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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            of this laſt Line, and the Line E D G, which was
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            to be demonſtrated.</s>
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        <div xml:id="echoid-div77" type="section" level="1" n="42">
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            <emph style="sc">Remarks</emph>
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          <p>
            <s xml:id="echoid-s642" xml:space="preserve">33. </s>
            <s xml:id="echoid-s643" xml:space="preserve">By this Demonſtration it appears, that there
              <lb/>
            is no Neceſſity in taking G O exactly equal to
              <lb/>
            the Eye’s Diſtance, and O F equal to its Height:
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            </s>
            <s xml:id="echoid-s644" xml:space="preserve">But it is ſufficient if they have the ſame Propor-
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            tion, as the aforeſaid Diſtance has to the Height. </s>
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            Likewiſe there is no Neceſſity in aſſuming the
              <lb/>
            Points G and F, in a Line parallel to the Baſe
              <lb/>
            Line; </s>
            <s xml:id="echoid-s646" xml:space="preserve">for any other Line paſſing through the
              <lb/>
            Eye O may be uſed at Pleaſure. </s>
            <s xml:id="echoid-s647" xml:space="preserve">For Example,
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            let g O f be a Line any how drawn through the
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            Eye O, and take the Point g at Pleaſure in this
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            Line, through which draw alſo the Line g N I
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            at Pleaſure, cutting the Horizontal Line in N,
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            and the Baſe Line in I; </s>
            <s xml:id="echoid-s648" xml:space="preserve">and draw the Line O N,
              <lb/>
            and through the Point I, draw the Line I f pa-
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            rallelthereto, cutting the Line g O f in f.</s>
            <s xml:id="echoid-s649" xml:space="preserve"/>
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            <s xml:id="echoid-s650" xml:space="preserve">This being done, the Points g and f may be
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            uſed inſtead of G and F: </s>
            <s xml:id="echoid-s651" xml:space="preserve">for among all the
              <lb/>
            Lines that can be drawn (as G N I) it is mani-
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            ſeſt, that g N will always be to g I:</s>
            <s xml:id="echoid-s652" xml:space="preserve">: g O: </s>
            <s xml:id="echoid-s653" xml:space="preserve">g f,
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            which is ſufficient for the Demonſtration.</s>
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          <p>
            <s xml:id="echoid-s655" xml:space="preserve">If the Point f be firſt determin’d, the Point g
              <lb/>
            muſt be found by an Operation quite contrary
              <lb/>
            to that we have laid down.</s>
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            <s xml:id="echoid-s657" xml:space="preserve">34. </s>
            <s xml:id="echoid-s658" xml:space="preserve">When nothing is determinate, we
              <lb/>
            may (a Baſe Line being firſt drawn) take at
              <lb/>
            Pleaſure, in another Line any how drawn,
              <lb/>
            the three Points g O f; </s>
            <s xml:id="echoid-s659" xml:space="preserve">ſo that in this Caſe, there
              <lb/>
            is no Manner of Neceſſity to uſe Compaſſes, in
              <lb/>
            throwing any Figure whatſoever, which is on
              <lb/>
            the Geometrical Plane, into Perſpective. </s>
            <s xml:id="echoid-s660" xml:space="preserve">But
              <lb/>
            if after having thus work’d, the Point of Sight,
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            Height and Diſtance of the Eye be requir’d, </s>
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