Gravesande, Willem Jacob 's, An essay on perspective

Table of contents

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[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.
[111.] Problem I.
[112.] Example.
[113.] Problem II.
[114.] Operation.
[115.] Demonstration.
[116.] Proe. III.
[117.] Operation.
[118.] Demonstration.
[119.] Prob. IV.
[120.] CHAP. V.
[121.] Problem I.
[122.] Problem II.
[123.] Operation.
[124.] Demonstration.
[125.] Remark.
[126.] Problem III.
[127.] Method II.
[128.] Operation.
[129.] Demonstration.
[130.] Method III.
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              <pb o="52" file="0096" n="109" rhead="An ESSAY"/>
            viſible Portions of the ſaid Baſes. </s>
            <s xml:id="echoid-s1268" xml:space="preserve">Note, This
              <lb/>
            Method may be demonſtrated without Algebra,
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            but it would be very long.</s>
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        <div xml:id="echoid-div177" type="section" level="1" n="93">
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            <emph style="sc">Problem</emph>
          IX.</head>
          <p style="it">
            <s xml:id="echoid-s1270" xml:space="preserve">68. </s>
            <s xml:id="echoid-s1271" xml:space="preserve">To find the Accidental Point of ſeveral pa-
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            rallel Lines, which are inclin’d to the Geome-
              <lb/>
            trical Plane.</s>
            <s xml:id="echoid-s1272" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1273" xml:space="preserve">Let A B be the Direction of one of the Lines,
              <lb/>
              <note position="left" xlink:label="note-0096-01" xlink:href="note-0096-01a" xml:space="preserve">Fig. 36.</note>
            whoſe accidental Point is ſought; </s>
            <s xml:id="echoid-s1274" xml:space="preserve">and ECP, the
              <lb/>
            Angle that the ſaid Lines make with the Geo-
              <lb/>
            metrical Plane.</s>
            <s xml:id="echoid-s1275" xml:space="preserve"/>
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        <div xml:id="echoid-div179" type="section" level="1" n="94">
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            <emph style="sc">Operation</emph>
          .</head>
          <p>
            <s xml:id="echoid-s1276" xml:space="preserve">Draw a Line, O D, thro’ the Eye O, parallel
              <lb/>
            to A B, and thro’ the Point D, wherein it cuts
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            the Horizontal Line, and which is the acciden-
              <lb/>
            tal Point of the Directions of the given Lines,
              <lb/>
            draw D F perpendicular to the ſaid Horizontal
              <lb/>
            Line; </s>
            <s xml:id="echoid-s1277" xml:space="preserve">in which aſſume D G, equal to DO. </s>
            <s xml:id="echoid-s1278" xml:space="preserve">Fi-
              <lb/>
            nally, thro’ the Point G, draw the Line G F,
              <lb/>
            making an Angle with the Horizontal Line, equal
              <lb/>
            to E C P; </s>
            <s xml:id="echoid-s1279" xml:space="preserve">and then the Point F, (the Interſection
              <lb/>
            of this Line) and the Perpendicular D F, is the
              <lb/>
            accidental Point ſought.</s>
            <s xml:id="echoid-s1280" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1281" xml:space="preserve">Note, When the Lines are inclin’d towards
              <lb/>
            the perſpective Plane, D F and G F muſt be
              <lb/>
            drawn below the Horizontal Line: </s>
            <s xml:id="echoid-s1282" xml:space="preserve">And, contra-
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            riwiſe, when the ſaid Lines are inclin’d towards
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            the oppoſite Part of the perſpective Plane, the
              <lb/>
            aforeſaid Lines muſt be drawn above the ſaid
              <lb/>
            Horizontal Line, as is done here.</s>
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