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

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        <div xml:id="echoid-div198" type="section" level="1" n="71">
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            <s xml:id="echoid-s2700" xml:space="preserve">
              <pb o="117" file="0173" n="189" rhead="HOROLOG. OSCILLATOR."/>
            rum quæ ex paraboloidibus naſcuntur conſtructionem, du-
              <lb/>
              <note position="right" xlink:label="note-0173-01" xlink:href="note-0173-01a" xml:space="preserve">
                <emph style="sc">De linea-</emph>
                <lb/>
                <emph style="sc">RUMCUR.</emph>
                <lb/>
                <emph style="sc">VARUM</emph>
                <lb/>
                <emph style="sc">EVOLUTIO-</emph>
                <lb/>
                <emph style="sc">NE.</emph>
              </note>
            cendæ ſunt lineæ D B Z, quæ ad datum punctum B ſecent
              <lb/>
            curvas A B, ſive ipſarum tangentes B H, ad angulos re-
              <lb/>
            ctos; </s>
            <s xml:id="echoid-s2701" xml:space="preserve">dicemus in univerſum quomodo hæ tangentes inve-
              <lb/>
            niantur. </s>
            <s xml:id="echoid-s2702" xml:space="preserve">In æquatione itaque, quæ cujusque curvæ naturam
              <lb/>
            explicat, quales æquationes duabus tabellis præcedentibus
              <lb/>
            exponuntur, conſiderare oportet quæ ſint exponentes pote-
              <lb/>
            ſtatum x & </s>
            <s xml:id="echoid-s2703" xml:space="preserve">y, & </s>
            <s xml:id="echoid-s2704" xml:space="preserve">facere ut, ſicut exponens poteſtatis x ad
              <lb/>
            exponentem poteſtatis y, ita ſit S K ad K H. </s>
            <s xml:id="echoid-s2705" xml:space="preserve">Juncta enim
              <lb/>
            H B curvam in B continget. </s>
            <s xml:id="echoid-s2706" xml:space="preserve">Velut in tertia hyperboloide,
              <lb/>
            cujus æquatio eſt x y
              <emph style="super">2</emph>
            = a
              <emph style="super">3</emph>
            : </s>
            <s xml:id="echoid-s2707" xml:space="preserve">quia exponens poteſtatis x eſt
              <lb/>
            1, poteſtatis autem y exponens 2; </s>
            <s xml:id="echoid-s2708" xml:space="preserve">oportet eſſe ut 1 ad 2 ita
              <lb/>
            S K ad K H. </s>
            <s xml:id="echoid-s2709" xml:space="preserve">Horum autem demonſtrationem noverunt
              <lb/>
            analyticæ artis periti, qui jam pridem omnes has lineas con-
              <lb/>
            templari cœperunt; </s>
            <s xml:id="echoid-s2710" xml:space="preserve">& </s>
            <s xml:id="echoid-s2711" xml:space="preserve">non ſolum paraboloidum iſtarum,
              <lb/>
            ſed & </s>
            <s xml:id="echoid-s2712" xml:space="preserve">ſpatiorum quorundam infinitorum, inter hyperboloi-
              <lb/>
            des & </s>
            <s xml:id="echoid-s2713" xml:space="preserve">aſymptotos interjectorum, plana ſolidaque dimenſi
              <lb/>
            ſunt. </s>
            <s xml:id="echoid-s2714" xml:space="preserve">Quod quidem & </s>
            <s xml:id="echoid-s2715" xml:space="preserve">nos, facili atque univerſali metho-
              <lb/>
            do, expedire poſſemus, ex ſola tangentium proprietate ſum-
              <lb/>
            pta demonſtratione. </s>
            <s xml:id="echoid-s2716" xml:space="preserve">Sed illa non ſunt hujus loci.</s>
            <s xml:id="echoid-s2717" xml:space="preserve"/>
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          <figure number="73">
            <image file="0173-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0173-01"/>
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        <div xml:id="echoid-div212" type="section" level="1" n="72">
          <head xml:id="echoid-head96" xml:space="preserve">HOROLOGII OSCILLATORII
            <lb/>
          PARS QUARTA.</head>
          <head xml:id="echoid-head97" style="it" xml:space="preserve">De centro Oſcillationis.</head>
          <p>
            <s xml:id="echoid-s2718" xml:space="preserve">CEntrorum Oſcillationis, ſeu Agitationis, inveſtigatio-
              <lb/>
            nem olim mihi, fere adhuc puero, aliiſque multis, do-
              <lb/>
            ctiſſimus Merſennus propoſuit, celebre admodum inter illius
              <lb/>
            temporis Geometras problema, prout ex litteris ejus ad me
              <lb/>
            datis colligo, nec non ex Carteſii haud pridem editis, qui-
              <lb/>
            bus ad Merſennianas ſuper his rebus reſponſum continetur.
              <lb/>
            </s>
            <s xml:id="echoid-s2719" xml:space="preserve">Poſtulabat autem centra illa ut invenirem in circuli </s>
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