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

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        <div xml:id="echoid-div137" type="section" level="1" n="49">
          <pb o="88" file="0132" n="142" rhead="CHRISTIANI HUGENII"/>
          <p>
            <s xml:id="echoid-s1958" xml:space="preserve">Quod ſi tota cycloidis cavitas perfecta ponatur, conſtat
              <lb/>
              <note position="left" xlink:label="note-0132-01" xlink:href="note-0132-01a" xml:space="preserve">
                <emph style="sc">De motu</emph>
                <lb/>
                <emph style="sc">IN CY-</emph>
                <lb/>
                <emph style="sc">CLOIDE</emph>
              .</note>
            mobile, poſtquam per arcum B A deſcenderit, inde conti-
              <lb/>
            nuato motu per alterum ipſi æqualem arcum aſcenſurum
              <note symbol="*" position="left" xlink:label="note-0132-02" xlink:href="note-0132-02a" xml:space="preserve">Prop. 9.
                <lb/>
              huj.</note>
            atque in eo tantundem temporis atque deſcendendo conſum-
              <lb/>
            pturum . </s>
            <s xml:id="echoid-s1959" xml:space="preserve">Deinde rurſus per A ad B perventurum, ac
              <note symbol="*" position="left" xlink:label="note-0132-03" xlink:href="note-0132-03a" xml:space="preserve">Prop. 11.
                <lb/>
              huj.</note>
            larum ejusmodi reciprocationum, in magnis parvisve cycloi-
              <lb/>
            dis arcubus peractarum, tempora fore ad tempus caſus per-
              <lb/>
            pendicularis per axem D A, ſicut circumferentia circuli tota
              <lb/>
            ad diametrum ſuam.</s>
            <s xml:id="echoid-s1960" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div141" type="section" level="1" n="50">
          <head xml:id="echoid-head72" xml:space="preserve">PROPOSITIO XXVI.</head>
          <p style="it">
            <s xml:id="echoid-s1961" xml:space="preserve">Iisdem poſitis, ſi ducatur inſuper recta horizonta-
              <lb/>
              <note position="left" xlink:label="note-0132-04" xlink:href="note-0132-04a" xml:space="preserve">TAB. XI.
                <lb/>
              Fig. 1.</note>
            lis H I quæ arcum B A ſecet in I, circumferen-
              <lb/>
            tiam vero F H A in H: </s>
            <s xml:id="echoid-s1962" xml:space="preserve">dico tempus per arcum
              <lb/>
            B I, ad tempus per arcum I A poſt B I, eam ra-
              <lb/>
            tionem habere quam arcus circumferentiæ F H ad
              <lb/>
            H A.</s>
            <s xml:id="echoid-s1963" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1964" xml:space="preserve">Occurrat enim recta H I tangenti B G in K, axi D A in
              <lb/>
            L. </s>
            <s xml:id="echoid-s1965" xml:space="preserve">Eſt itaque tempus per arcum B A, ad tempus motus æ-
              <lb/>
            quabilis per B G cum celeritate dimidia ex B G, ſicut arcus
              <lb/>
            F H A ad rectam F A . </s>
            <s xml:id="echoid-s1966" xml:space="preserve">Tempus autem dicti motus
              <note symbol="*" position="left" xlink:label="note-0132-05" xlink:href="note-0132-05a" xml:space="preserve">Prop. 24.
                <lb/>
              huj.</note>
            bilis per B G, eſt ad tempus motus æquabilis per B K, cum
              <lb/>
            eadem celeritate dimidia ex B G, ſicut B G ad B K longi-
              <lb/>
            tudine, hoc eſt, ſicut F A ad F L. </s>
            <s xml:id="echoid-s1967" xml:space="preserve">Et rurſus tempus mo-
              <lb/>
            tus æquabilis, cum dicta celeritate, per B K, ad tempus
              <lb/>
            per arcum B I, ſicut F L ad arcum F H . </s>
            <s xml:id="echoid-s1968" xml:space="preserve">Igitur ex
              <note symbol="*" position="left" xlink:label="note-0132-06" xlink:href="note-0132-06a" xml:space="preserve">Prop. 24.
                <lb/>
              huj.</note>
            quo erit tempus per arcum B A ad tempus per B I, ut ar-
              <lb/>
            cus F H A ad F H. </s>
            <s xml:id="echoid-s1969" xml:space="preserve">Et dividendo, & </s>
            <s xml:id="echoid-s1970" xml:space="preserve">convertendo, tem-
              <lb/>
            pus per B I, ad tempus per I A poſt B I, ut arcus F H
              <lb/>
            ad H A. </s>
            <s xml:id="echoid-s1971" xml:space="preserve">quod erat demonſtrandum.</s>
            <s xml:id="echoid-s1972" xml:space="preserve"/>
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