Gravesande, Willem Jacob 's, An essay on perspective

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        <div xml:id="echoid-div118" type="section" level="1" n="65">
          <pb o="32" file="0064" n="71" rhead="An ESSAY"/>
          <p>
            <s xml:id="echoid-s823" xml:space="preserve">To demonſtrate which, draw the Line D L M
              <lb/>
            thro’ the Point D, parallel to a b s. </s>
            <s xml:id="echoid-s824" xml:space="preserve">Then, be-
              <lb/>
            cauſe the Triangles D M O and D L i are ſimi-
              <lb/>
            lar, we have,</s>
          </p>
          <p>
            <s xml:id="echoid-s825" xml:space="preserve">D M = as: </s>
            <s xml:id="echoid-s826" xml:space="preserve">D L = ab:</s>
            <s xml:id="echoid-s827" xml:space="preserve">: M O: </s>
            <s xml:id="echoid-s828" xml:space="preserve">L i. </s>
            <s xml:id="echoid-s829" xml:space="preserve">Again,
              <lb/>
            in the precedent Figure, the Triangles A S C and
              <lb/>
            A B E are ſimilar: </s>
            <s xml:id="echoid-s830" xml:space="preserve">Whence,
              <lb/>
            A S: </s>
            <s xml:id="echoid-s831" xml:space="preserve">A B:</s>
            <s xml:id="echoid-s832" xml:space="preserve">: C S: </s>
            <s xml:id="echoid-s833" xml:space="preserve">E B.</s>
            <s xml:id="echoid-s834" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s835" xml:space="preserve">The three firſt Terms of theſe two Progreſſions
              <lb/>
            are the ſame: </s>
            <s xml:id="echoid-s836" xml:space="preserve">For CS is equal to M O, ſince
              <lb/>
            they are each the Difference of the Height of the
              <lb/>
            Eye, and that of the given Point; </s>
            <s xml:id="echoid-s837" xml:space="preserve">and conſe-
              <lb/>
            quently, E B is equal to L i: </s>
            <s xml:id="echoid-s838" xml:space="preserve">But B I was made
              <lb/>
            equal to B E, pl{us} FC the Height of the given
              <lb/>
            Point above the Geometrical Plane; </s>
            <s xml:id="echoid-s839" xml:space="preserve">and b i is
              <lb/>
            equal to Li, pl{us} b L; </s>
            <s xml:id="echoid-s840" xml:space="preserve">which being equal to aD,
              <lb/>
            is likewiſe the Height of the given Point above
              <lb/>
            the Geometrical Plane; </s>
            <s xml:id="echoid-s841" xml:space="preserve">whence the Lines B I
              <lb/>
            and b i are equal. </s>
            <s xml:id="echoid-s842" xml:space="preserve">Which was to be demon-
              <lb/>
            ſtrated.</s>
            <s xml:id="echoid-s843" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s844" xml:space="preserve">Note, When the Height of the given Point is
              <lb/>
            greater than the Height of the Eye, E B muſt
              <lb/>
            be taken from that firſt Height, to have the
              <lb/>
            Magnitude of B I.</s>
            <s xml:id="echoid-s845" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div120" type="section" level="1" n="66">
          <head xml:id="echoid-head70" xml:space="preserve">
            <emph style="sc">Prob</emph>
          . VI.</head>
          <head xml:id="echoid-head71" style="it" xml:space="preserve">52. To throm a Pyramid, or Cone, into Perſpective.</head>
          <p>
            <s xml:id="echoid-s846" xml:space="preserve">Now, to throw a Pyramid into perſpective,
              <lb/>
              <note position="left" xlink:label="note-0064-01" xlink:href="note-0064-01a" xml:space="preserve">Fig. 20.</note>
            the Appearance of its Baſe and Center muſt
              <note symbol="*" position="left" xlink:label="note-0064-02" xlink:href="note-0064-02a" xml:space="preserve">46.</note>
            found : </s>
            <s xml:id="echoid-s847" xml:space="preserve">After which, Lines muſt be drawn
              <note symbol="*" position="left" xlink:label="note-0064-03" xlink:href="note-0064-03a" xml:space="preserve">50.</note>
            the Repreſentation of the Vertex, to the Ap-
              <lb/>
            pearance of thoſe Angles of the Baſe that are
              <lb/>
            viſible; </s>
            <s xml:id="echoid-s848" xml:space="preserve">and then the Perſpective ſought will be
              <lb/>
            had.</s>
            <s xml:id="echoid-s849" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s850" xml:space="preserve">And to throw a Cone into perſpective, the
              <lb/>
              <note position="left" xlink:label="note-0064-04" xlink:href="note-0064-04a" xml:space="preserve">Fig. 21.</note>
            Repreſentation of its Baſe and Vertex muſt
              <note symbol="*" position="left" xlink:label="note-0064-05" xlink:href="note-0064-05a" xml:space="preserve">46.</note>
            </s>
          </p>
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