Gravesande, Willem Jacob 's, An essay on perspective

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        <div xml:id="echoid-div154" type="section" level="1" n="83">
          <p>
            <s xml:id="echoid-s1110" xml:space="preserve">
              <pb o="43" file="0083" n="94" rhead="on PERSPECTIVE."/>
            Priſm is greater than the Height of the Eye, the
              <lb/>
            precedent Method is the ſhorteſt.</s>
            <s xml:id="echoid-s1111" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div156" type="section" level="1" n="84">
          <head xml:id="echoid-head90" xml:space="preserve">
            <emph style="sc">Problem</emph>
          IX.</head>
          <p style="it">
            <s xml:id="echoid-s1112" xml:space="preserve">62. </s>
            <s xml:id="echoid-s1113" xml:space="preserve">To throw a Concave Body into Perſpective.</s>
            <s xml:id="echoid-s1114" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Fig. 28.</note>
          <p>
            <s xml:id="echoid-s1115" xml:space="preserve">Having firſt ſound the Perſpective of the ſaid
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            Body, afterwards find the Appearance of its
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            Cavity, in conſidering the Cavity as a new
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            Body.</s>
            <s xml:id="echoid-s1116" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div157" type="section" level="1" n="85">
          <head xml:id="echoid-head91" xml:space="preserve">
            <emph style="sc">Problem</emph>
          X.</head>
          <p style="it">
            <s xml:id="echoid-s1117" xml:space="preserve">63. </s>
            <s xml:id="echoid-s1118" xml:space="preserve">To throw a Sphere into Perſpective.</s>
            <s xml:id="echoid-s1119" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Fig. 29.</note>
          <p>
            <s xml:id="echoid-s1120" xml:space="preserve">Let A be the Seat of the Centre of the Sphere;
              <lb/>
            </s>
            <s xml:id="echoid-s1121" xml:space="preserve">then the Point I the Perſpective of the Centre
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            muſt be found, and the Line IV drawn to
              <note symbol="*" position="right" xlink:label="note-0083-03" xlink:href="note-0083-03a" xml:space="preserve">50.</note>
            Point of Sight V. </s>
            <s xml:id="echoid-s1122" xml:space="preserve">This being done, raiſe V F per-
              <lb/>
            pendicular to V I, which make equal to the
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            Diſtance from the Eye to the perſpective Plane;
              <lb/>
            </s>
            <s xml:id="echoid-s1123" xml:space="preserve">and in this Perpendicular continued, take V P
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            equal to the Diſtance from the Centre of the
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            Sphere to the perſpective Plane. </s>
            <s xml:id="echoid-s1124" xml:space="preserve">Through the
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            Point P draw P Q parallel to V I cutting a Line
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            drawn from F through I, in Q; </s>
            <s xml:id="echoid-s1125" xml:space="preserve">and about Q as
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            a Centre, with the Semidiameter of the Sphere,
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            draw the Circle C B, to which from the Point F,
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            draw the Tangents F C and F B, cutting the
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            Line I V in the Points G and E. </s>
            <s xml:id="echoid-s1126" xml:space="preserve">On the Line
              <lb/>
            G E deſcribe the ſemicircle E D T G, wherein
              <lb/>
            draw the Line G D perpendicular to F I, which
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            biſect in H, and about H, as a Centre with the Ra-
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            dius H D, deſcribe the Arc of a Circle, L D R, cut-
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            ting the Line F I in the Points L and R. </s>
            <s xml:id="echoid-s1127" xml:space="preserve">Take
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            the Chord G T in the Semicircle E D T G equal
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            to R L, and deſcribe a Semicircle T m G upon
              <lb/>
            G T; </s>
            <s xml:id="echoid-s1128" xml:space="preserve">in which Semicircle draw ſeveral Lines,
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            as m n Perpendicular to G T; </s>
            <s xml:id="echoid-s1129" xml:space="preserve">and cutting </s>
          </p>
        </div>
      </text>
    </echo>
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