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

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          <p>
            <s xml:id="echoid-s2345" xml:space="preserve">
              <pb o="105" file="0155" n="168" rhead="HOROLOG. OSCILLATOR."/>
            mul ſuperficiei exhibeatur circulus æqualis. </s>
            <s xml:id="echoid-s2346" xml:space="preserve">cujus exemplum
              <lb/>
              <note position="right" xlink:label="note-0155-01" xlink:href="note-0155-01a" 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>
            in caſu uno cæteris ſimpliciore ſufficiet attuliſſe.</s>
            <s xml:id="echoid-s2347" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2348" xml:space="preserve">Sit ſphæroides latum cujus axis S I, ſectio per axem el-
              <lb/>
            lipſis S T I K; </s>
            <s xml:id="echoid-s2349" xml:space="preserve">cujus ellipſis centrum O, axis major T K.
              <lb/>
            </s>
            <s xml:id="echoid-s2350" xml:space="preserve">
              <note position="right" xlink:label="note-0155-02" xlink:href="note-0155-02a" xml:space="preserve">TAB. XIV.
                <lb/>
              Fig. 2.</note>
            ponatur autem ellipſis hæc ejusmodi, ut latus transverſum
              <lb/>
            T K habeat ad latus rectum eam rationem, quam linea ſe-
              <lb/>
            cundum extremam & </s>
            <s xml:id="echoid-s2351" xml:space="preserve">mediam rationem ſecta, ad partem ſui
              <lb/>
            majorem.</s>
            <s xml:id="echoid-s2352" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2353" xml:space="preserve">Sumatur B C potentia dupla ad S O, item B A potentia
              <lb/>
            dupla ad O K. </s>
            <s xml:id="echoid-s2354" xml:space="preserve">& </s>
            <s xml:id="echoid-s2355" xml:space="preserve">ſint hæ quatuor continue proportionales
              <lb/>
            B C, B A, B F, B E, & </s>
            <s xml:id="echoid-s2356" xml:space="preserve">ponatur E P æqualis E A. </s>
            <s xml:id="echoid-s2357" xml:space="preserve">In-
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            telligatur jam conoides hyperbolicum Q F. </s>
            <s xml:id="echoid-s2358" xml:space="preserve">N, cujus axis
              <lb/>
            F P; </s>
            <s xml:id="echoid-s2359" xml:space="preserve">axi adjecta, ſive {1/2} latus transverſum F B; </s>
            <s xml:id="echoid-s2360" xml:space="preserve">dimidium
              <lb/>
            latus rectum æquale B C.</s>
            <s xml:id="echoid-s2361" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s2362" xml:space="preserve">Hujus conoidis ſuperficies curva, unà cum ſuperficie ſphæ-
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            roidis S I, æquabitur circulo cujus datus erit radius M L,
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            qui nempe poſſit quadratum T K cum duplo quadrato S I.</s>
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        <div xml:id="echoid-div191" type="section" level="1" n="69">
          <head xml:id="echoid-head93" style="it" xml:space="preserve">Curvæ parabolicæ æqualem rectam lineam
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          invenire.</head>
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            <s xml:id="echoid-s2364" xml:space="preserve">SIt parabolæ portio A B C, cujus axis B K, baſis A C
              <lb/>
              <note position="right" xlink:label="note-0155-03" xlink:href="note-0155-03a" xml:space="preserve">TAB. XIV.
                <lb/>
              Fig. 3.</note>
            axi ad angulos rectos; </s>
            <s xml:id="echoid-s2365" xml:space="preserve">& </s>
            <s xml:id="echoid-s2366" xml:space="preserve">oporteat curvæ A B C rectam
              <lb/>
            æqualem invenire.</s>
            <s xml:id="echoid-s2367" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2368" xml:space="preserve">Accipiatur baſi dimidiæ A K æqualis recta I E, quæ pro-
              <lb/>
            ducatur ad H, ut ſit I H æqualis A G, quæ parabolam in
              <lb/>
            puncto baſis A contingens, cum axe producto convenit in G.
              <lb/>
            </s>
            <s xml:id="echoid-s2369" xml:space="preserve">Sit jam portio hyperbolæ D E F, vertice E, centro I de-
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            ſcriptæ, cujusque diameter ſit E H; </s>
            <s xml:id="echoid-s2370" xml:space="preserve">baſis vero D H F or-
              <lb/>
            dinatim ad diametrum applicata. </s>
            <s xml:id="echoid-s2371" xml:space="preserve">Latus rectum pro lubitu
              <lb/>
            ſumi poteſt. </s>
            <s xml:id="echoid-s2372" xml:space="preserve">Quod ſi jam ſuper baſi D F intelligatur paral-
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            lelogrammum conſtitutum D P Q F, quod portioni D E F
              <lb/>
            æquale ſit; </s>
            <s xml:id="echoid-s2373" xml:space="preserve">ejus latus P Q ita ſecabit diametrum hyperbolæ
              <lb/>
            in R, ut R I ſit æqualis curvæ parabolicæ A B, cujus du-
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            pla eſt A B C.</s>
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          </p>
          <p>
            <s xml:id="echoid-s2375" xml:space="preserve">Apparet igitur hinc quomodo à quadratura hyperbolæ
              <lb/>
            pendeat curvæ parabolicæ menſura, & </s>
            <s xml:id="echoid-s2376" xml:space="preserve">illa ab hac viciſſim.</s>
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