Gravesande, Willem Jacob 's, An essay on perspective

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        <div xml:id="echoid-div136" type="section" level="1" n="75">
          <p>
            <s xml:id="echoid-s957" xml:space="preserve">
              <pb o="38" file="0076" n="86" rhead="An ESSAY"/>
            there; </s>
            <s xml:id="echoid-s958" xml:space="preserve">and finally e A here, E A in that Fi-
              <lb/>
            gure.</s>
            <s xml:id="echoid-s959" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s960" xml:space="preserve">This being ſuppoſed, o f is parallel to e
              <note symbol="*" position="left" xlink:label="note-0076-01" xlink:href="note-0076-01a" xml:space="preserve">27.</note>
            and conſequently the Triangle o f a is ſimilar
              <lb/>
            to the Triangle a e A, and therefore we have this
              <lb/>
            Proportion.</s>
            <s xml:id="echoid-s961" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s962" xml:space="preserve">o f: </s>
            <s xml:id="echoid-s963" xml:space="preserve">f a:</s>
            <s xml:id="echoid-s964" xml:space="preserve">: A e: </s>
            <s xml:id="echoid-s965" xml:space="preserve">e o.
              <lb/>
            </s>
            <s xml:id="echoid-s966" xml:space="preserve">Comp.</s>
            <s xml:id="echoid-s967" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s968" xml:space="preserve">o f + a f: </s>
            <s xml:id="echoid-s969" xml:space="preserve">f a:</s>
            <s xml:id="echoid-s970" xml:space="preserve">: A e + e a: </s>
            <s xml:id="echoid-s971" xml:space="preserve">e a.
              <lb/>
            </s>
            <s xml:id="echoid-s972" xml:space="preserve">Altern.</s>
            <s xml:id="echoid-s973" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s974" xml:space="preserve">o f + a f: </s>
            <s xml:id="echoid-s975" xml:space="preserve">A e + e a:</s>
            <s xml:id="echoid-s976" xml:space="preserve">: f a: </s>
            <s xml:id="echoid-s977" xml:space="preserve">e a.
              <lb/>
            </s>
            <s xml:id="echoid-s978" xml:space="preserve">Comp. </s>
            <s xml:id="echoid-s979" xml:space="preserve">and Perm.</s>
            <s xml:id="echoid-s980" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s981" xml:space="preserve">o f + f a + Ae + e a : </s>
            <s xml:id="echoid-s982" xml:space="preserve">o f + f a :</s>
            <s xml:id="echoid-s983" xml:space="preserve">: f a + e a : </s>
            <s xml:id="echoid-s984" xml:space="preserve">f a.</s>
            <s xml:id="echoid-s985" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s986" xml:space="preserve">This laſt Proportion being reduced to the pre-
              <lb/>
            cedent Figure, we ſhall have this,</s>
          </p>
          <p style="it">
            <s xml:id="echoid-s987" xml:space="preserve">O A : </s>
            <s xml:id="echoid-s988" xml:space="preserve">o a : </s>
            <s xml:id="echoid-s989" xml:space="preserve">: </s>
            <s xml:id="echoid-s990" xml:space="preserve">F D : </s>
            <s xml:id="echoid-s991" xml:space="preserve">F a.</s>
            <s xml:id="echoid-s992" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s993" xml:space="preserve">Again, becauſe the Triangles O A L and O a G
              <lb/>
            are ſimilar, we ſhall have</s>
          </p>
          <p style="it">
            <s xml:id="echoid-s994" xml:space="preserve">O A: </s>
            <s xml:id="echoid-s995" xml:space="preserve">O a : </s>
            <s xml:id="echoid-s996" xml:space="preserve">: </s>
            <s xml:id="echoid-s997" xml:space="preserve">A L : </s>
            <s xml:id="echoid-s998" xml:space="preserve">a G.</s>
            <s xml:id="echoid-s999" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1000" xml:space="preserve">And ſince the Triangle F E D and F a H are
              <lb/>
            ſimilar;</s>
            <s xml:id="echoid-s1001" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1002" xml:space="preserve">F E : </s>
            <s xml:id="echoid-s1003" xml:space="preserve">F a : </s>
            <s xml:id="echoid-s1004" xml:space="preserve">: </s>
            <s xml:id="echoid-s1005" xml:space="preserve">D E : </s>
            <s xml:id="echoid-s1006" xml:space="preserve">H a.</s>
            <s xml:id="echoid-s1007" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1008" xml:space="preserve">And ſo if theſe three laſt Propoſitions be con-
              <lb/>
            ſider’d, we ſhall have</s>
          </p>
          <p style="it">
            <s xml:id="echoid-s1009" xml:space="preserve">A L : </s>
            <s xml:id="echoid-s1010" xml:space="preserve">a G : </s>
            <s xml:id="echoid-s1011" xml:space="preserve">: </s>
            <s xml:id="echoid-s1012" xml:space="preserve">D E : </s>
            <s xml:id="echoid-s1013" xml:space="preserve">H a.</s>
            <s xml:id="echoid-s1014" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1015" xml:space="preserve">But D E was made equal to A L, and there-
              <lb/>
            fore a G or a I is alſo equal to a H, which is
              <note symbol="*" position="left" xlink:label="note-0076-02" xlink:href="note-0076-02a" xml:space="preserve">56.</note>
            qual to the Repreſentation ſought. </s>
            <s xml:id="echoid-s1016" xml:space="preserve">Which was
              <lb/>
            to be demonſtrated.</s>
            <s xml:id="echoid-s1017" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div140" type="section" level="1" n="76">
          <head xml:id="echoid-head82" xml:space="preserve">
            <emph style="sc">Method</emph>
          III.</head>
          <p>
            <s xml:id="echoid-s1018" xml:space="preserve">58. </s>
            <s xml:id="echoid-s1019" xml:space="preserve">Near one of the Sides of the perſpective
              <lb/>
              <note position="left" xlink:label="note-0076-03" xlink:href="note-0076-03a" xml:space="preserve">Fig. 25.</note>
            Plane, raiſe the Perpendicular C B to the Baſe
              <lb/>
            Line, equal to the Height of the Eye, in which
              <lb/>
            take B L equal in length to twice the Perpen-
              <lb/>
            dicular, whoſe Perſpective is requir’d. </s>
            <s xml:id="echoid-s1020" xml:space="preserve">Let S </s>
          </p>
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    </echo>
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