Gravesande, Willem Jacob 's, An essay on perspective

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              <pb o="22" file="0046" n="49" rhead="An ESSAY"/>
            of this laſt Line, and the Line E D G, which was
              <lb/>
            to be demonſtrated.</s>
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          </p>
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        <div xml:id="echoid-div77" type="section" level="1" n="42">
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            <emph style="sc">Remarks</emph>
          .</head>
          <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:
              <lb/>
            </s>
            <s xml:id="echoid-s644" xml:space="preserve">But it is ſufficient if they have the ſame Propor-
              <lb/>
            tion, as the aforeſaid Diſtance has to the Height. </s>
            <s xml:id="echoid-s645" xml:space="preserve">
              <lb/>
            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,
              <lb/>
            let g O f be a Line any how drawn through the
              <lb/>
            Eye O, and take the Point g at Pleaſure in this
              <lb/>
            Line, through which draw alſo the Line g N I
              <lb/>
            at Pleaſure, cutting the Horizontal Line in N,
              <lb/>
            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-
              <lb/>
            rallelthereto, cutting the Line g O f in f.</s>
            <s xml:id="echoid-s649" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s650" xml:space="preserve">This being done, the Points g and f may be
              <lb/>
            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-
              <lb/>
            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,
              <lb/>
            which is ſufficient for the Demonſtration.</s>
            <s xml:id="echoid-s654" xml:space="preserve"/>
          </p>
          <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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          <p>
            <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,
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            the three Points g O f; </s>
            <s xml:id="echoid-s659" xml:space="preserve">ſo that in this Caſe, there
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            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,
              <lb/>
            Height and Diſtance of the Eye be requir’d, </s>
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