Gravesande, Willem Jacob 's, An essay on perspective

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        <div xml:id="echoid-div161" type="section" level="1" n="87">
          <p>
            <s xml:id="echoid-s1158" xml:space="preserve">
              <pb o="46" file="0086" n="97" rhead="An ESSAY"/>
            G m T, biſects the Axis G E: </s>
            <s xml:id="echoid-s1159" xml:space="preserve">For if a Line be
              <lb/>
            drawn from T to E, it will be perpendicular to G T,
              <lb/>
            and conſequently parallel to m n: </s>
            <s xml:id="echoid-s1160" xml:space="preserve">Whence the con-
              <lb/>
            jugate Axis of the Curve G q E, is equal to the
              <lb/>
            conjugate Axis of the Ellipſis to be drawn: </s>
            <s xml:id="echoid-s1161" xml:space="preserve">And
              <lb/>
            therefore we are only to prove, that the Curve paſ-
              <lb/>
            ſing through the Points q, is an Ellipſis. </s>
            <s xml:id="echoid-s1162" xml:space="preserve">Which may
              <lb/>
            be ſbewnthus.</s>
            <s xml:id="echoid-s1163" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1164" xml:space="preserve">The Parts G n of the Line G T, are Propor-
              <lb/>
            tional to the Parts G p of the Line G E: </s>
            <s xml:id="echoid-s1165" xml:space="preserve">Whence
              <lb/>
            the Rectangles under G p and p E, are Proportional
              <lb/>
            to the Rectangles under G n and n T; </s>
            <s xml:id="echoid-s1166" xml:space="preserve">but theſe laſt
              <lb/>
            Rectangles are equal to the Squares of the Ordinates
              <lb/>
            n m, which Squares are equal to the Squares of the
              <lb/>
            Ordinates p q; </s>
            <s xml:id="echoid-s1167" xml:space="preserve">therefore theſe laſt Squares are Pro-
              <lb/>
            portional to the Rectangles under G p and p E, which
              <lb/>
            is a Property of the Ellipſis.</s>
            <s xml:id="echoid-s1168" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div162" type="section" level="1" n="88">
          <head xml:id="echoid-head94" xml:space="preserve">
            <emph style="sc">Definition</emph>
          .</head>
          <p>
            <s xml:id="echoid-s1169" xml:space="preserve">The ſemicircular Part h m of a Column, en-
              <lb/>
              <note position="left" xlink:label="note-0086-01" xlink:href="note-0086-01a" xml:space="preserve">Fig. 33.</note>
            compaſſing the ſame like a Ring, is called the
              <lb/>
            Torus.</s>
            <s xml:id="echoid-s1170" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div164" type="section" level="1" n="89">
          <head xml:id="echoid-head95" xml:space="preserve">
            <emph style="sc">Problem</emph>
          XI.</head>
          <p style="it">
            <s xml:id="echoid-s1171" xml:space="preserve">64. </s>
            <s xml:id="echoid-s1172" xml:space="preserve">To throw the Torus of a Column into Per-
              <lb/>
            ſpective.</s>
            <s xml:id="echoid-s1173" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1174" xml:space="preserve">Let B N C be the Baſe of the Column in the
              <lb/>
              <note position="left" xlink:label="note-0086-02" xlink:href="note-0086-02a" xml:space="preserve">Fig. 32.</note>
            Geometrical Plane; </s>
            <s xml:id="echoid-s1175" xml:space="preserve">draw a Line from the Cen-
              <lb/>
            ter A to the Station Point S, which biſect in the
              <lb/>
            Point R, and deſcribe the Arc of a Circle B A C
              <lb/>
            about the Point R, as a Center with the Radius R A.</s>
            <s xml:id="echoid-s1176" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1177" xml:space="preserve">Let X be the Profile of the Column, in which
              <lb/>
              <note position="left" xlink:label="note-0086-03" xlink:href="note-0086-03a" xml:space="preserve">Fig. 33.</note>
            draw the Line z 36, through the Center of the
              <lb/>
            ſemicircle h m, parallel to the Baſe of the Co-
              <lb/>
            lumn; </s>
            <s xml:id="echoid-s1178" xml:space="preserve">and in the Line s a, which goes through
              <lb/>
            the Center of the Column, parallel to its </s>
          </p>
        </div>
      </text>
    </echo>
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