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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            Perpendiculars f P, O H, muſt be let fall from
              <lb/>
            the Points f and O, on the Baſe Line, and the
              <lb/>
            Line P g drawn; </s>
            <s xml:id="echoid-s661" xml:space="preserve">then the Point V, wherein it
              <lb/>
            cuts the Perpendicular O H, is the Point of Sight
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            ſought, and the Parts O V, and V H determine
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            the Height and Diſtance of the Eye.</s>
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        <div xml:id="echoid-div78" type="section" level="1" n="43">
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            <emph style="sc">Method</emph>
          V.</head>
          <p style="it">
            <s xml:id="echoid-s663" xml:space="preserve">35. </s>
            <s xml:id="echoid-s664" xml:space="preserve">When the Appearance of a Point is known,</s>
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            <s xml:id="echoid-s665" xml:space="preserve">Let A be a Point in the Geometrical Plane,
              <lb/>
              <note position="right" xlink:label="note-0047-01" xlink:href="note-0047-01a" xml:space="preserve">Fig. 11.</note>
            and a its Repreſentation in the perſpective Plane,
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            it is requir’d to find the Appearance of the
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            Point B.</s>
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        <div xml:id="echoid-div80" type="section" level="1" n="44">
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            <emph style="sc">Operation</emph>
          ,
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          Without Compaſſes.</head>
          <p>
            <s xml:id="echoid-s667" xml:space="preserve">Draw a Line from the Point B to the Eye O,
              <lb/>
            and another from the Point E, wherein the
              <lb/>
            ſaid Line continued, cuts the Baſe Line, to the
              <lb/>
            Point A; </s>
            <s xml:id="echoid-s668" xml:space="preserve">then draw the Line E a, and where
              <lb/>
            it cuts B O, is the Point b ſought.</s>
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        <div xml:id="echoid-div81" type="section" level="1" n="45">
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            <emph style="sc">Demonstration</emph>
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          <p>
            <s xml:id="echoid-s670" xml:space="preserve">The Point E is its own Repreſentation; </s>
            <s xml:id="echoid-s671" xml:space="preserve">and
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            becauſe the Point a is the Repreſentation of A,
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            the Line E a is that of E A. </s>
            <s xml:id="echoid-s672" xml:space="preserve">Now ſince the
              <lb/>
            Point B is in the Line E A, the Appearance of
              <lb/>
            this Point will be likewiſe in E a, as alſo
              <note symbol="*" position="right" xlink:label="note-0047-02" xlink:href="note-0047-02a" xml:space="preserve">27.</note>
            B O; </s>
            <s xml:id="echoid-s673" xml:space="preserve">therefore it is in b the Interſection of the
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            Lines E a, and B O.</s>
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        <div xml:id="echoid-div83" type="section" level="1" n="46">
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            <emph style="sc">Remark</emph>
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            <s xml:id="echoid-s675" xml:space="preserve">37. </s>
            <s xml:id="echoid-s676" xml:space="preserve">If the Point A be in the Line B O, or
              <lb/>
            the Line B A be parallel, or a very little inclined
              <lb/>
            to the Baſe Line, we cannot then uſe this </s>
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