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

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            <s xml:id="echoid-s2431" xml:space="preserve">
              <pb o="108" file="0160" n="174" rhead="CHRISTIANI HUGENII"/>
            evolutione lineæ A E H M, quadrans C L evolutione ſimi-
              <lb/>
              <note position="left" xlink:label="note-0160-01" xlink:href="note-0160-01a" 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>
            lis huic oppoſitæ C O M. </s>
            <s xml:id="echoid-s2432" xml:space="preserve">Eſt enim hæc in ſectione utraque
              <lb/>
            diverſitas, quod cum principium quidem curvæ E H M,
              <lb/>
            tam in ellipſi quam in hyperbola, ſit punctum E, ſumpta
              <lb/>
            A E æquali {1/2} lateris recti; </s>
            <s xml:id="echoid-s2433" xml:space="preserve">in hyperbola in infinitum inde
              <lb/>
            dicta linea extenditur, at in ellipſi finitur in puncto axis
              <lb/>
            minoris M, ſumpta L M æquali {1/2} lateris recti, ſecundum
              <lb/>
            quod poſſunt ordinatim applicatæ ad dictum minorem axem.
              <lb/>
            </s>
            <s xml:id="echoid-s2434" xml:space="preserve">Namque hos terminos eſſe hujus curvæ, facile apparebit or-
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            tum ejus conſideranti, quodque in ellipſi eſt ſicut A D ad
              <lb/>
            D E, ita L M ad M D.</s>
            <s xml:id="echoid-s2435" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2436" xml:space="preserve">Horum autem demonſtrationi non immorabimur, ſed ad
              <lb/>
            ipſam methodum tradendam pergemus, qua & </s>
            <s xml:id="echoid-s2437" xml:space="preserve">hæ curvæ ex
              <lb/>
            ſectionibus conicis, & </s>
            <s xml:id="echoid-s2438" xml:space="preserve">aliæ innumeræ ex aliis quibuſcun-
              <lb/>
            que datis inveniuntur.</s>
            <s xml:id="echoid-s2439" xml:space="preserve"/>
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        <div xml:id="echoid-div198" type="section" level="1" n="71">
          <head xml:id="echoid-head95" xml:space="preserve">PROPOSITIO XI.</head>
          <p>
            <s xml:id="echoid-s2440" xml:space="preserve">DAtâ lineâ curvâ, invenire aliam cujus evolu-
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            tione illa deſcribatur; </s>
            <s xml:id="echoid-s2441" xml:space="preserve">& </s>
            <s xml:id="echoid-s2442" xml:space="preserve">oſtendere quod ex
              <lb/>
            unaquaque curva geometrica, alia curva itidem
              <lb/>
            geometrica exiſtat, cui recta linea æqualis dari
              <lb/>
            poſſit.</s>
            <s xml:id="echoid-s2443" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2444" xml:space="preserve">Sit curva quæpiam, vel pars ejus, in partem unam infle-
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              <note position="left" xlink:label="note-0160-02" xlink:href="note-0160-02a" xml:space="preserve">TAB. XV.
                <lb/>
              Fig. 4. & 5.</note>
            xa A B F, & </s>
            <s xml:id="echoid-s2445" xml:space="preserve">recta K L, ad quam puncta omnia referan-
              <lb/>
            tur; </s>
            <s xml:id="echoid-s2446" xml:space="preserve">& </s>
            <s xml:id="echoid-s2447" xml:space="preserve">oporteat invenire curvam aliam, ut D E, cujus
              <lb/>
            evolutione ipſa A B F deſcribatur.</s>
            <s xml:id="echoid-s2448" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2449" xml:space="preserve">Ponatur jam inventa; </s>
            <s xml:id="echoid-s2450" xml:space="preserve">& </s>
            <s xml:id="echoid-s2451" xml:space="preserve">quoniam tangentes omnes curvæ
              <lb/>
            D E, neceſſe eſt occurrere lineæ A B F, ex evolutione de-
              <lb/>
            ſcriptæ, ad angulos rectos; </s>
            <s xml:id="echoid-s2452" xml:space="preserve">patet quoque viciſſim eas quæ
              <lb/>
            ipſi A B F ad rectos angulos inſiſtunt, ut B D, F E, ta-
              <lb/>
            cturas evolutam C D E.</s>
            <s xml:id="echoid-s2453" xml:space="preserve"/>
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            <s xml:id="echoid-s2454" xml:space="preserve">Intelligantur autem puncta B, F, inter ſe proxima; </s>
            <s xml:id="echoid-s2455" xml:space="preserve">& </s>
            <s xml:id="echoid-s2456" xml:space="preserve">ſi-
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            quidem à parte A evolutio incipere ponatur, ulteriuſque in-
              <lb/>
            de diſtet F quam B, etiam contactus E ulterius quam </s>
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