Gravesande, Willem Jacob 's, An essay on perspective

Table of contents

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[41.] Demonstration.
[42.] Remarks.
[43.] Method V.
[44.] Operation, Without Compaſſes.
[45.] Demonstration.
[46.] Remark.
[47.] Corollary.
[48.] Method VI.
[49.] Operation.
[50.] Demonstration.
[51.] Remarks.
[52.] Corollary.
[53.] Problem II.
[54.] Remark.
[55.] Problem III.
[56.] Method. II.
[57.] Problem IV.
[58.] Example I.
[59.] Example II.
[60.] Remarks.
[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.
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            and drawing a Line from the Point I to the
              <lb/>
            other Point of Diſtance; </s>
            <s xml:id="echoid-s538" xml:space="preserve">which, by its Inter-
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            ſection with E D, will give the Appearance of
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            the Point A.</s>
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        <div xml:id="echoid-div61" type="section" level="1" n="31">
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            <emph style="sc">Method</emph>
          II.</head>
          <p>
            <s xml:id="echoid-s540" xml:space="preserve">26. </s>
            <s xml:id="echoid-s541" xml:space="preserve">γ is the Horizontal Plane, X the Perſpe-
              <lb/>
            ctive Plane, Z the Geometrical Plane, O the Eye,
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            D C the Horizontal Line, B E the Baſe Line, and
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            A the given Point.</s>
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          <note position="left" xml:space="preserve">Fig. 8.</note>
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            <emph style="sc">Operation</emph>
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          <p>
            <s xml:id="echoid-s543" xml:space="preserve">Draw a Line from the Point A, to the Eye O, cut-
              <lb/>
            ting the Baſe Line in the Point B, and the Horizon-
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            tal Line in the Point C: </s>
            <s xml:id="echoid-s544" xml:space="preserve">Then aſſume B E in the
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            Baſe Line, equal to B A; </s>
            <s xml:id="echoid-s545" xml:space="preserve">and C D in the Hori-
              <lb/>
            zontal Line, equal to C O; </s>
            <s xml:id="echoid-s546" xml:space="preserve">and join the Points
              <lb/>
            E and D, by a Line cutting the Line A O in
              <lb/>
            the Point a; </s>
            <s xml:id="echoid-s547" xml:space="preserve">which will be the Appearance
              <lb/>
            ſought.</s>
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        <div xml:id="echoid-div63" type="section" level="1" n="33">
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            <emph style="sc">Demonstration</emph>
          .</head>
          <p>
            <s xml:id="echoid-s549" xml:space="preserve">27. </s>
            <s xml:id="echoid-s550" xml:space="preserve">The Triangle O D C in the Horizontal
              <lb/>
            Plane, is ſimilar to the Triangle A B E in the
              <lb/>
            Geometrical Plane; </s>
            <s xml:id="echoid-s551" xml:space="preserve">and conſequently A B is pa-
              <lb/>
            rallel to O C, and A E to O D. </s>
            <s xml:id="echoid-s552" xml:space="preserve">But the Appear-
              <lb/>
            ance of A muſt be in the Lines B C, and E D;</s>
            <s xml:id="echoid-s553" xml:space="preserve">
              <note symbol="*" position="left" xlink:label="note-0040-02" xlink:href="note-0040-02a" xml:space="preserve">
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              13.</note>
            and therefore it will be in a, their Interſection.</s>
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        <div xml:id="echoid-div65" type="section" level="1" n="34">
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            <emph style="sc">Remarks</emph>
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          <p>
            <s xml:id="echoid-s555" xml:space="preserve">28. </s>
            <s xml:id="echoid-s556" xml:space="preserve">If the Place wherein the Eye ought to be in
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            the Horizontal Plane be not known, but the Point
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            of Sight is; </s>
            <s xml:id="echoid-s557" xml:space="preserve">then, to find the Place of the Eye,
              <lb/>
            a Perpendicular muſt be rais’d from the Point </s>
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