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

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        <div xml:id="echoid-div92" type="section" level="1" n="38">
          <pb o="72" file="0108" n="114" rhead="CHRISTIANI HUGENII"/>
          <p>
            <s xml:id="echoid-s1568" xml:space="preserve">Item rurſus oſtenditur angulus L V C major L C V. </s>
            <s xml:id="echoid-s1569" xml:space="preserve">Qua-
              <lb/>
              <note position="left" xlink:label="note-0108-01" xlink:href="note-0108-01a" xml:space="preserve">
                <emph style="sc">De de-</emph>
                <lb/>
                <emph style="sc">SCENSU</emph>
                <lb/>
                <emph style="sc">GRAVIUM</emph>
              .</note>
            re C V P, qui cum L V C duos rectos æquat, minor erit
              <lb/>
            quam V C D. </s>
            <s xml:id="echoid-s1570" xml:space="preserve">Atqui addendo ad V C D angulum D C N,
              <lb/>
            fit V C N; </s>
            <s xml:id="echoid-s1571" xml:space="preserve">& </s>
            <s xml:id="echoid-s1572" xml:space="preserve">auferendo ab C V P angulum P V N, fit
              <lb/>
            C V N. </s>
            <s xml:id="echoid-s1573" xml:space="preserve">Ergo angulus V C N omnino major quam C V N.
              <lb/>
            </s>
            <s xml:id="echoid-s1574" xml:space="preserve">In triangulo itaque C V N, latus V N majus erit quam
              <lb/>
            C N. </s>
            <s xml:id="echoid-s1575" xml:space="preserve">Eſt autem ipſi V N æqualis C A ſive C M. </s>
            <s xml:id="echoid-s1576" xml:space="preserve">Ergo & </s>
            <s xml:id="echoid-s1577" xml:space="preserve">
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            C M major quam C N, ideoque punctum circumferentiæ
              <lb/>
            M erit ultra curvam N A B à centro C remotum. </s>
            <s xml:id="echoid-s1578" xml:space="preserve">Itaque
              <lb/>
            conſtat circumferentiam M A F tangere curvam in puncto A. </s>
            <s xml:id="echoid-s1579" xml:space="preserve">
              <lb/>
            quod erat demonſtrandum.</s>
            <s xml:id="echoid-s1580" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s1581" xml:space="preserve">Quod ſi punctum curvæ per quod tangens ducenda eſt,
              <lb/>
            ſit illud ipſum ubi regula curvam ſecat, erit tangens quæſi-
              <lb/>
            ta ſemper regulæ perpendicularis; </s>
            <s xml:id="echoid-s1582" xml:space="preserve">ut facile eſſet oſtendere.</s>
            <s xml:id="echoid-s1583" xml:space="preserve"/>
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        <div xml:id="echoid-div98" type="section" level="1" n="39">
          <head xml:id="echoid-head61" xml:space="preserve">PROPOSITIO XVI.</head>
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            <s xml:id="echoid-s1584" xml:space="preserve">SI circuli circumferentiam, cujus centrum E, ſe-
              <lb/>
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                <emph style="sc">De motu</emph>
                <lb/>
                <emph style="sc">IN</emph>
                <emph style="sc">Cy-</emph>
                <lb/>
                <emph style="sc">CLOIDE</emph>
              .</note>
            cent rectæ duæ parallelæ A F, B G, quarum
              <lb/>
              <note position="left" xlink:label="note-0108-03" xlink:href="note-0108-03a" xml:space="preserve">TAB. VIII.
                <lb/>
              Fig. 2.</note>
            utraque ad eandem partem centri transeat, vel
              <lb/>
            altera A F per centrum ipſum: </s>
            <s xml:id="echoid-s1585" xml:space="preserve">& </s>
            <s xml:id="echoid-s1586" xml:space="preserve">à puncto A,
              <lb/>
            quo centro propior circumferentiam ſecat, ducatur
              <lb/>
            recta ipſam contingens: </s>
            <s xml:id="echoid-s1587" xml:space="preserve">dico partem hujus A B, à
              <lb/>
            parallela utraque interceptam, minorem eſſe arcu
              <lb/>
            A C, ab utraque eadem parallela intercepto.</s>
            <s xml:id="echoid-s1588" xml:space="preserve"/>
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            <s xml:id="echoid-s1589" xml:space="preserve">Ducatur enim arcui A C ſubtenſa recta A C. </s>
            <s xml:id="echoid-s1590" xml:space="preserve">Quia ergo
              <lb/>
            angulus B A F eſt æqualis ei quem capit portio circuli A H F,
              <lb/>
            quæ vel major eſt ſemicirculo vel ſemicirculus, erit proinde
              <lb/>
            angulus B A F, vel minor recto vel rectus; </s>
            <s xml:id="echoid-s1591" xml:space="preserve">ideoque angu-
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            lus A B C vel major recto vel rectus. </s>
            <s xml:id="echoid-s1592" xml:space="preserve">Quare in triangulo
              <lb/>
            A B C latus A C, angulo B ſubtenſum, majus erit latere
              <lb/>
            A B. </s>
            <s xml:id="echoid-s1593" xml:space="preserve">ſed idem latus A C minus eſt arcu A C. </s>
            <s xml:id="echoid-s1594" xml:space="preserve">Ergo omni-
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            no & </s>
            <s xml:id="echoid-s1595" xml:space="preserve">A B arcu A C minor erit.</s>
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