Gravesande, Willem Jacob 's, An essay on perspective

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        <div xml:id="echoid-div69" type="section" level="1" n="37">
          <pb o="20" file="0042" n="44" rhead="An ESSAY"/>
          <p>
            <s xml:id="echoid-s578" xml:space="preserve">Now, it is evident, that to prove the
              <note symbol="@" position="left" xlink:label="note-0042-01" xlink:href="note-0042-01a" xml:space="preserve">27.</note>
            pearance of A is in the Line C H, we need but
              <lb/>
            demonſtrate that O D is parallel to A E; </s>
            <s xml:id="echoid-s579" xml:space="preserve">which
              <lb/>
            may be done thus:</s>
            <s xml:id="echoid-s580" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s581" xml:space="preserve">Becauſe the Triangles O G V, and A B F, are
              <lb/>
            ſimilar.
              <lb/>
            </s>
            <s xml:id="echoid-s582" xml:space="preserve">A F: </s>
            <s xml:id="echoid-s583" xml:space="preserve">A B:</s>
            <s xml:id="echoid-s584" xml:space="preserve">: O G: </s>
            <s xml:id="echoid-s585" xml:space="preserve">O V: </s>
            <s xml:id="echoid-s586" xml:space="preserve">
              <lb/>
            altern. </s>
            <s xml:id="echoid-s587" xml:space="preserve">
              <lb/>
            A F: </s>
            <s xml:id="echoid-s588" xml:space="preserve">O G:</s>
            <s xml:id="echoid-s589" xml:space="preserve">: A B: </s>
            <s xml:id="echoid-s590" xml:space="preserve">O V: </s>
            <s xml:id="echoid-s591" xml:space="preserve">
              <lb/>
            Divid. </s>
            <s xml:id="echoid-s592" xml:space="preserve">and altern. </s>
            <s xml:id="echoid-s593" xml:space="preserve">the firſt
              <lb/>
            Proportion. </s>
            <s xml:id="echoid-s594" xml:space="preserve">
              <lb/>
            AF—AB (=CF): </s>
            <s xml:id="echoid-s595" xml:space="preserve">O G—O V=HG:</s>
            <s xml:id="echoid-s596" xml:space="preserve">:AB:</s>
            <s xml:id="echoid-s597" xml:space="preserve">OV.</s>
            <s xml:id="echoid-s598" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s599" xml:space="preserve">But becauſe the Triangles E C F, H G D are
              <lb/>
            ſimilar.
              <lb/>
            </s>
            <s xml:id="echoid-s600" xml:space="preserve">C F: </s>
            <s xml:id="echoid-s601" xml:space="preserve">H G :</s>
            <s xml:id="echoid-s602" xml:space="preserve">: E F : </s>
            <s xml:id="echoid-s603" xml:space="preserve">G D.</s>
            <s xml:id="echoid-s604" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s605" xml:space="preserve">Now, by obſerving the two laſt Proportions of
              <lb/>
            the other two Triangles,
              <lb/>
            E F: </s>
            <s xml:id="echoid-s606" xml:space="preserve">G D:</s>
            <s xml:id="echoid-s607" xml:space="preserve">: A F: </s>
            <s xml:id="echoid-s608" xml:space="preserve">O G,
              <lb/>
            And the Angle A F E, being equal to the Angle
              <lb/>
            O G D, the Triangles A E F and O D G are
              <lb/>
            ſimilar; </s>
            <s xml:id="echoid-s609" xml:space="preserve">and therefore A E is parallel to O D:
              <lb/>
            </s>
            <s xml:id="echoid-s610" xml:space="preserve">Which was to be demonſtrated.</s>
            <s xml:id="echoid-s611" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s612" xml:space="preserve">After the ſame manner we prove, that the
              <lb/>
            Appearance of the Point A is in the Line L I,
              <lb/>
            and conſequently is in the Interſection of this
              <lb/>
            Line and HC.</s>
            <s xml:id="echoid-s613" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div71" type="section" level="1" n="38">
          <head xml:id="echoid-head40" xml:space="preserve">
            <emph style="sc">Remark</emph>
          .</head>
          <p>
            <s xml:id="echoid-s614" xml:space="preserve">Altho’ this Method appears more difficult than
              <lb/>
            the precedent one, as to the Geometrical Conſi-
              <lb/>
            deration thereof, yet the Operation is eaſier, if
              <lb/>
            the Points are not too far diſtant from the Baſe
              <lb/>
            Line: </s>
            <s xml:id="echoid-s615" xml:space="preserve">For Lines may well enough be drawn by
              <lb/>
            Gueſs, or Sight only, to touch Circles, and Cir-
              <lb/>
            cles to touch Lines.</s>
            <s xml:id="echoid-s616" xml:space="preserve"/>
          </p>
        </div>
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    </echo>
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