Gravesande, Willem Jacob 's, An essay on perspective

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        <div xml:id="echoid-div113" type="section" level="1" n="62">
          <pb o="31" file="0063" n="70" rhead="on PERSPECTIVE."/>
        </div>
        <div xml:id="echoid-div115" type="section" level="1" n="63">
          <head xml:id="echoid-head66" xml:space="preserve">
            <emph style="sc">Prob</emph>
          . V.</head>
          <head xml:id="echoid-head67" style="it" xml:space="preserve">50. To find the Repreſentation of a Point, elevated
            <lb/>
          above the Geometrical Planc.</head>
          <p>
            <s xml:id="echoid-s807" xml:space="preserve">Let G S be the Geometrical Line, and S the
              <lb/>
              <note position="right" xlink:label="note-0063-01" xlink:href="note-0063-01a" xml:space="preserve">Fig. 18.</note>
            Station Point: </s>
            <s xml:id="echoid-s808" xml:space="preserve">Make S F, in the Geometrical
              <lb/>
            Line, equal to the Height of the Eye; </s>
            <s xml:id="echoid-s809" xml:space="preserve">and let
              <lb/>
            A be the Seat of the given Line.</s>
            <s xml:id="echoid-s810" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div117" type="section" level="1" n="64">
          <head xml:id="echoid-head68" xml:space="preserve">
            <emph style="sc">Operation</emph>
          .</head>
          <p>
            <s xml:id="echoid-s811" xml:space="preserve">Aſſume F C in the Geometrical Line, equal to
              <lb/>
            the Height of the Eye, above the Geometrical
              <lb/>
            Plane: </s>
            <s xml:id="echoid-s812" xml:space="preserve">Then draw Lines from the Point A to
              <lb/>
            the Points S and C, and on the Point B, the In-
              <lb/>
            terſection of the Line AS and the Baſe Line,
              <lb/>
            raiſe the Perpendicular BI to the Baſe Line,
              <lb/>
            equal to E B, plus FC; </s>
            <s xml:id="echoid-s813" xml:space="preserve">and the Point I will be
              <lb/>
            the Perſpective ſought.</s>
            <s xml:id="echoid-s814" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div118" type="section" level="1" n="65">
          <head xml:id="echoid-head69" xml:space="preserve">
            <emph style="sc">Demonstration</emph>
          .</head>
          <p>
            <s xml:id="echoid-s815" xml:space="preserve">51. </s>
            <s xml:id="echoid-s816" xml:space="preserve">Let us ſuppoſe a Plane to paſs thro’ the
              <lb/>
            given Point, and the Eye perpendicular to the
              <lb/>
            Geometrical Plane; </s>
            <s xml:id="echoid-s817" xml:space="preserve">then it is manifeſt, that the
              <lb/>
            Interſection of theſe two Planes is the Line
              <lb/>
            A B S, and the Interſection of the ſaid ſuppos’d
              <lb/>
            Plane and the perſpective Plane, is B I. </s>
            <s xml:id="echoid-s818" xml:space="preserve">Now,
              <lb/>
            let X be this ſuppos’d Plane; </s>
            <s xml:id="echoid-s819" xml:space="preserve">a, b, s, the Point
              <lb/>
              <note position="right" xlink:label="note-0063-02" xlink:href="note-0063-02a" xml:space="preserve">Fig. 19.</note>
            mark’d with the ſame Letters in the precedent
              <lb/>
            Figure, bi the Interſection of this Plane and
              <lb/>
            the perſpective Plane; </s>
            <s xml:id="echoid-s820" xml:space="preserve">O the Eye, and D the
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            propos’d Point: </s>
            <s xml:id="echoid-s821" xml:space="preserve">We are to prove, that if O D
              <lb/>
            be drawn, the Line B I of the precedent Figure
              <lb/>
            will be equal to b i in this Figure.</s>
            <s xml:id="echoid-s822" xml:space="preserve"/>
          </p>
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