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

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        <div xml:id="echoid-div166" type="section" level="1" n="61">
          <pb o="97" file="0145" n="157" rhead="HOROLOG. OSCILLATOR."/>
          <p>
            <s xml:id="echoid-s2154" xml:space="preserve">Et apparet, ſi dimidiam cycloidem, ipſi A B C gemel-
              <lb/>
              <note position="right" xlink:label="note-0145-01" xlink:href="note-0145-01a" xml:space="preserve">
                <emph style="sc">De linea-</emph>
                <lb/>
                <emph style="sc">RUM CUR-</emph>
                <lb/>
                <emph style="sc">VARUM</emph>
                <lb/>
                <emph style="sc">EVOLUTIO-</emph>
                <lb/>
                <emph style="sc">NE.</emph>
              </note>
            lam, contrario ſitu ab altera parte lineæ C G diſponamus,
              <lb/>
            velut C N, ejus evolutione, vel etiam dum filum, jam
              <lb/>
            extenſum in C F, circa eam replicatur, alteram ſemicy-
              <lb/>
            cloidem F N fili extremitate deſcriptum iri, quæ ſimul
              <lb/>
            cum priore A E F integram conſtituat.</s>
            <s xml:id="echoid-s2155" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2156" xml:space="preserve">Atque ex his, & </s>
            <s xml:id="echoid-s2157" xml:space="preserve">propoſitione 25 de deſcenſu gravium, ma-
              <lb/>
            nifeſtum jam eſt quod ſupra in Conſtructione Horologii de
              <lb/>
            æquabili penduli motu dictum fuit. </s>
            <s xml:id="echoid-s2158" xml:space="preserve">Patet enim perpendicu-
              <lb/>
            lum, inter laminas binas, ſecundum ſemicycloidem inflexas,
              <lb/>
            ſuſpenſum agitatumque, motu ſuo cycloidis arcum deſcri-
              <lb/>
            bere, ac proinde æqualibus temporibus quaſlibet ejus reci-
              <lb/>
            procationes abſolvi. </s>
            <s xml:id="echoid-s2159" xml:space="preserve">Non refert enim utrum in ſuperficie,
              <lb/>
            ſecundum cycloidem curvata, mobile feratur, an filo alliga-
              <lb/>
            tum lineam ipſam in aëre percurrat, cum utrobique eandem
              <lb/>
            libertatem, eandemque in omnibus curvæ punctis inclina-
              <lb/>
            tionem ad motum habeat.</s>
            <s xml:id="echoid-s2160" xml:space="preserve"/>
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        <div xml:id="echoid-div169" type="section" level="1" n="62">
          <head xml:id="echoid-head86" xml:space="preserve">PROPOSITIO VII.</head>
          <p style="it">
            <s xml:id="echoid-s2161" xml:space="preserve">Cyclois linea ſui axis, ſive diametri circuli ge-
              <lb/>
            nitoris, quadrupla eſt.</s>
            <s xml:id="echoid-s2162" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2163" xml:space="preserve">Repetita enim figura præcedenti: </s>
            <s xml:id="echoid-s2164" xml:space="preserve">cum poſt totam ſemi-
              <lb/>
              <note position="right" xlink:label="note-0145-02" xlink:href="note-0145-02a" xml:space="preserve">TAB. XVI.
                <lb/>
              Fig. 1.</note>
            cycloidem A B C evolutam, filum occupet rectam C F,
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            quæ dupla eſt A D, proptarea quod axes cycloidum A B C,
              <lb/>
            A E F ſunt æquales; </s>
            <s xml:id="echoid-s2165" xml:space="preserve">apparet ſemicycloidem ipſam A B C,
              <lb/>
            filo ſibi circum applicito æqualem, duplam eſſe ſui axis A D,
              <lb/>
            ac totam proinde cycloidem axis ſui quadruplam.</s>
            <s xml:id="echoid-s2166" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2167" xml:space="preserve">Apparet etiam tangentem B E, quæ refert partem fili ex-
              <lb/>
            tenſam, antea curvæ parti B A applicatam, huic ipſi longi-
              <lb/>
            tudine æquari. </s>
            <s xml:id="echoid-s2168" xml:space="preserve">Eſt autem B E dupla ipſius B K, ſive A H,
              <lb/>
            quoniam in propoſitione quinta oſtenſum eſt K E ipſi A H
              <lb/>
            æqualem eſſe. </s>
            <s xml:id="echoid-s2169" xml:space="preserve">Itaque pars cycloidis A B rectæ A H, ſive
              <lb/>
            B K, dupla erit: </s>
            <s xml:id="echoid-s2170" xml:space="preserve">exiſtente nimirum B H parallela baſi
              <lb/>
            cycloidis: </s>
            <s xml:id="echoid-s2171" xml:space="preserve">idque ubicunque in ea punctum B ſumptum fue-
              <lb/>
            rit.</s>
            <s xml:id="echoid-s2172" xml:space="preserve"/>
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