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

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            <s xml:id="echoid-s1443" xml:space="preserve">
              <pb o="68" file="0102" n="107" rhead="CHRISTIANI HUGENII"/>
            nis intercepto, & </s>
            <s xml:id="echoid-s1444" xml:space="preserve">in eandem partem cavo. </s>
            <s xml:id="echoid-s1445" xml:space="preserve">Ergo & </s>
            <s xml:id="echoid-s1446" xml:space="preserve">F D
              <lb/>
              <note position="left" xlink:label="note-0102-01" xlink:href="note-0102-01a" xml:space="preserve">
                <emph style="sc">De de-</emph>
                <lb/>
                <emph style="sc">SCENSU</emph>
                <lb/>
                <emph style="sc">GRAVIUM</emph>
              .</note>
            eodem arcu B D major erit: </s>
            <s xml:id="echoid-s1447" xml:space="preserve">quare conſtat propoſitum.</s>
            <s xml:id="echoid-s1448" xml:space="preserve"/>
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        <div xml:id="echoid-div89" type="section" level="1" n="36">
          <head xml:id="echoid-head58" xml:space="preserve">PROPOSITIO XIII.</head>
          <p style="it">
            <s xml:id="echoid-s1449" xml:space="preserve">IIsdem poſitis, ſi recta A B occurrat ipſi D G in-
              <lb/>
              <note position="left" xlink:label="note-0102-02" xlink:href="note-0102-02a" xml:space="preserve">TAB. VI.
                <lb/>
              Fig. 6.</note>
            tra circulum; </s>
            <s xml:id="echoid-s1450" xml:space="preserve">Dico arcum B D, rectis G D,
              <lb/>
            A B interceptum, majorem eſſe recta D F.</s>
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          <p>
            <s xml:id="echoid-s1452" xml:space="preserve">Jungatur enim D C & </s>
            <s xml:id="echoid-s1453" xml:space="preserve">ducatur arcui D B ſubtenſa D B.
              <lb/>
            </s>
            <s xml:id="echoid-s1454" xml:space="preserve">Quoniam ergo angulus A B D æqualis A C D, hoc eſt,
              <lb/>
            angulo A D G; </s>
            <s xml:id="echoid-s1455" xml:space="preserve">angulus autem D F B major angulo A D F,
              <lb/>
            ſive A D G; </s>
            <s xml:id="echoid-s1456" xml:space="preserve">erit idem D F B etiam major D B F. </s>
            <s xml:id="echoid-s1457" xml:space="preserve">Ergo
              <lb/>
            in triangulo D F B latus D B majus latere D F; </s>
            <s xml:id="echoid-s1458" xml:space="preserve">unde mul-
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            to magis arcus D B ſuperabit eandem D F. </s>
            <s xml:id="echoid-s1459" xml:space="preserve">Quare conſtat
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            propoſitum.</s>
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          <head xml:id="echoid-head59" xml:space="preserve">PROPOSITIO XIV.</head>
          <p style="it">
            <s xml:id="echoid-s1461" xml:space="preserve">SIt cyclois A B C cujus baſis A C axis B D.
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            </s>
            <s xml:id="echoid-s1462" xml:space="preserve">Quomodo autem generetur ex definitione & </s>
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            deſcriptione mechanica ſuperius traditis ſatis ma-
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            nifeſtum arbitror. </s>
            <s xml:id="echoid-s1464" xml:space="preserve">Et circa axem B D, circulus
              <lb/>
            deſcriptus ſit B G D, & </s>
            <s xml:id="echoid-s1465" xml:space="preserve">à quolibet puncto E in cy-
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            cloide ſumpto agatur E F baſi A C parallela, quæ
              <lb/>
            occurrat axi B D in F, ſecetque circumferentiam
              <lb/>
            B G D in G, Dico rectam G E arcui G B æqua-
              <lb/>
            lem eſſe.</s>
            <s xml:id="echoid-s1466" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1467" xml:space="preserve">Deſcribatur enim per E punctum circulus L E K ipſi
              <lb/>
            B G D æqualis, quique tangat baſin cycloidis in K, & </s>
            <s xml:id="echoid-s1468" xml:space="preserve">du-
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            catur diameter K L. </s>
            <s xml:id="echoid-s1469" xml:space="preserve">Eſt igitur recta A K arcui E K æqua-
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            lis; </s>
            <s xml:id="echoid-s1470" xml:space="preserve">ſed tota A D æqualis ſemicircumferentiæ K E L; </s>
            <s xml:id="echoid-s1471" xml:space="preserve">ergo
              <lb/>
            K D æqualis arcui E L ſive G B. </s>
            <s xml:id="echoid-s1472" xml:space="preserve">Eſt autem K D ſive N F
              <lb/>
            æqualis E G, quoniam E N æqualis G F, & </s>
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            utrique N G. </s>
            <s xml:id="echoid-s1474" xml:space="preserve">Ergo conſtat & </s>
            <s xml:id="echoid-s1475" xml:space="preserve">G E æqualem eſſe arcui G B.</s>
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