Gravesande, Willem Jacob 's, An essay on perspective

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        <div xml:id="echoid-div179" type="section" level="1" n="94">
          <pb o="53" file="0099" n="113" rhead="on PERSPECTIVE."/>
        </div>
        <div xml:id="echoid-div180" type="section" level="1" n="95">
          <head xml:id="echoid-head101" xml:space="preserve">
            <emph style="sc">Demonstration</emph>
          .</head>
          <p>
            <s xml:id="echoid-s1284" xml:space="preserve">If a Plane be conceiv’d to paſs thro’ the Eye,
              <lb/>
            perpendicular to the Geometrical Plane, and paral-
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            lel to the given Lines; </s>
            <s xml:id="echoid-s1285" xml:space="preserve">it is evident, that the ſaid
              <lb/>
            Plane will cut the Horizontal Plane in the Line
              <lb/>
            O D, and the perſpective Plane in D F. </s>
            <s xml:id="echoid-s1286" xml:space="preserve">It is,
              <lb/>
            moreover, manifeſt, that a Line drawn thro’ the
              <lb/>
            Eye, parallel to the given Line, is in the ſaid
              <lb/>
            Plane, and (with the Line O D) makes an An-
              <lb/>
            gle, equal to the Angle E C P, below the Hori-
              <lb/>
            zontal Plane, if the Lines be inclin’d towards
              <lb/>
            the perſpective Plane, and above it, if they in-
              <lb/>
            cline to the oppoſite ſide; </s>
            <s xml:id="echoid-s1287" xml:space="preserve">whence this laſt Line
              <lb/>
            makes a right-angled Triangle with O D and
              <lb/>
            D F, whoſe Angle at the Point O, is equal to
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            the Angle C E P. </s>
            <s xml:id="echoid-s1288" xml:space="preserve">But D G F is likewiſe a
              <lb/>
            right-angled Triangle, as having the Angle at the
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            Point G, equal to ECP; </s>
            <s xml:id="echoid-s1289" xml:space="preserve">therefore theſe two
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            Triangles are ſimilar. </s>
            <s xml:id="echoid-s1290" xml:space="preserve">And ſince the Side D G
              <lb/>
            is equal to the Side D O, the Triangles are alſo
              <lb/>
            equal: </s>
            <s xml:id="echoid-s1291" xml:space="preserve">Therefore the Line D F, being common
              <lb/>
            to theſe two Triangles; </s>
            <s xml:id="echoid-s1292" xml:space="preserve">the Point F, is the
              <lb/>
            Point wherein the Line, paſſing thro’ the Eye
              <lb/>
            parallel to the given Line, meets the Per-
              <lb/>
            ſpective Plane: </s>
            <s xml:id="echoid-s1293" xml:space="preserve">And this Point is the acciden- tal one ſought.</s>
            <s xml:id="echoid-s1294" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1295" xml:space="preserve">Note, This Demonſtration as well regards
              <lb/>
              <note symbol="*" position="right" xlink:label="note-0099-01" xlink:href="note-0099-01a" xml:space="preserve">13, 14.</note>
            inclin’d Lines entirely ſeparate from the Geo-
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            metrical Plane, as thoſe that meet it in one of
              <lb/>
            their Extremes only.</s>
            <s xml:id="echoid-s1296" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div182" type="section" level="1" n="96">
          <head xml:id="echoid-head102" xml:space="preserve">
            <emph style="sc">Problem</emph>
          X.</head>
          <p style="it">
            <s xml:id="echoid-s1297" xml:space="preserve">69. </s>
            <s xml:id="echoid-s1298" xml:space="preserve">To find the Repreſentation of one or more
              <lb/>
            Lines, inclin’d to the Geometrical Plane.
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            </s>
            <s xml:id="echoid-s1299" xml:space="preserve">
              <note position="right" xlink:label="note-0099-02" xlink:href="note-0099-02a" xml:space="preserve">Fig. 36.</note>
            </s>
          </p>
          <p>
            <s xml:id="echoid-s1300" xml:space="preserve">Let A be a Point given in the Geometrical
              <lb/>
            Plane; </s>
            <s xml:id="echoid-s1301" xml:space="preserve">whereon ſtands a Line, whoſe Length,
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            Direction, and Angle of Inclination is known.</s>
            <s xml:id="echoid-s1302" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
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