Gravesande, Willem Jacob 's, An essay on perspective

Table of contents

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[61.] Example III. 48. To throw a circle into Perſpective.
[62.] Remarks.
[63.] Prob. V. 50. To find the Repreſentation of a Point, elevated above the Geometrical Planc.
[64.] Operation.
[65.] Demonstration.
[66.] Prob. VI. 52. To throm a Pyramid, or Cone, into Perſpective.
[67.] 53. To determine the viſible Part of the Baſe of a Cone.
[68.] Operation.
[69.] Demonstration.
[70.] Remarks.
[71.] Problem VII. 55. To find the Perſpective of a Line, perpendicular to the Geometrical Plane.
[72.] Operation.
[73.] Demonstration.
[74.] Method II.
[75.] Demonstration.
[76.] Method III.
[77.] Operation, Without Compaſſes.
[78.] Demonstration.
[79.] Scholium.
[80.] Corollary.
[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.
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          <pb o="31" file="0063" n="70" rhead="on PERSPECTIVE."/>
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        <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
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            Line, equal to the Height of the Eye; </s>
            <s xml:id="echoid-s809" xml:space="preserve">and let
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            A be the Seat of the given Line.</s>
            <s xml:id="echoid-s810" xml:space="preserve"/>
          </p>
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        <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
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            the Height of the Eye, above the Geometrical
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            Plane: </s>
            <s xml:id="echoid-s812" xml:space="preserve">Then draw Lines from the Point A to
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            the Points S and C, and on the Point B, the In-
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            terſection of the Line AS and the Baſe Line,
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            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
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            the Perſpective ſought.</s>
            <s xml:id="echoid-s814" xml:space="preserve"/>
          </p>
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        <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
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            Geometrical Plane; </s>
            <s xml:id="echoid-s817" xml:space="preserve">then it is manifeſt, that the
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            Interſection of theſe two Planes is the Line
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            A B S, and the Interſection of the ſaid ſuppos’d
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            Plane and the perſpective Plane, is B I. </s>
            <s xml:id="echoid-s818" xml:space="preserve">Now,
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            let X be this ſuppos’d Plane; </s>
            <s xml:id="echoid-s819" xml:space="preserve">a, b, s, the Point
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              <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
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            Figure, bi the Interſection of this Plane and
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            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
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            be drawn, the Line B I of the precedent Figure
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            will be equal to b i in this Figure.</s>
            <s xml:id="echoid-s822" xml:space="preserve"/>
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