Gravesande, Willem Jacob 's, An essay on perspective

Table of contents

< >
[81.] Problem VIII.
[82.] To do this another Way.
[83.] Demonstration.
[84.] Problem IX.
[85.] Problem X.
[86.] Demonstration.
[87.] EG: EN:: GY: NM.
[88.] Definition.
[89.] Problem XI.
[90.] Lemma.
[91.] Demonstration.
[92.] Remarks.
[93.] Problem IX.
[94.] Operation.
[95.] Demonstration.
[96.] Problem X.
[97.] Operation.
[98.] Demonstration.
[99.] Remarks.
[100.] Method II. 70. By the accidental Point of inclin’d Lines.
[101.] Operation.
[102.] Demonstration.
[103.] Method. III.
[104.] Operation.
[105.] Method IV.
[106.] Prob. XIV.
[107.] Example I.
[108.] Example II.
[109.] Conclusion.
[110.] CHAP. IV.
< >
page |< < (81) of 237 > >|
    <echo version="1.0RC">
      <text xml:lang="en" type="free">
        <div xml:id="echoid-div294" type="section" level="1" n="158">
          <p>
            <s xml:id="echoid-s1889" xml:space="preserve">
              <pb o="81" file="0143" n="165" rhead="on PERSPECTIVE."/>
            the given Lines; </s>
            <s xml:id="echoid-s1890" xml:space="preserve">and conſequently L, or
              <note symbol="*" position="right" xlink:label="note-0143-01" xlink:href="note-0143-01a" xml:space="preserve">13, 14.</note>
            will be the Accidental Point ſought.</s>
            <s xml:id="echoid-s1891" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div296" type="section" level="1" n="159">
          <head xml:id="echoid-head165" xml:space="preserve">
            <emph style="sc">Prob</emph>
          . IV.</head>
          <p style="it">
            <s xml:id="echoid-s1892" xml:space="preserve">99. </s>
            <s xml:id="echoid-s1893" xml:space="preserve">To find the Repreſentation of one or more
              <lb/>
            Lines inclined to the Geometrical Plane.</s>
            <s xml:id="echoid-s1894" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1895" xml:space="preserve">Let a b be the Perſpective of the Direction of
              <lb/>
              <note position="right" xlink:label="note-0143-02" xlink:href="note-0143-02a" xml:space="preserve">Fig. 56.</note>
            the given Line: </s>
            <s xml:id="echoid-s1896" xml:space="preserve">Now the Length of its Directi-
              <lb/>
            on may be determin’d, by means of the Tri-
              <lb/>
            angle ECP, according to the Directions of n. </s>
            <s xml:id="echoid-s1897" xml:space="preserve">69.
              <lb/>
            </s>
            <s xml:id="echoid-s1898" xml:space="preserve">This being done, the Line b X muſt be drawn
              <lb/>
            through the Point b, equal to E P, and this re-
              <lb/>
            preſents a Perpendicular to the Geometrical
              <lb/>
            Plane; </s>
            <s xml:id="echoid-s1899" xml:space="preserve">then a X being drawn, will be the Re-
              <lb/>
            preſentation ſought.</s>
            <s xml:id="echoid-s1900" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div298" type="section" level="1" n="160">
          <head xml:id="echoid-head166" xml:space="preserve">
            <emph style="sc">Method</emph>
          II.</head>
          <p style="it">
            <s xml:id="echoid-s1901" xml:space="preserve">100. </s>
            <s xml:id="echoid-s1902" xml:space="preserve">To ſolve the ſame Problem by means of the
              <lb/>
            accidental Points F and T, the one being that of the
              <lb/>
            Lines propoſed; </s>
            <s xml:id="echoid-s1903" xml:space="preserve">and the other, that of the Perpen-
              <lb/>
              <note position="right" xlink:label="note-0143-03" xlink:href="note-0143-03a" xml:space="preserve">Fig. 56.</note>
            diculars to the Geometrical Plane.</s>
            <s xml:id="echoid-s1904" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div300" type="section" level="1" n="161">
          <head xml:id="echoid-head167" xml:space="preserve">
            <emph style="sc">Operation</emph>
          .</head>
          <p>
            <s xml:id="echoid-s1905" xml:space="preserve">Draw a Line from the Point F through the
              <lb/>
            Point a, which interſect in the Point X, by ano-
              <lb/>
            ther Line drawn from the Point T through b:
              <lb/>
            </s>
            <s xml:id="echoid-s1906" xml:space="preserve">and then a X will be the Perſpective ſought.</s>
            <s xml:id="echoid-s1907" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div301" type="section" level="1" n="162">
          <head xml:id="echoid-head168" xml:space="preserve">
            <emph style="sc">Method</emph>
          III.</head>
          <p>
            <s xml:id="echoid-s1908" xml:space="preserve">101. </s>
            <s xml:id="echoid-s1909" xml:space="preserve">The ſame Things being given as in the
              <lb/>
              <note position="right" xlink:label="note-0143-04" xlink:href="note-0143-04a" xml:space="preserve">Fig. 101.</note>
            aforegoing Method, draw a I through the Point
              <lb/>
            a, equal to E P, repreſenting a Line perpendicu-
              <lb/>
            lar to the Geometrical Plane. </s>
            <s xml:id="echoid-s1910" xml:space="preserve">Then draw a pa-
              <lb/>
            rallel to F T through the Point I, whoſe </s>
          </p>
        </div>
      </text>
    </echo>