Gravesande, Willem Jacob 's, An essay on perspective

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        <div xml:id="echoid-div289" type="section" level="1" n="154">
          <p>
            <s xml:id="echoid-s1867" xml:space="preserve">
              <pb o="80" file="0142" n="164" rhead="An ESSAY"/>
            to the Length of the ſaid Perpendiculars: </s>
            <s xml:id="echoid-s1868" xml:space="preserve">And
              <lb/>
            therefore</s>
          </p>
        </div>
        <div xml:id="echoid-div290" type="section" level="1" n="155">
          <head xml:id="echoid-head161" xml:space="preserve">H I: T H:: a X: a T.</head>
          <p>
            <s xml:id="echoid-s1869" xml:space="preserve">But in the Conſtruction of this Problem, be-
              <lb/>
            cauſe the Triangles T C D and T H G, are
              <lb/>
            ſimilar;</s>
            <s xml:id="echoid-s1870" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1871" xml:space="preserve">H G = H I: </s>
            <s xml:id="echoid-s1872" xml:space="preserve">T H:</s>
            <s xml:id="echoid-s1873" xml:space="preserve">: C D = a X: </s>
            <s xml:id="echoid-s1874" xml:space="preserve">T D = a T;
              <lb/>
            </s>
            <s xml:id="echoid-s1875" xml:space="preserve">and conſequently H I and a X, repreſent Perpen-
              <lb/>
            diculars of the ſame Length. </s>
            <s xml:id="echoid-s1876" xml:space="preserve">Which was to be
              <lb/>
            demonſtrated.</s>
            <s xml:id="echoid-s1877" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div291" type="section" level="1" n="156">
          <head xml:id="echoid-head162" xml:space="preserve">
            <emph style="sc">Prob</emph>
          . III.</head>
          <p style="it">
            <s xml:id="echoid-s1878" xml:space="preserve">98. </s>
            <s xml:id="echoid-s1879" xml:space="preserve">To find the accidental Point of any Number
              <lb/>
            of parallel Lines inclined to the Geometrical Plane.</s>
            <s xml:id="echoid-s1880" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1881" xml:space="preserve">Let a b be the Perſpective of the Direction
              <lb/>
              <note position="left" xlink:label="note-0142-01" xlink:href="note-0142-01a" xml:space="preserve">Fig. 55.</note>
            of one of the given Lines.</s>
            <s xml:id="echoid-s1882" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div293" type="section" level="1" n="157">
          <head xml:id="echoid-head163" xml:space="preserve">
            <emph style="sc">Operation</emph>
          .</head>
          <p>
            <s xml:id="echoid-s1883" xml:space="preserve">Draw the Line F T L, parallel to a b, through
              <lb/>
            the accidental Point T of the Lines perpendicu-
              <lb/>
            lar to the Geometrical Plane; </s>
            <s xml:id="echoid-s1884" xml:space="preserve">and at the Point
              <lb/>
            T, raiſe the Perpendicular T G, which make e-
              <lb/>
            qual to the Diſtance of the Eye from the per-
              <lb/>
            ſpective Plane; </s>
            <s xml:id="echoid-s1885" xml:space="preserve">then draw the Line G L, or
              <lb/>
            G F, ſo that the Angle T L G, or T F G, be e-
              <lb/>
            qual to the Angle of the Inclination of the given
              <lb/>
            Lines; </s>
            <s xml:id="echoid-s1886" xml:space="preserve">and the Point L, will be the Accidental
              <lb/>
            Point ſought, if the given Lines incline to-
              <lb/>
            wards b; </s>
            <s xml:id="echoid-s1887" xml:space="preserve">but if they incline towards a, F will
              <lb/>
            be the Accidental Point.</s>
            <s xml:id="echoid-s1888" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div294" type="section" level="1" n="158">
          <head xml:id="echoid-head164" xml:space="preserve">
            <emph style="sc">Demonstration</emph>
          .</head>
          <p>
            <s xml:id="echoid-s1889" xml:space="preserve">It is manifeſt by Conſtruction, that if T G be
              <lb/>
            ſuppoſed to be raiſed perpendicularly to the Geo-
              <lb/>
            metrical Plane, G L or G F, will be parallel </s>
          </p>
        </div>
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    </echo>
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