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

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              <pb o="79" file="0119" n="127" rhead="HOROLOG. OSCILLATOR."/>
            A D, erunt anguli ad circumferentiam ipſis inſiſtentes,
              <lb/>
              <note position="right" xlink:label="note-0119-01" xlink:href="note-0119-01a" xml:space="preserve">
                <emph style="sc">De motu</emph>
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                <emph style="sc">IN</emph>
                <emph style="sc">Cy-</emph>
                <lb/>
                <emph style="sc">CLOIDE</emph>
              .</note>
            E D A, A B D æquales. </s>
            <s xml:id="echoid-s1741" xml:space="preserve">Itaque in triangulis A B D,
              <lb/>
            A D F, æquales anguli A B D, A D F. </s>
            <s xml:id="echoid-s1742" xml:space="preserve">Communis au-
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            tem utrique eſt angulus ad A. </s>
            <s xml:id="echoid-s1743" xml:space="preserve">Ergo dicti trianguli ſimiles
              <lb/>
            erunt, ideoque B A ad A D ut A D ad A F.</s>
            <s xml:id="echoid-s1744" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s1745" xml:space="preserve">Sit jam punctum interſectionis f extra circulum, & </s>
            <s xml:id="echoid-s1746" xml:space="preserve">du-
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            catur b H parallela D E, quæ occurrat rectæ A D in H.
              <lb/>
            </s>
            <s xml:id="echoid-s1747" xml:space="preserve">Itaque ſecundum jam demonſtrata erit ut D A ad A b, ita
              <lb/>
            A b ad A H, hoc eſt, ita A f ad A D: </s>
            <s xml:id="echoid-s1748" xml:space="preserve">Ideoque rurſus
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            proportionales erunt A f, A D, A b. </s>
            <s xml:id="echoid-s1749" xml:space="preserve">Quare conſtat propo-
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            ſitum.</s>
            <s xml:id="echoid-s1750" xml:space="preserve"/>
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          <head xml:id="echoid-head69" xml:space="preserve">PROPOSITIO XXIII.</head>
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            <s xml:id="echoid-s1751" xml:space="preserve">SIt Cyclois A B C, cujus vertex A deorſum con-
              <lb/>
              <note position="right" xlink:label="note-0119-02" xlink:href="note-0119-02a" xml:space="preserve">TAB. IX.
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              Fig. 5.</note>
            verſus ſit, axe A D ad perpendiculum erecto;
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            <s xml:id="echoid-s1752" xml:space="preserve">ſumptoque in ea quolibet puncto B, ducatur inde
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            deorſum recta B I quæ Cycloidem tangat, terminetur-
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            que recta horizontali A I. </s>
            <s xml:id="echoid-s1753" xml:space="preserve">recta vero B F ad axem
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            perpendicularis agatur, & </s>
            <s xml:id="echoid-s1754" xml:space="preserve">diviſa bifariam F A in
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            X, ſuper ea deſcribatur ſemicirculus F H A. </s>
            <s xml:id="echoid-s1755" xml:space="preserve">Du-
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            ctâ deinde per punctum quodlibet G in curva B A
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            ſumptum, rectâ Σ G parallelâ B F, quæ circum-
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            ferentiæ F H A occurrat in H, axi A D in Σ, in-
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            telligantur per puncta G & </s>
            <s xml:id="echoid-s1756" xml:space="preserve">H rectæ tangentes u-
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            triusque curvæ, earumque tangentium partes iis-
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            dem duabus horizontalibus M S, N T interceptæ
              <lb/>
            ſint M N, S T. </s>
            <s xml:id="echoid-s1757" xml:space="preserve">Iisdemque rectis M S, N T in-
              <lb/>
            cludantur tangentis B I pars O P, & </s>
            <s xml:id="echoid-s1758" xml:space="preserve">axis D A
              <lb/>
            pars Q R.</s>
            <s xml:id="echoid-s1759" xml:space="preserve"/>
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          <p style="it">
            <s xml:id="echoid-s1760" xml:space="preserve">Quibus ita ſe habentibus, dico tempus quo gra-
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            ve percurret rectam M N, celeritate </s>
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