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">
          <p>
            <s xml:id="echoid-s2653" xml:space="preserve">
              <pb o="115" file="0171" n="187" rhead="HOROLOG. OSCILLATOR."/>
            rum curvarum, hoc eſt, ſicut punctum D modo inventum
              <lb/>
              <note position="right" xlink:label="note-0171-01" xlink:href="note-0171-01a" 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>
            fuit.</s>
            <s xml:id="echoid-s2654" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2655" xml:space="preserve">Denique, quæcunque fuerit ex paraboloidum genere cur-
              <lb/>
            va S A B, ſemper æque facile curvam aliam, cujus evolu-
              <lb/>
            tione ipſa deſcribatur, quæque propterea rectæ adæquari
              <lb/>
            poſſit, per puncta inveniri comperimus. </s>
            <s xml:id="echoid-s2656" xml:space="preserve">Atque adeo con-
              <lb/>
            ſtructionem univerſalem ſequenti tabella exhibemus; </s>
            <s xml:id="echoid-s2657" xml:space="preserve">quæ
              <lb/>
            quousque libuerit extendi poterit.</s>
            <s xml:id="echoid-s2658" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">
            <lb/>
          # a x = y
            <emph style="super">2</emph>
          # # B M + 2 B Z
            <lb/>
          # a
            <emph style="super">2</emph>
          x = y
            <emph style="super">3</emph>
          # # {1/2} B M + {3/2} B Z
            <lb/>
          Si # a x
            <emph style="super">2</emph>
          = y
            <emph style="super">3</emph>
          # Erit # 2 B M + 3 B Z # = # B D.
            <lb/>
          # a x
            <emph style="super">3</emph>
          = y
            <emph style="super">4</emph>
          # # 3 B M + 4 B Z
            <lb/>
          # a
            <emph style="super">3</emph>
          x = y
            <emph style="super">4</emph>
          # # {1/3} B M + {4/3} B Z
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s2659" xml:space="preserve">Sit S B parabola, vel paraboloidum aliqua, cujus vertex
              <lb/>
              <note position="right" xlink:label="note-0171-03" xlink:href="note-0171-03a" xml:space="preserve">TAB XVII.
                <lb/>
              Fig. 2.</note>
            S; </s>
            <s xml:id="echoid-s2660" xml:space="preserve">recta S K vel axis, vel axi perpendicularis, ad quam re-
              <lb/>
            feruntur æquatione puncta paraboloidis; </s>
            <s xml:id="echoid-s2661" xml:space="preserve">& </s>
            <s xml:id="echoid-s2662" xml:space="preserve">ipſa quidem S K
              <lb/>
            ſemper ad partem cavam ducta intelligitur; </s>
            <s xml:id="echoid-s2663" xml:space="preserve">cui perpendicu-
              <lb/>
            laris S Z. </s>
            <s xml:id="echoid-s2664" xml:space="preserve">Ponendo jam S K = x; </s>
            <s xml:id="echoid-s2665" xml:space="preserve">B K = y, quæ à pun-
              <lb/>
            cto quovis curvæ perpendicularis eſt ipſi S K; </s>
            <s xml:id="echoid-s2666" xml:space="preserve">& </s>
            <s xml:id="echoid-s2667" xml:space="preserve">latere re-
              <lb/>
            cto curvæ = a; </s>
            <s xml:id="echoid-s2668" xml:space="preserve">prior pars tabellæ, quæ ad ſiniſtram eſt,
              <lb/>
            naturam ſingularum paraboloidum ſingulis æquationibus ex-
              <lb/>
            plicat. </s>
            <s xml:id="echoid-s2669" xml:space="preserve">Quibus reſpondent in parte dextra quantitates lineæ
              <lb/>
            B D, quæ ſi curvæ S B inſiſtat ad angulos rectos, exhibi-
              <lb/>
            tura ſit punctum D in curva quæſita C D. </s>
            <s xml:id="echoid-s2670" xml:space="preserve">Exempli gratia,
              <lb/>
            ſi S B eſt parabola quæ ex coni ſectione fit, ei ſcimus con-
              <lb/>
            venire æquationem tabellæ primam, a x = y
              <emph style="super">2</emph>
            ; </s>
            <s xml:id="echoid-s2671" xml:space="preserve">cui reſpon-
              <lb/>
            det ab altera parte B M + 2 B Z = B D. </s>
            <s xml:id="echoid-s2672" xml:space="preserve">Unde longitudo
              <lb/>
            lineæ B D cognoſcitur, adeoque inventio quotlibet puncto-
              <lb/>
            rum curvæ C D. </s>
            <s xml:id="echoid-s2673" xml:space="preserve">Quam quidem, hoc caſu, paraboloidem
              <lb/>
            eſſe ſupra demonſtratum fuit, eam nempe, cujus æquatio
              <lb/>
            tertia eſt hujus tabellæ.</s>
            <s xml:id="echoid-s2674" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2675" xml:space="preserve">Conſtruitur autem tabella hoc pacto, ut B M ſumatur
              <lb/>
            multiplex ſecundum numerum qui eſt exponens poteſtatis x
              <lb/>
            in æquatione; </s>
            <s xml:id="echoid-s2676" xml:space="preserve">B Z vero, multiplex ſecundum exponentem
              <lb/>
            poteſtatis y; </s>
            <s xml:id="echoid-s2677" xml:space="preserve">ex his autem utrisque compoſitæ accipiatur
              <lb/>
            pars denominata ab exponente poteſtatis a.</s>
            <s xml:id="echoid-s2678" xml:space="preserve"/>
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