Gravesande, Willem Jacob 's, An essay on perspective

List of thumbnails

< >
71
71 (32) 		72
72 (33)
73
73 (34) 		74
74 (35)
75
75 (36) 		76
76
77
77 		78
78
79
79 		80
80
< >
page |< < (35) of 237 > >|
    <echo version="1.0RC">
      <text xml:lang="en" type="free">
        <div xml:id="echoid-div126" type="section" level="1" n="69">
          <pb o="35" file="0067" n="74" rhead="on PERSPECTIVE."/>
          <p style="it">
            <s xml:id="echoid-s890" xml:space="preserve">And the Triangles D P m and D G n are ſimilar:
              <lb/>
            </s>
            <s xml:id="echoid-s891" xml:space="preserve">Wherefore
              <lb/>
            D G: </s>
            <s xml:id="echoid-s892" xml:space="preserve">D P: </s>
            <s xml:id="echoid-s893" xml:space="preserve">G n:</s>
            <s xml:id="echoid-s894" xml:space="preserve">: P m. </s>
            <s xml:id="echoid-s895" xml:space="preserve">
              <lb/>
            And
              <lb/>
            G H: </s>
            <s xml:id="echoid-s896" xml:space="preserve">P Q:</s>
            <s xml:id="echoid-s897" xml:space="preserve">: G n: </s>
            <s xml:id="echoid-s898" xml:space="preserve">P m.</s>
            <s xml:id="echoid-s899" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s900" xml:space="preserve">The Triangles B A N and L A M are ſimilar:
              <lb/>
            </s>
            <s xml:id="echoid-s901" xml:space="preserve">Therefore,
              <lb/>
            BA: </s>
            <s xml:id="echoid-s902" xml:space="preserve">AL:</s>
            <s xml:id="echoid-s903" xml:space="preserve">: AN: </s>
            <s xml:id="echoid-s904" xml:space="preserve">AM. </s>
            <s xml:id="echoid-s905" xml:space="preserve">
              <lb/>
            But the three firſt Terms of the two laſt Proportions,
              <lb/>
            are equal between themſelves; </s>
            <s xml:id="echoid-s906" xml:space="preserve">whence P m is alſo
              <lb/>
            equal to A M. </s>
            <s xml:id="echoid-s907" xml:space="preserve">Which was to be demonſtrated.</s>
            <s xml:id="echoid-s908" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div127" type="section" level="1" n="70">
          <head xml:id="echoid-head75" xml:space="preserve">
            <emph style="sc">Remarks</emph>
          .</head>
          <p>
            <s xml:id="echoid-s909" xml:space="preserve">54. </s>
            <s xml:id="echoid-s910" xml:space="preserve">When the Height of the Cone is greater
              <lb/>
            than the Height of the Eye, the Points, G and
              <lb/>
            H, will fall below the Point D; </s>
            <s xml:id="echoid-s911" xml:space="preserve">in which Caſe,
              <lb/>
            the Lines A B and A C muſt be produc’d, till
              <lb/>
            they cut the Circle in the Points l and f, oppo-
              <lb/>
            ſite to L and F: </s>
            <s xml:id="echoid-s912" xml:space="preserve">Then lIf will be the viſible
              <lb/>
            Part of the Baſe.</s>
            <s xml:id="echoid-s913" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s914" xml:space="preserve">When the Cone is inclin’d, ſo that T (for Ex-
              <lb/>
            ample) is the Seat of its Vertex; </s>
            <s xml:id="echoid-s915" xml:space="preserve">AT muſt be
              <lb/>
            drawn: </s>
            <s xml:id="echoid-s916" xml:space="preserve">And then having aſſum’d P D equal to
              <lb/>
            the perpendicular Height of the Cone, and Pt
              <lb/>
            equal to A T; </s>
            <s xml:id="echoid-s917" xml:space="preserve">the Line t D x muſt be drawn;
              <lb/>
            </s>
            <s xml:id="echoid-s918" xml:space="preserve">and the Part T X, taken in A T, equal to G x. </s>
            <s xml:id="echoid-s919" xml:space="preserve">
              <lb/>
            Alſo, X S muſt be drawn, and A s, equal and
              <lb/>
            parallel thereto.</s>
            <s xml:id="echoid-s920" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s921" xml:space="preserve">This being done; </s>
            <s xml:id="echoid-s922" xml:space="preserve">the ſame Method muſt be
              <lb/>
            apply’d here, that I have laid down for the up-
              <lb/>
            right Cone; </s>
            <s xml:id="echoid-s923" xml:space="preserve">with this Difference only, that the
              <lb/>
            Point s muſt be us’d inſtead of the Station Point
              <lb/>
            S. </s>
            <s xml:id="echoid-s924" xml:space="preserve">But when the Height of the Cone is greater
              <lb/>
            than the Height of the Eye, the Point X muſt
              <lb/>
            be aſſum’d in the Line T A, between the Points
              <lb/>
            T and A.</s>
            <s xml:id="echoid-s925" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum