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="42" file="0080" n="90" rhead="An ESSAY"/>
            B and C, which will be the two moſt extreme
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            ones that can be ſeen.</s>
            <s xml:id="echoid-s1099" xml:space="preserve"/>
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        <div xml:id="echoid-div152" type="section" level="1" n="82">
          <head xml:id="echoid-head88" style="it" xml:space="preserve">To do this another Way.</head>
          <p>
            <s xml:id="echoid-s1100" xml:space="preserve">61. </s>
            <s xml:id="echoid-s1101" xml:space="preserve">If the upper Face of the Cylinder or Priſm
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              <note position="left" xlink:label="note-0080-01" xlink:href="note-0080-01a" xml:space="preserve">Fig. 26,
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              27.</note>
            be otherwiſe requir’d to be found, the ſame Things
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            being given as in the foregoing Method, we draw
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            the Line P Q in the perſpective Plane, parallel
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            to the Baſe Line, whoſe Diſtance therefrom we
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            make equal to the Height of the Priſm or Cy-
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            linder, whoſe Perſpective is requir’d. </s>
            <s xml:id="echoid-s1102" xml:space="preserve">Then we
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            change its Geometrical Plane, ſo that the Baſe
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            Line coincides with P Q, and that in this Tran-
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            ſpoſition a Perpendicular to the Baſe Line coin-
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            cides with this ſame Perpendicular continued to-
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              <note symbol="*" position="left" xlink:label="note-0080-02" xlink:href="note-0080-02a" xml:space="preserve">46.</note>
            wards P Q. </s>
            <s xml:id="echoid-s1103" xml:space="preserve">Finally we find the Perſpective of the Baſe of the Priſm or Cylinder, thus changed
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            in Situation by uſing P Q for a Baſe Line, and
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            the ſaid Perſpective is the Repreſentation of their
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            upper Faces.</s>
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        <div xml:id="echoid-div154" type="section" level="1" n="83">
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            <emph style="sc">Demonstration</emph>
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          <p>
            <s xml:id="echoid-s1105" xml:space="preserve">If we ſuppoſe the Plane of the upper Surface
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            of the Priſm to be continued, it will meet the
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            Perſpective Plane in P Q; </s>
            <s xml:id="echoid-s1106" xml:space="preserve">and the upper Face
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            in this Plane continued, will have the ſame
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            Situation in Reſpect to P Q, as the Baſe hath
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            on the Geometrical Plane with Regard to the
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            Baſe Line. </s>
            <s xml:id="echoid-s1107" xml:space="preserve">If then the ſaid continued Plane be
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            conceived to lye on the perſpective Plane, the
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            upper Faces of the Priſm or Cylinder, will be
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            as the Baſes changed in the Manner aforeſaid;
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            </s>
            <s xml:id="echoid-s1108" xml:space="preserve">therefore the Appearance of the ſaid Baſes
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            changed, will be that of the upper Surfaces.</s>
            <s xml:id="echoid-s1109" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1110" xml:space="preserve">Note, By folding the Paper it is eaſy to
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            tranſpoſe Figures, and when the Height of </s>
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