Gravesande, Willem Jacob 's, An essay on perspective

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        <div xml:id="echoid-div32" type="section" level="1" n="13">
          <p style="it">
            <s xml:id="echoid-s290" xml:space="preserve">
              <pb o="7" file="0025" n="25" rhead="on PERSPECTIVE."/>
            the Geometrical Plane, make Angles with the baſe
              <lb/>
            Line, equal to thoſe Angles that the Lines whereof
              <lb/>
            they are the Appearances, make with the Parallels
              <lb/>
            to the baſe Line, which cut them; </s>
            <s xml:id="echoid-s291" xml:space="preserve">and conſequently
              <lb/>
            the ſaid Appearances are parallel between them-
              <lb/>
            ſelves.</s>
            <s xml:id="echoid-s292" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s293" xml:space="preserve">This is evident, becauſe the Appearances of
              <lb/>
            Lines parallel to the baſe Line, are parallel to
              <lb/>
            the ſaid Line; </s>
            <s xml:id="echoid-s294" xml:space="preserve">and the Appearances of the in-
              <lb/>
            clined Lines are parallel to theſe Lines.</s>
            <s xml:id="echoid-s295" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div33" type="section" level="1" n="14">
          <head xml:id="echoid-head16" xml:space="preserve">
            <emph style="sc">Theorem</emph>
          II.</head>
          <p style="it">
            <s xml:id="echoid-s296" xml:space="preserve">8, 9. </s>
            <s xml:id="echoid-s297" xml:space="preserve">The Repreſentation of a Figure, parallel to
              <lb/>
            the perſpective Plane, is ſimilar to the ſaid Figure; </s>
            <s xml:id="echoid-s298" xml:space="preserve">and
              <lb/>
            the Sides of the ſaid Figure are to their Repreſen-
              <lb/>
            tations, as the Diſtance of the Eye from the Plane
              <lb/>
            of the Figure, to the Diſtance of the Eye from the
              <lb/>
            perſpective Plane.</s>
            <s xml:id="echoid-s299" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s300" xml:space="preserve">The given Figure is A B C D. </s>
            <s xml:id="echoid-s301" xml:space="preserve">We are firſt to
              <lb/>
              <note position="right" xlink:label="note-0025-01" xlink:href="note-0025-01a" xml:space="preserve">Fig. 4.</note>
            prove, that its Repreſentation a b c d, is ſimilar
              <lb/>
            thereto; </s>
            <s xml:id="echoid-s302" xml:space="preserve">that is, that the correſponding Angles
              <lb/>
            of theſe two Figures A B C D, a b c d, are equal,
              <lb/>
            and their Sides proportional.</s>
            <s xml:id="echoid-s303" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s304" xml:space="preserve">I. </s>
            <s xml:id="echoid-s305" xml:space="preserve">The Angles are equal, becauſe the
              <note symbol="*" position="right" xlink:label="note-0025-02" xlink:href="note-0025-02a" xml:space="preserve">4.</note>
            of which the two Figures conſiſt, are parallel be-
              <lb/>
            tween themſelves.</s>
            <s xml:id="echoid-s306" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s307" xml:space="preserve">II. </s>
            <s xml:id="echoid-s308" xml:space="preserve">In the ſimilar Triangles A D O, and a d o,
              <lb/>
            we have
              <lb/>
            A D: </s>
            <s xml:id="echoid-s309" xml:space="preserve">a d : </s>
            <s xml:id="echoid-s310" xml:space="preserve">: </s>
            <s xml:id="echoid-s311" xml:space="preserve">O D : </s>
            <s xml:id="echoid-s312" xml:space="preserve">O d.</s>
            <s xml:id="echoid-s313" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s314" xml:space="preserve">And in the ſimilar Triangles O D C, and O d c,
              <lb/>
            we have
              <lb/>
            D C : </s>
            <s xml:id="echoid-s315" xml:space="preserve">d c : </s>
            <s xml:id="echoid-s316" xml:space="preserve">: </s>
            <s xml:id="echoid-s317" xml:space="preserve">O D : </s>
            <s xml:id="echoid-s318" xml:space="preserve">O d.
              <lb/>
            </s>
            <s xml:id="echoid-s319" xml:space="preserve">then
              <lb/>
            A D: </s>
            <s xml:id="echoid-s320" xml:space="preserve">a d : </s>
            <s xml:id="echoid-s321" xml:space="preserve">: </s>
            <s xml:id="echoid-s322" xml:space="preserve">D c : </s>
            <s xml:id="echoid-s323" xml:space="preserve">d c. </s>
            <s xml:id="echoid-s324" xml:space="preserve">
              <lb/>
            altern. </s>
            <s xml:id="echoid-s325" xml:space="preserve">
              <lb/>
            A D : </s>
            <s xml:id="echoid-s326" xml:space="preserve">D C : </s>
            <s xml:id="echoid-s327" xml:space="preserve">: </s>
            <s xml:id="echoid-s328" xml:space="preserve">a d : </s>
            <s xml:id="echoid-s329" xml:space="preserve">d c.</s>
            <s xml:id="echoid-s330" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s331" xml:space="preserve">And conſequently the Sides A D, and D C of
              <lb/>
            the Figure A B C D, are Proportional to </s>
          </p>
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