Gravesande, Willem Jacob 's, An essay on perspective

List of thumbnails

< >
91
91 		92
92
93
93 		94
94 (43)
95
95 (44) 		96
96 (45)
97
97 (46) 		98
98
99
99 		100
100
< >
page |< < (51) of 237 > >|
    <echo version="1.0RC">
      <text xml:lang="en" type="free">
        <div xml:id="echoid-div170" type="section" level="1" n="91">
          <p style="it">
            <s xml:id="echoid-s1246" xml:space="preserve">
              <pb o="51" file="0095" n="108" rhead="on PERSPECTIVE."/>
            s i by x, and i h be y; </s>
            <s xml:id="echoid-s1247" xml:space="preserve">it is manifeſt, that i 4 = a 5
              <lb/>
            being Algebraially Expreſſed, will be {ydy/dx}</s>
          </p>
          <p style="it">
            <s xml:id="echoid-s1248" xml:space="preserve">Again, the ſimilar Triangles, s a 5 and s i g give
              <lb/>
            s a (e): </s>
            <s xml:id="echoid-s1249" xml:space="preserve">a 5 ({ydy/dx}):</s>
            <s xml:id="echoid-s1250" xml:space="preserve">: s i (x): </s>
            <s xml:id="echoid-s1251" xml:space="preserve">i g ({xydx/edx}) Alſo by
              <lb/>
            the Conſtruction of Figure 32,
              <lb/>
            A S (e): </s>
            <s xml:id="echoid-s1252" xml:space="preserve">A P = i h (y):</s>
            <s xml:id="echoid-s1253" xml:space="preserve">: A P (y): </s>
            <s xml:id="echoid-s1254" xml:space="preserve">A I ({yy/e});
              <lb/>
            </s>
            <s xml:id="echoid-s1255" xml:space="preserve">Whence it follows, ſince I G = i g, that A G =
              <lb/>
            (I G - A I) = {xyd/cdx} - {yy/e}. </s>
            <s xml:id="echoid-s1256" xml:space="preserve">And conſequently, H
              <lb/>
            and F are the Seats of the two Points whoſe Perſpe-
              <lb/>
            ctive is required, and thoſe Points are both in a
              <lb/>
            Plane parallel to the Geometrical Plane, which is the
              <lb/>
            height of 21 above the Geometrical Plane.</s>
            <s xml:id="echoid-s1257" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1258" xml:space="preserve">If the precedent Calculation be apply’d to the Lower
              <lb/>
            Part of the Torus, the Expreſſion {xydy/edx} - {yy/e}, will
              <lb/>
            be chang’d into this, - {xydy/edx} - {yy/e;</s>
            <s xml:id="echoid-s1259" xml:space="preserve">} which ſhews that
              <lb/>
            theſe two Quantities muſt be aſſumed on the ſame Side
              <lb/>
            of A, viz. </s>
            <s xml:id="echoid-s1260" xml:space="preserve">towards S. </s>
            <s xml:id="echoid-s1261" xml:space="preserve">Moreover 9 q, inthe Line
              <lb/>
            9 m, is equal to {xydy/edx}; </s>
            <s xml:id="echoid-s1262" xml:space="preserve">for 98 ({ydy/e}) = i 4.
              <lb/>
            </s>
            <s xml:id="echoid-s1263" xml:space="preserve">Which ſhews that M and L are alſo the Seats of two
              <lb/>
            Points whoſe Perſpective muſt be found, and which are
              <lb/>
            both in a Plane parallel to the Geometrical Plane, and
              <lb/>
            above it the Height of 29.</s>
            <s xml:id="echoid-s1264" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div175" type="section" level="1" n="92">
          <head xml:id="echoid-head98" xml:space="preserve">
            <emph style="sc">Remarks</emph>
          .</head>
          <p>
            <s xml:id="echoid-s1265" xml:space="preserve">67. </s>
            <s xml:id="echoid-s1266" xml:space="preserve">This Problem may be likewiſe ſolved in
              <lb/>
            conſidering the Torus of a Column as made up of
              <lb/>
            an infinite Number of Baſes of Cones, whoſe Al-
              <lb/>
            titudes are determin’d by the concurrence of the
              <lb/>
            Tangents of the Semicircular Concavity of the
              <lb/>
            Axis of the Column; </s>
            <s xml:id="echoid-s1267" xml:space="preserve">and then determining
              <note symbol="*" position="right" xlink:label="note-0095-01" xlink:href="note-0095-01a" xml:space="preserve">53.</note>
            </s>
          </p>
        </div>
      </text>
    </echo>
Impressum