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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            preſentations being join’d, will give the Perſpe-
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            ctive ſought. </s>
            <s xml:id="echoid-s783" xml:space="preserve">The ſame may be done, in draw-
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            ing the Chords thro’a Point, whoſe Repreſenta-
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            tion is known.</s>
            <s xml:id="echoid-s784" xml:space="preserve"/>
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        <div xml:id="echoid-div113" type="section" level="1" n="62">
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            <emph style="sc">Remarks</emph>
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          <p style="it">
            <s xml:id="echoid-s785" xml:space="preserve">49. </s>
            <s xml:id="echoid-s786" xml:space="preserve">Let G I be the Geometrical Line; </s>
            <s xml:id="echoid-s787" xml:space="preserve">and thro’
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              <note position="left" xlink:label="note-0058-01" xlink:href="note-0058-01a" xml:space="preserve">Fig. 16.</note>
            the Center P of the Circle, whoſe Perſpective is
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            ſought, let fall the Perpendicular P F upon the ſaid
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            Line G I, which biſect in the Point R. </s>
            <s xml:id="echoid-s788" xml:space="preserve">About R,
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            as a Center, and with the Radius R P, deſcribe an
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            Arc of a Circle M P N, cutting the given Circle in
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            the Points M and N. </s>
            <s xml:id="echoid-s789" xml:space="preserve">Now, if the Perſpective of
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            L H and N M be found, the two Conjugate Dia-
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            meters of an Ellipſis, which is the Repreſentation of
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            the given Circle, will be bad. </s>
            <s xml:id="echoid-s790" xml:space="preserve">And, an Ellipſis may
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            be drawn by ſome one of the Methods laid down by
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            thoſe who have treated of Conick Sections.</s>
            <s xml:id="echoid-s791" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s792" xml:space="preserve">I ſhall not ſpend time here in demonſtrating the
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            Truth of this. </s>
            <s xml:id="echoid-s793" xml:space="preserve">See Prop. </s>
            <s xml:id="echoid-s794" xml:space="preserve">10. </s>
            <s xml:id="echoid-s795" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s796" xml:space="preserve">2. </s>
            <s xml:id="echoid-s797" xml:space="preserve">of the great
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            Latin Treatiſe of Conic Sections, written by M. </s>
            <s xml:id="echoid-s798" xml:space="preserve">de
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            la Hire; </s>
            <s xml:id="echoid-s799" xml:space="preserve">the Demonſtration of which may be here
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            apply’d. </s>
            <s xml:id="echoid-s800" xml:space="preserve">If we conſider, 1. </s>
            <s xml:id="echoid-s801" xml:space="preserve">That Lines drawn from
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            the Points M and N to the Point F, will touch the
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            Circle in the ſaid Points M and N. </s>
            <s xml:id="echoid-s802" xml:space="preserve">2. </s>
            <s xml:id="echoid-s803" xml:space="preserve">That the
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            viſual Rays, going from the Eye towards all the Parts
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            of the Circumference of the Circle, form a Cone,
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            3. </s>
            <s xml:id="echoid-s804" xml:space="preserve">That the Appearance of the Circle, is the Section
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            of a Cone, made by the perſpective Plane. </s>
            <s xml:id="echoid-s805" xml:space="preserve">Finally,
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            That the Line G I ought to be conceiv’d, as being
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            the Interſection of the Geometrical Plane, and a
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            Plane paſſing thro’ the Eye parallel to the perſpective
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            Plane.</s>
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