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

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        <div xml:id="echoid-div148" type="section" level="1" n="54">
          <pb o="90" file="0134" n="144" rhead="CHRISTIANI HUGENII"/>
        </div>
        <div xml:id="echoid-div149" type="section" level="1" n="55">
          <head xml:id="echoid-head79" xml:space="preserve">IV.</head>
          <note position="left" xml:space="preserve">
            <emph style="sc">De linea-</emph>
            <lb/>
            <emph style="sc">RUM CUR-</emph>
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            <emph style="sc">VARUM</emph>
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            <emph style="sc">EVOLUTIO-</emph>
            <lb/>
            <emph style="sc">NE</emph>
          .</note>
          <p style="it">
            <s xml:id="echoid-s1986" xml:space="preserve">Illa vero cui filum circumplicatum erat, dicatur
              <lb/>
            Evoluta. </s>
            <s xml:id="echoid-s1987" xml:space="preserve">In figura ſuperiori, A B C eſt evoluta,
              <lb/>
              <note position="left" xlink:label="note-0134-02" xlink:href="note-0134-02a" xml:space="preserve">TAB. XI.
                <lb/>
              Fig. 2.</note>
            A D E deſcripta ex evolutione A B C, ut nempe
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            cum extremitas fili ex A venit in D, pars fili ex-
              <lb/>
            tenſa ſit D B recta, reliqua parte B C adhuc ap-
              <lb/>
            plicata curvæ A B C. </s>
            <s xml:id="echoid-s1988" xml:space="preserve">Manifeſtum eſt autem D B
              <lb/>
            tangere evolutam in B.</s>
            <s xml:id="echoid-s1989" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div151" type="section" level="1" n="56">
          <head xml:id="echoid-head80" xml:space="preserve">PROPOSITIOI.</head>
          <p style="it">
            <s xml:id="echoid-s1990" xml:space="preserve">R Ecta omnis, quæ evolutam tangit, occurret li-
              <lb/>
            @eæ ex evolutione deſcriptæ ad angulos rectos.</s>
            <s xml:id="echoid-s1991" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1992" xml:space="preserve">Sit A B evoluta, A H vero quæ ex evolutione illius de-
              <lb/>
              <note position="left" xlink:label="note-0134-03" xlink:href="note-0134-03a" xml:space="preserve">TAB. XI.
                <lb/>
              Fig. 3.</note>
            ſcripta eſt. </s>
            <s xml:id="echoid-s1993" xml:space="preserve">Recta autem F D C, tangens curvam A D in D,
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            occurrat in C curvæ A C H. </s>
            <s xml:id="echoid-s1994" xml:space="preserve">Dico ei occurrere ad angulos
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            rectos: </s>
            <s xml:id="echoid-s1995" xml:space="preserve">hoc eſt, ſi ducatur C E recta perpendicularis C D,
              <lb/>
            dico eam in C tangere curvam A C H. </s>
            <s xml:id="echoid-s1996" xml:space="preserve">Quia enim D C
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            tangit evolutam in D, apparet ipſam referre poſitionem fili
              <lb/>
            tunc cum ejus extremitas pervenit in C. </s>
            <s xml:id="echoid-s1997" xml:space="preserve">Quod ſi igitur o-
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            ſtenderimus filum, in tota reliqua deſcriptione curvæ A C H,
              <lb/>
            nusquam pertingere ad rectam C E præterquam in C pun-
              <lb/>
            cto, manifeſtum erit rectam C E ibidem curvam A C H
              <lb/>
            contingere.</s>
            <s xml:id="echoid-s1998" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1999" xml:space="preserve">Sumatur punctum aliquod in A C præter C, quod ſit H,
              <lb/>
            ſitque primo remotius à principio evolutionis A quam pun-
              <lb/>
            ctum C, & </s>
            <s xml:id="echoid-s2000" xml:space="preserve">intelligatur pars libera eſſe H G, cum extremi-
              <lb/>
            tate ſua ad H pervenit. </s>
            <s xml:id="echoid-s2001" xml:space="preserve">Tangit ergo H G lineam A B in G.
              <lb/>
            </s>
            <s xml:id="echoid-s2002" xml:space="preserve">Cumque interea dum deſcribitur pars curvæ C H, evolu-
              <lb/>
            tus ſit arcus D G, occurret C D à parte D producta ipſi
              <lb/>
            H G, ut in F. </s>
            <s xml:id="echoid-s2003" xml:space="preserve">Ponatur autem G H occurrere rectæ C E
              <lb/>
            in E. </s>
            <s xml:id="echoid-s2004" xml:space="preserve">Quia igitur duæ ſimul D F, F G, majores ſunt quam
              <lb/>
            D G, ſive curva ea fuerit ſive recta: </s>
            <s xml:id="echoid-s2005" xml:space="preserve">fiet addendo utrinque
              <lb/>
            rectam D C, ut rectæ C F, F G ſimul majores ſint </s>
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