Gravesande, Willem Jacob 's, An essay on perspective

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        <div xml:id="echoid-div120" type="section" level="1" n="66">
          <p>
            <s xml:id="echoid-s850" xml:space="preserve">
              <pb o="33" file="0065" n="72" rhead="on PERSPECTIVE."/>
            firſt found ; </s>
            <s xml:id="echoid-s851" xml:space="preserve">and then if Lines be drawn
              <note symbol="*" position="right" xlink:label="note-0065-01" xlink:href="note-0065-01a" xml:space="preserve">47.</note>
            the Repreſentation of the Vertex touching the
              <lb/>
            Repreſentation of the Baſe, the Repreſentation
              <lb/>
            of the Cone will be had.</s>
            <s xml:id="echoid-s852" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s853" xml:space="preserve">But ſince, according to this Manner, we are
              <lb/>
            obliged to find the Perſpective of all the Baſe;
              <lb/>
            </s>
            <s xml:id="echoid-s854" xml:space="preserve">whereas it often cannot be all ſeen; </s>
            <s xml:id="echoid-s855" xml:space="preserve">we may de-
              <lb/>
            termine, by the following Method, what Part
              <lb/>
            of the Baſe is viſible, and ſo only find the Re-
              <lb/>
            preſentation thereof. </s>
            <s xml:id="echoid-s856" xml:space="preserve">And then, to compleat
              <lb/>
            the Cone, we draw Lines from the Extremities
              <lb/>
            of the viſible Part of the Baſe, to the Repreſen-
              <lb/>
            tation of the Vertex.</s>
            <s xml:id="echoid-s857" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div123" type="section" level="1" n="67">
          <head xml:id="echoid-head72" style="it" xml:space="preserve">53. To determine the viſible Part of the Baſe of
            <lb/>
          a Cone.</head>
          <p>
            <s xml:id="echoid-s858" xml:space="preserve">Let the Circle L I F be the Baſe of a Cone
              <lb/>
              <note position="right" xlink:label="note-0065-02" xlink:href="note-0065-02a" xml:space="preserve">Fig. 21.</note>
            in the Geometrical Plane, and A the Center
              <lb/>
            thereof.</s>
            <s xml:id="echoid-s859" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div125" type="section" level="1" n="68">
          <head xml:id="echoid-head73" xml:space="preserve">
            <emph style="sc">Operation</emph>
          .</head>
          <p>
            <s xml:id="echoid-s860" xml:space="preserve">Aſſume P Q ſomewhere in the Baſe Line,
              <lb/>
            equal to the Semidiameter of the Circle L F;
              <lb/>
            </s>
            <s xml:id="echoid-s861" xml:space="preserve">and from the Point P, raiſe P D G perpendicu-
              <lb/>
            lar to the Baſe Line, meeting the Horizontal
              <lb/>
            Line in G; </s>
            <s xml:id="echoid-s862" xml:space="preserve">and in this Perpendicular, make
              <lb/>
            P D equal to the Height of the Cone; </s>
            <s xml:id="echoid-s863" xml:space="preserve">and draw
              <lb/>
            the Line Q D H, meeting the Horizontal Line
              <lb/>
            in H. </s>
            <s xml:id="echoid-s864" xml:space="preserve">Then, about the Point A as a Center,
              <lb/>
            and with the Radius G H, draw the Circle B C E; </s>
            <s xml:id="echoid-s865" xml:space="preserve">
              <lb/>
            and from the ſaid Point A, draw a Line to the
              <lb/>
            Station Point S: </s>
            <s xml:id="echoid-s866" xml:space="preserve">Biſect A S in R; </s>
            <s xml:id="echoid-s867" xml:space="preserve">and about
              <lb/>
            R, as a Center, with the Radius R A, deſcribe
              <lb/>
            the Circular Arc B A C, cutting the Circle BEC
              <lb/>
            in the Points B and C. </s>
            <s xml:id="echoid-s868" xml:space="preserve">Draw the Lines B A F,
              <lb/>
            and C A L; </s>
            <s xml:id="echoid-s869" xml:space="preserve">and the viſible Portion, (L I F) </s>
          </p>
        </div>
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    </echo>
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