Gravesande, Willem Jacob 's, An essay on perspective

Table of contents

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[11.] Corollary I.
[12.] Corollary II.
[13.] Corollary III.
[14.] Theorem II.
[15.] Corollary I.
[16.] Corollary II.
[17.] Theorem III.
[18.] Theorem IV.
[19.] Corollary I.
[20.] Corollary II.
[21.] Corollary III.
[22.] Corollary IV.
[23.] Theorem V.
[24.] Theorem VI.
[25.] Corollary.
[26.] CHAP. III.
[27.] Problem I.
[28.] Operation.
[29.] Demonstration.
[30.] Remarks.
[31.] Method II.
[32.] Operation.
[33.] Demonstration.
[34.] Remarks.
[35.] Method III.
[36.] Operation.
[37.] Demonstration.
[38.] Remark.
[39.] Method. IV.
[40.] Operation, Without Compaſſes.
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            a right Line drawn from the Eye parallel to the pro-
              <lb/>
            poſed Line, terminates.</s>
            <s xml:id="echoid-s378" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s379" xml:space="preserve">The Line C D being continued, will meet
              <unsure/>
              <lb/>
              <note position="left" xlink:label="note-0030-01" xlink:href="note-0030-01a" xml:space="preserve">Fig. 5.</note>
            the perſpective Plane in the Point E. </s>
            <s xml:id="echoid-s380" xml:space="preserve">We are
              <lb/>
            to prove, that its Appearance is a Part of the
              <lb/>
            Line E H, drawn from the Point E, to the
              <lb/>
            Point H, whereat the Line O H proceeding
              <lb/>
            from the Eye parallel to the given Line C D,
              <lb/>
            terminates.</s>
            <s xml:id="echoid-s381" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s382" xml:space="preserve">The Interſection of the perſpective Plane,
              <lb/>
            and the Plane O D C, is the Repreſentation of the
              <lb/>
            given Line. </s>
            <s xml:id="echoid-s383" xml:space="preserve">Now the Plane O D C, is a Part of the
              <lb/>
            Plane paſſing through the parallels O H and EC.</s>
            <s xml:id="echoid-s384" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s385" xml:space="preserve">Therefore, this Repreſentation is a Part of the
              <lb/>
            Interſection of the laſt mentioned Plane, and
              <lb/>
            perſpective Plane; </s>
            <s xml:id="echoid-s386" xml:space="preserve">which Interſection is E H.</s>
            <s xml:id="echoid-s387" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div43" type="section" level="1" n="19">
          <head xml:id="echoid-head21" xml:space="preserve">
            <emph style="sc">Corollary</emph>
          I.</head>
          <p style="it">
            <s xml:id="echoid-s388" xml:space="preserve">14. </s>
            <s xml:id="echoid-s389" xml:space="preserve">All Lines parallel between themſelves, and be-
              <lb/>
            ing produced, do fall upon the perſpective Plane, have
              <lb/>
            Repreſentations, which being produced, will all con-
              <lb/>
            cur in one Point.</s>
            <s xml:id="echoid-s390" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s391" xml:space="preserve">This is evident, becauſe but only one Line
              <lb/>
            O H can be drawn from the Eye O, to the per-
              <lb/>
            ſpective Plane, parallel to the ſaid Parallels, and
              <lb/>
            becauſe all their Repreſentations are Parts of
              <lb/>
            Lines concurring in the Point H.</s>
            <s xml:id="echoid-s392" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s393" xml:space="preserve">And this Point is called the accidental Point of the
              <lb/>
              <note position="left" xlink:label="note-0030-02" xlink:href="note-0030-02a" xml:space="preserve">Def. 17.</note>
            ſaid Parallels.</s>
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        <div xml:id="echoid-div45" type="section" level="1" n="20">
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            <emph style="sc">Corollary</emph>
          II.</head>
          <p style="it">
            <s xml:id="echoid-s395" xml:space="preserve">15. </s>
            <s xml:id="echoid-s396" xml:space="preserve">Two or more parallel Lines, which being produ-
              <lb/>
            ced, do fall on the perſpective Plane, parallel to the Geo-
              <lb/>
            metrical Plane, have their accidental Point in the
              <lb/>
            Horizontal Line.</s>
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