Gravesande, Willem Jacob 's, An essay on perspective

Page concordance

< >
Scan Original
61 28
62 29
63 30
64
65
66
67
68
69
70 31
71 32
72 33
73 34
74 35
75 36
76
77
78
79
80
81
82
83
84
85 37
86 38
87 39
88 40
89 41
90 42
< >
page |< < (49) of 237 > >|
    <echo version="1.0RC">
      <text xml:lang="en" type="free">
        <div xml:id="echoid-div170" type="section" level="1" n="91">
          <pb o="49" file="0093" n="106" rhead="on PERSPECTIVE."/>
          <p>
            <s xml:id="echoid-s1212" xml:space="preserve">The Demonſtration of the
              <emph style="sc">Problem</emph>
            .</s>
            <s xml:id="echoid-s1213" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1214" xml:space="preserve">66. </s>
            <s xml:id="echoid-s1215" xml:space="preserve">The Torus of the Column muſt be conceiv’d as
              <lb/>
            made up of an Infinite Number of Circular Planes,
              <lb/>
            lying one upon another. </s>
            <s xml:id="echoid-s1216" xml:space="preserve">And it is evident that
              <lb/>
            the Reaſon why each of thoſe Circles cannot be wholly
              <lb/>
            ſeen, is becauſe that which is immediately under it
              <lb/>
            hides a Part thereof; </s>
            <s xml:id="echoid-s1217" xml:space="preserve">from whence it follows, that
              <lb/>
            if the Plane of one oſ theſe Circles be every way
              <lb/>
            continu’d, and the Circle immediately under it, be
              <lb/>
            thrown into Perſpective upon it, (which
              <note symbol="*" position="right" xlink:label="note-0093-01" xlink:href="note-0093-01a" xml:space="preserve">8.</note>
            is alſo a Circle) the two Points of Interſection of this
              <lb/>
            Repreſentation, and the Circle in the Plane, will deter-
              <lb/>
            mine the viſible Part of the ſaid Repreſentation; </s>
            <s xml:id="echoid-s1218" xml:space="preserve">and
              <lb/>
            conſequently if the Repreſentation of theſe two Points
              <lb/>
            of Interſection be found upon the Perſpective Plane, we
              <lb/>
            ſhall have two Points of the Perſpective of the Torus of
              <lb/>
            the propoſed Column. </s>
            <s xml:id="echoid-s1219" xml:space="preserve">This is what I have done in the
              <lb/>
            Solution of the Problem, as we ſhall now Analytically
              <lb/>
            demonſtrate.</s>
            <s xml:id="echoid-s1220" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1221" xml:space="preserve">Let O be the Eye, A M a part of the Torus of
              <lb/>
              <note position="right" xlink:label="note-0093-02" xlink:href="note-0093-02a" xml:space="preserve">Fig. 35.</note>
            the Column, A P a Perpendicular to the Baſe paſſing
              <lb/>
            through the Center of the Column, and A B a
              <lb/>
            Parallel to the Baſe, drawn thro’ the Center B of
              <lb/>
            the Semicircle Concavity of the Torus. </s>
            <s xml:id="echoid-s1222" xml:space="preserve">Let M P be
              <lb/>
            a Semidiameter of one of the Circles ſpoken of in the
              <lb/>
            the beginning of this Demonſtration. </s>
            <s xml:id="echoid-s1223" xml:space="preserve">Then if the
              <lb/>
            Line m p be drawn parallel and infinitely near C M P
              <lb/>
            and the Lines m O and p O are drawn cutting M P
              <lb/>
            in D and T, it is evident that D T, which is in the
              <lb/>
            Plane of the Circle paſſing thro’ M P, will be the
              <lb/>
            Semidiameter of the Perſpective of the Circle imme-
              <lb/>
            diately underneath.</s>
            <s xml:id="echoid-s1224" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1225" xml:space="preserve">Now let fall the Perpendicular O S from the Eye
              <lb/>
            to the Line A B, and continue the Lines M P and
              <lb/>
            m p, till they meet the ſaid Perpendicular in the Points
              <lb/>
            Q and q. </s>
            <s xml:id="echoid-s1226" xml:space="preserve">Moreover, continue the Line M P to </s>
          </p>
        </div>
      </text>
    </echo>
Impressum