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

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          <pb o="87" file="0131" n="141" rhead="HOROLOG. OSCILLATOR."/>
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        <div xml:id="echoid-div137" type="section" level="1" n="49">
          <head xml:id="echoid-head71" xml:space="preserve">PROPOSITIO XXV.</head>
          <note position="right" xml:space="preserve">
            <emph style="sc">De motu</emph>
            <lb/>
            <emph style="sc">IN CY-</emph>
            <lb/>
            <emph style="sc">CLOIDE</emph>
          .</note>
          <p style="it">
            <s xml:id="echoid-s1938" xml:space="preserve">IN Cycloide cujus axis ad perpendiculum erectus
              <lb/>
            eſt, vertice deorſum ſpectante, tempora deſcen-
              <lb/>
            ſus quibus mobile, à quocunque in ea puncto dimis-
              <lb/>
            ſum, ad punctum imum verticis pervenit, ſunt in-
              <lb/>
            ter ſe æqualia; </s>
            <s xml:id="echoid-s1939" xml:space="preserve">habentque ad tempus caſus perpen-
              <lb/>
            dicularis per totum axem cycloidis eam rationem,
              <lb/>
            quam ſemicircumferentia circuli ad diametrum.</s>
            <s xml:id="echoid-s1940" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1941" xml:space="preserve">Eſto cyclois A B C cujus vertex A deorſum ſpectet, axis
              <lb/>
              <note position="right" xlink:label="note-0131-02" xlink:href="note-0131-02a" xml:space="preserve">TAB. XI.
                <lb/>
              Fig. 1.</note>
            vero A D ad perpendiculum erectus ſit, & </s>
            <s xml:id="echoid-s1942" xml:space="preserve">à puncto quovis
              <lb/>
            in cycloide ſumpto, velut B; </s>
            <s xml:id="echoid-s1943" xml:space="preserve">deſcendat mobile impetu na-
              <lb/>
            turali per arcum B A, ſive per ſuperficiem ita inflexam. </s>
            <s xml:id="echoid-s1944" xml:space="preserve">Di-
              <lb/>
            co tempus deſcenſus hujus eſſe ad tempus caſus per axem
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            D A, ſicut ſemicircumferentia circuli ad diametrum. </s>
            <s xml:id="echoid-s1945" xml:space="preserve">Quo
              <lb/>
            demonſtrato, etiam tempora deſcenſus, per quoslibet cy-
              <lb/>
            cloidis arcus ad A terminatos, inter ſe æqualia eſſe conſta-
              <lb/>
            bit.</s>
            <s xml:id="echoid-s1946" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1947" xml:space="preserve">Deſcribatur ſuper axe D A ſemicirculus, cujus circumfe-
              <lb/>
            rentiam ſecet recta B F, baſi D C parallela, in E; </s>
            <s xml:id="echoid-s1948" xml:space="preserve">junctâ-
              <lb/>
            que E A, ducatur ei parallela B G, quæ quidem cycloidem
              <lb/>
            tanget in B. </s>
            <s xml:id="echoid-s1949" xml:space="preserve">Eadem vero occurrat rectæ horizontali per A
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            ductæ in G: </s>
            <s xml:id="echoid-s1950" xml:space="preserve">ſitque etiam ſuper F A deſcriptus ſemicirculus
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            F H A.</s>
            <s xml:id="echoid-s1951" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1952" xml:space="preserve">Eſt igitur, per præcedentem, tempus deſcenſus per ar-
              <lb/>
            cum cycloidis B A, ad tempus motus æquabilis per rectam
              <lb/>
            B G cum celeritate dimidia ex B G, ſicut arcus ſemicirculi
              <lb/>
            F H A ad rectam F A. </s>
            <s xml:id="echoid-s1953" xml:space="preserve">Tempus vero dicti motus æquabilis
              <lb/>
            per B G, æquatur tempori deſcenſus naturaliter accelerati
              <lb/>
            per eandem B G, ſive per E A, quæ ipſi parallela eſt & </s>
            <s xml:id="echoid-s1954" xml:space="preserve">
              <lb/>
            æqualis, hoc eſt, tempori deſcenſus accelerati per axem
              <lb/>
            D A. </s>
            <s xml:id="echoid-s1955" xml:space="preserve">Itaque tempus per arcum B A, erit quoque ad
              <note symbol="*" position="right" xlink:label="note-0131-03" xlink:href="note-0131-03a" xml:space="preserve">Prop. 6.
                <lb/>
              Galil. de
                <lb/>
              motu Accel.</note>
            pus deſcenſus per axem D A, ut ſemicirculi circumferentia
              <lb/>
            F H A ad diametrum F A. </s>
            <s xml:id="echoid-s1956" xml:space="preserve">quod erat demonſtrandum.</s>
            <s xml:id="echoid-s1957" xml:space="preserve"/>
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