Gravesande, Willem Jacob 's, An essay on perspective

Table of contents

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[171.] Problem V.
[172.] Remarks.
[173.] CHAP. VIII. Of mechanically ſhortning the Operations of Perſpective. 1. WHEN the perſpective Plane is ſup-pos’d perpendicular or upright. Problem I.
[174.] Operation.
[175.] Method II.
[176.] Prob. II.
[177.] Operation.
[178.] Method II.
[179.] Method III.
[180.] The Demonſtration of the two laſt Ways.
[181.] II. When the Perſpective Plane is inclined. Prob. III.
[182.] Prob. IV.
[183.] Remarks.
[184.] III. When the Perſpective Plane is Parallel or Horizontal. Prob. V.
[185.] Operation.
[186.] Demonstration.
[187.] Remarks.
[188.] Prob. VI.
[189.] Demonstration.
[190.] Prob. VII.
[191.] CHAP. IX.
[192.] Prob. I. 122. To draw Vertical Dials.
[193.] Demonstration.
[194.] Remark.
[195.] Prob. II. 123. To draw inclining Dials.
[196.] The Uſe of the Camera Obscura in Deſigning. Advertisement.
[197.] The Uſe of the Camera Obscura in Deſigning. Definition.
[198.] Theorem I.
[199.] Theorem II.
[200.] The Deſcription of the Firſt Machine.
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            ſentation of the Figure which is in the ſecond
              <lb/>
            Plane, is likewiſe ſimilar to the Figure which is
              <lb/>
            in the Geometrical Plane, and the Lines com-
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            poſing this Appearance to the correſpondent
              <lb/>
            Lines in the ſecond Plane, as the Eye’s Diſtance
              <lb/>
            from the perſpective Plane, is to its Diſtance
              <lb/>
            from the before ſuppoſed Plane. </s>
            <s xml:id="echoid-s2146" xml:space="preserve">But by means
              <lb/>
            of the Threads faſtned in the Manner aforeſaid,
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            we find the Repreſentation of a Figure, whoſe
              <lb/>
            Lines are in the aforenamed Proportion:</s>
            <s xml:id="echoid-s2147" xml:space="preserve">
              <note symbol="*" position="left" xlink:label="note-0166-01" xlink:href="note-0166-01a" xml:space="preserve">118.</note>
            Whence this Figure is the Perſpective ſought,
              <lb/>
            and is ſituated as it ought to be, with regard to
              <lb/>
            the Repreſentations of the Figures in the Geo-
              <lb/>
            metrical Plane; </s>
            <s xml:id="echoid-s2148" xml:space="preserve">becauſe theſe Figures are ſo
              <lb/>
            ſlid, that the Appearance of the Perpen-
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            dicular in the Point B, is only a Point. </s>
            <s xml:id="echoid-s2149" xml:space="preserve">The
              <lb/>
            ſaid Appearances are alſo in their proper Poſiti-
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            ons, becauſe the Line B Q, is made to coincide
              <lb/>
            with O N.</s>
            <s xml:id="echoid-s2150" xml:space="preserve"/>
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          <p style="it">
            <s xml:id="echoid-s2151" xml:space="preserve">120. </s>
            <s xml:id="echoid-s2152" xml:space="preserve">For Solar Shadows in all Situations of the Per-
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            ſpective Plane.</s>
            <s xml:id="echoid-s2153" xml:space="preserve"/>
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        <div xml:id="echoid-div349" type="section" level="1" n="190">
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            <emph style="sc">Prob</emph>
          . VII.</head>
          <p style="it">
            <s xml:id="echoid-s2154" xml:space="preserve">6. </s>
            <s xml:id="echoid-s2155" xml:space="preserve">To find the Repreſentations of the Shadows of
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            any Number of Points, being at the ſame Height
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            above the Geometrical Plane.</s>
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          <p>
            <s xml:id="echoid-s2157" xml:space="preserve">Find a Point in the Geometrical Plane,
              <note symbol="*" position="left" xlink:label="note-0166-02" xlink:href="note-0166-02a" xml:space="preserve">103.</note>
            is the Shadow of one of the given Points: </s>
            <s xml:id="echoid-s2158" xml:space="preserve">Tranſ-
              <lb/>
            poſe the Figures in the Geometrical Plane, ſo that
              <lb/>
            the Seat of the ſaid given Point coincides with
              <lb/>
            its Shadow; </s>
            <s xml:id="echoid-s2159" xml:space="preserve">and the Line drawn through the
              <lb/>
            ſaid Seat, and the Shadow of the given Point,
              <lb/>
            coincides with its Prolongation. </s>
            <s xml:id="echoid-s2160" xml:space="preserve">Then if ac-
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            cording to the Situation of the perſpective Plane,
              <lb/>
            the Repreſentations of the Seats of the </s>
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