Gravesande, Willem Jacob 's, An essay on perspective

Table of Notes

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              <pb o="63" file="0115" n="132" rhead="on PERSPECTIVE."/>
            been drawn from the Baſe Line, equal to a fifth
              <lb/>
            Part of the Eye’s Diſtance, and ſo on. </s>
            <s xml:id="echoid-s1492" xml:space="preserve">Now
              <lb/>
            A is a Point whoſe Repreſentation is requir’d.</s>
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        <div xml:id="echoid-div223" type="section" level="1" n="117">
          <head xml:id="echoid-head123" xml:space="preserve">
            <emph style="sc">Operation</emph>
          .</head>
          <p>
            <s xml:id="echoid-s1494" xml:space="preserve">Draw the Lines A F and A P, from the Point
              <lb/>
            A to the Points F and P, cutting the Baſe Line
              <lb/>
            in the Points E and B; </s>
            <s xml:id="echoid-s1495" xml:space="preserve">then draw the Lines E G
              <lb/>
            and B Q, which continue till they interſect
              <lb/>
            each other in a, which is the Repreſentation
              <lb/>
            ſought.</s>
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        <div xml:id="echoid-div224" type="section" level="1" n="118">
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            <emph style="sc">Demonstration</emph>
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          <p>
            <s xml:id="echoid-s1497" xml:space="preserve">Let us ſuppoſe the perſpective Plane continu-
              <lb/>
            ed, C D the Horizontal Line, and O the Eye
              <lb/>
            denoted in the Horizontal Plane. </s>
            <s xml:id="echoid-s1498" xml:space="preserve">It is evi-
              <lb/>
            dent by Conſtruction, that the Line G F
              <note symbol="*" position="right" xlink:label="note-0115-01" xlink:href="note-0115-01a" xml:space="preserve">77.</note>
            tinued, paſſes through the Eye O; </s>
            <s xml:id="echoid-s1499" xml:space="preserve">produce the
              <lb/>
            Line G S a, until it meets the Horizontal Line
              <lb/>
            in D, and draw the Line O D. </s>
            <s xml:id="echoid-s1500" xml:space="preserve">Let fall the
              <lb/>
            Perpendicular G N R, from the Point G upon
              <lb/>
            the Horizontal Line, which interſect in R, by
              <lb/>
            the Line O R, paſſing through the Eye parallel
              <lb/>
            to the Horizontal Line. </s>
            <s xml:id="echoid-s1501" xml:space="preserve">Now by Conſtruction,
              <lb/>
            G M is {1/3} of M N; </s>
            <s xml:id="echoid-s1502" xml:space="preserve">and conſequently it is {1/4} of
              <lb/>
            G N; </s>
            <s xml:id="echoid-s1503" xml:space="preserve">M Z is likewiſe {1/4} of N R: </s>
            <s xml:id="echoid-s1504" xml:space="preserve">Therefore</s>
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            <s xml:id="echoid-s1505" xml:space="preserve">G M: </s>
            <s xml:id="echoid-s1506" xml:space="preserve">M Z:</s>
            <s xml:id="echoid-s1507" xml:space="preserve">: G N: </s>
            <s xml:id="echoid-s1508" xml:space="preserve">N R.</s>
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            <s xml:id="echoid-s1510" xml:space="preserve">Compon. </s>
            <s xml:id="echoid-s1511" xml:space="preserve">and Altern.</s>
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            <s xml:id="echoid-s1513" xml:space="preserve">G M: </s>
            <s xml:id="echoid-s1514" xml:space="preserve">G N:</s>
            <s xml:id="echoid-s1515" xml:space="preserve">: G M + M Z = G Z: </s>
            <s xml:id="echoid-s1516" xml:space="preserve">G N
              <lb/>
            + N R = G R.</s>
            <s xml:id="echoid-s1517" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1518" xml:space="preserve">Becauſe the Triangles G M I and G N C are
              <lb/>
            ſimilar, we have</s>
          </p>
          <p style="it">
            <s xml:id="echoid-s1519" xml:space="preserve">G M: </s>
            <s xml:id="echoid-s1520" xml:space="preserve">G N:</s>
            <s xml:id="echoid-s1521" xml:space="preserve">: G I: </s>
            <s xml:id="echoid-s1522" xml:space="preserve">G C.</s>
            <s xml:id="echoid-s1523" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s1524" xml:space="preserve">The Triangles G Z F and G R O being alſo
              <lb/>
            ſimilar,</s>
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            <s xml:id="echoid-s1525" xml:space="preserve">G Z: </s>
            <s xml:id="echoid-s1526" xml:space="preserve">G R:</s>
            <s xml:id="echoid-s1527" xml:space="preserve">: G F: </s>
            <s xml:id="echoid-s1528" xml:space="preserve">G O.</s>
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Impressum