preserve">Et oporteat ad punctum cur-
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            væ A tangentem ducere. </s>
            <s xml:id="echoid-s1511" xml:space="preserve">Ducatur recta C A à puncto C,
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            ubi figura regulam tangebat cum punctum deſcribens eſſet
              <lb/>
            in A: </s>
            <s xml:id="echoid-s1512" xml:space="preserve">quod punctum contactus ſemper inveniri poteſt, ſiqui-
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            dem eo reducitur problema ut duæ rectæ inter ſe parallelæ
              <lb/>
            ducendæ ſint, quarum altera tranſeat per punctum deſcri-
              <lb/>
            bens in figuræ ambitu datum, altera figuram tangat, quæ-
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            que inter ſe diſtent quantum diſtat punctum datum A ab re-
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            gula L D: </s>
            <s xml:id="echoid-s1513" xml:space="preserve">dico ipſam C A occurrere curvæ ad angulos
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            rectos, ſive circumferentiam M A F deſcriptam centro C
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            radio C A, tangere curvam in puncto A, unde perpendicula-
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            ris ad A C, per punctum A, ducta curvam ibidem continget.</s>
            <s xml:id="echoid-s1514" xml:space="preserve"/>
          </p>
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            <s xml:id="echoid-s1515" xml:space="preserve">Ducatur enim C B primum ad punctum curvæ B, quod
              <lb/>
            diſtet ultra punctum A ab regula L D, intelligaturque figu-
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            ræ poſitus in B E D, cum punctum deſcribens eſſet in B,
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            contactus regulæ in D. </s>
            <s xml:id="echoid-s1516" xml:space="preserve">& </s>
            <s xml:id="echoid-s1517" xml:space="preserve">punctum curvæ quod erat in C,
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            cum punctum deſcribens eſſet in A, hìc jam ſublatum ſit in
              <lb/>
            E; </s>
            <s xml:id="echoid-s1518" xml:space="preserve">& </s>
            <s xml:id="echoid-s1519" xml:space="preserve">jungantur E C, E B, tangatque figuram in E recta
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            K H, occurrens regulæ in H.</s>
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            <s xml:id="echoid-s1521" xml:space="preserve">Quia ergo recta C D æqualis eſt curvæ E D; </s>
            <s xml:id="echoid-s1522" xml:space="preserve">eâdem ve-
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            ro curva major eſt utraque ſimul E H, H D; </s>
            <s xml:id="echoid-s1523" xml:space="preserve">erit E H ma-
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            jor quam C H. </s>
            <s xml:id="echoid-s1524" xml:space="preserve">Unde angulus E C H major quam C E H,
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            & </s>
            <s xml:id="echoid-s1525" xml:space="preserve">proinde E C L minor quam C E K. </s>
            <s xml:id="echoid-s1526" xml:space="preserve">Atqui addendo an-
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            gulum K E B, qui æqualis eſt L C A, ad K E C, fit an-
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            gulus C E B: </s>
            <s xml:id="echoid-s1527" xml:space="preserve">& </s>
            <s xml:id="echoid-s1528" xml:space="preserve">auferendo ab E C L angulum L C B, fit
              <lb/>
            E C B. </s>
            <s xml:id="echoid-s1529" xml:space="preserve">Ergo angulus C E B major omnino angulo E C B.
              <lb/>
            </s>
            <s xml:id="echoid-s1530" xml:space="preserve">Itaque in triangulo C E B, latus C B majus erit quam E B. </s>
            <s xml:id="echoid-s1531" xml:space="preserve">
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            ſed E B æquale patet eſſe C A, cum ſit idemmet ipſum unà
              <lb/>
            cum figura transpoſitum. </s>
            <s xml:id="echoid-s1532" xml:space="preserve">Ergo C B etiam major quam C A,
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            hoc eſt, quam C F. </s>
            <s xml:id="echoid-s1533" xml:space="preserve">unde conſtat punctum B eſſe extra cir-
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            cumferentiam M A F.</s>
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            <s xml:id="echoid-s1535" xml:space="preserve">Sit rurſus punctum N in curva ſumptum inter regulam
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            L D & </s>
            <s xml:id="echoid-s1536" xml:space="preserve">punctum A. </s>
            <s xml:id="echoid-s1537" xml:space="preserve">Cumque punctum deſcribens eſſet in N,
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            ponatur ſitus figuræ fuiſſe in V L, punctumque contactus L,
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            punctum verò quod tangebat prius regulam in C, ſit </s>
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