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

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            <s xml:id="echoid-s1692" xml:space="preserve">
              <pb o="77" file="0117" n="125" rhead="HOROLOG. OSCILLATOR."/>
            A B, brevius eſſe tempore per G H poſt N G ſive poſt F G.</s>
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          <note position="right" xml:space="preserve">
            <emph style="sc">De motu</emph>
            <lb/>
            <emph style="sc">IN</emph>
            <emph style="sc">Cy-</emph>
            <lb/>
            <emph style="sc">CLOIDE</emph>
          .</note>
          <p>
            <s xml:id="echoid-s1694" xml:space="preserve">Similiter oſtendetur, productis D C, K H ſurſum, do-
              <lb/>
            nec occurrant horizontali A F in O & </s>
            <s xml:id="echoid-s1695" xml:space="preserve">P, tempus per
              <lb/>
            C D poſt A B C, ſive poſt O C, brevius eſſe tempore per
              <lb/>
            H K poſt F G H ſive poſt P H. </s>
            <s xml:id="echoid-s1696" xml:space="preserve">Ac denique tempus per
              <lb/>
            D E poſt A B C D, brevius eſſe tempore per K L poſt
              <lb/>
            F G H K. </s>
            <s xml:id="echoid-s1697" xml:space="preserve">Quare totum tempus deſcenſus per A B C D E,
              <lb/>
            brevius erit tempore per F G H K L. </s>
            <s xml:id="echoid-s1698" xml:space="preserve">quod erat demon-
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            ſtrandum.</s>
            <s xml:id="echoid-s1699" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s1700" xml:space="preserve">Hinc vero manifeſtum eſt, conſiderando curvas lineas
              <lb/>
            tanquam ex innumeris rectis compoſitas, ſi fuerint duæ ſu-
              <lb/>
            perficies, ſecundum lineas curvas ejusdem altitudinis incli-
              <lb/>
            natæ, quarum in punctis quibuslibet æque altis major ſem-
              <lb/>
            per ſit inclinatio unius quam reliquæ, etiam tempore bre-
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            viori per minus inclinatam grave deſcenſurum quam per ma-
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            gis inclinatam.</s>
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          <p>
            <s xml:id="echoid-s1702" xml:space="preserve">Velut ſi ſint duæ ſuperficies inclinatæ ſecundum curvas
              <lb/>
              <note position="right" xlink:label="note-0117-02" xlink:href="note-0117-02a" xml:space="preserve">TAB. IX.
                <lb/>
              Fig. 2.</note>
            A B, C D, æqualis altitudinis, quarumque in punctis æ-
              <lb/>
            que altis quibuslibet E, F, major ſit inclinatio ipſius C D
              <lb/>
            quam A B, hoc eſt, ut recta tangens curvam C D in F,
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            magis inclinata ſit ad horizontem, quam quæ curvam A B
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            tangit in puncto E. </s>
            <s xml:id="echoid-s1703" xml:space="preserve">erit tempus deſcenſus per A B brevius
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            quam per C D.</s>
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            <s xml:id="echoid-s1705" xml:space="preserve">Idemque continget ſi altera linearum recta fuerit: </s>
            <s xml:id="echoid-s1706" xml:space="preserve">dum-
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            modo inclinatio rectæ, quæ ubique eſt eadem, major mi-
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            norve fuerit inclinatione curvæ in quolibet ſui puncto.</s>
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        <div xml:id="echoid-div116" type="section" level="1" n="45">
          <head xml:id="echoid-head67" xml:space="preserve">PROPOSITIO XXII.</head>
          <p style="it">
            <s xml:id="echoid-s1708" xml:space="preserve">SI in Cycloide cujus axis ad perpendiculum erectus
              <lb/>
            ſtat, vertice deorſum ſpectante, duæ portiones
              <lb/>
            curvæ æqualis altitudinis accipiantur, ſed quarum
              <lb/>
            altera propior ſit vertici; </s>
            <s xml:id="echoid-s1709" xml:space="preserve">erit tempus deſcenſus
              <lb/>
            per ſuperiorem, brevius tempore per inferiorem.</s>
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          <p>
            <s xml:id="echoid-s1711" xml:space="preserve">Sit Cyclois A B, cujus axis A C ad perpendiculum ere-
              <lb/>
              <note position="right" xlink:label="note-0117-03" xlink:href="note-0117-03a" xml:space="preserve">TAB. IX.
                <lb/>
              Fig. 3.</note>
            ctus, vertex A deorſum ſpectet; </s>
            <s xml:id="echoid-s1712" xml:space="preserve">& </s>
            <s xml:id="echoid-s1713" xml:space="preserve">accipiantur in ea </s>
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