Gravesande, Willem Jacob 's, An essay on perspective

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        <div xml:id="echoid-div275" type="section" level="1" n="145">
          <p>
            <s xml:id="echoid-s1791" xml:space="preserve">
              <pb o="76" file="0136" n="157" rhead="An ESSAY"/>
            Plane; </s>
            <s xml:id="echoid-s1792" xml:space="preserve">and at the Points R and S, raiſe the in-
              <lb/>
            definite perpendiculars R G and S M; </s>
            <s xml:id="echoid-s1793" xml:space="preserve">and aſſume
              <lb/>
            the Point M at Pleaſure on S M; </s>
            <s xml:id="echoid-s1794" xml:space="preserve">from which
              <lb/>
            raiſe the Perpendicular M N, equal to the given
              <lb/>
            Line, and draw the Lines M O and N O, cutting
              <lb/>
              <note position="left" xlink:label="note-0136-01" xlink:href="note-0136-01a" xml:space="preserve">Fig. 41.</note>
            the Line R G in the Points E and G. </s>
            <s xml:id="echoid-s1795" xml:space="preserve">Then
              <lb/>
            having drawn a Line at Pleaſure in the per-
              <lb/>
            ſpective Plane through the Point T, which is
              <lb/>
            that wherein a Perpendicular falling from the
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            Eye on the perſpective Plane meets it, aſſume
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            T H in the ſaid Line, equal to R E, and T I e-
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            qual to R G; </s>
            <s xml:id="echoid-s1796" xml:space="preserve">draw the Lines Ta, Ha, through
              <lb/>
            the Point a, the Perſpective of the Foot of the
              <lb/>
            given Perpendicular, and through the Point I,
              <lb/>
            the Line I X, parallel to Ha, and cutting Ta
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            in X, then a X will be the Appearance ſought.</s>
            <s xml:id="echoid-s1797" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div277" type="section" level="1" n="146">
          <head xml:id="echoid-head152" xml:space="preserve">
            <emph style="sc">Demonstration</emph>
          .</head>
          <p>
            <s xml:id="echoid-s1798" xml:space="preserve">It is manifeſt , that the Point T, is the
              <note symbol="*" position="left" xlink:label="note-0136-02" xlink:href="note-0136-02a" xml:space="preserve">13, 14.</note>
            dental Point of Lines perpendicular to the Geo-
              <lb/>
            metrical Plane; </s>
            <s xml:id="echoid-s1799" xml:space="preserve">and conſequently the Per-
              <lb/>
            ſpective ſought is a Part of T a. </s>
            <s xml:id="echoid-s1800" xml:space="preserve">Moreover, it
              <lb/>
            is manifeſt , that if the Feet and
              <note symbol="*" position="left" xlink:label="note-0136-03" xlink:href="note-0136-03a" xml:space="preserve">4.</note>
            of two equal right Lines, perpendicular to the
              <lb/>
            Geometrical Plane be joyn’d by Lines, theſe
              <lb/>
            Lines of Junction will have parallel Repreſen-
              <lb/>
            tations; </s>
            <s xml:id="echoid-s1801" xml:space="preserve">becauſe they are parallel to each other,
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            as likewiſe to the perſpective Plane. </s>
            <s xml:id="echoid-s1802" xml:space="preserve">And con-
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            ſequently, ſince H I, by Conſtruction, is the
              <lb/>
            Perſpective of a Line perpendicular to the
              <lb/>
            Geometrical Plane, and equal to the given Line,
              <lb/>
            and H a paſſes through the Appearances of the
              <lb/>
            Foot of the ſaid Perpendicular, and the given
              <lb/>
            Perpendicular; </s>
            <s xml:id="echoid-s1803" xml:space="preserve">I ſay, that X I, which is paral-
              <lb/>
            lel to Ha, and paſſes through the Extremity of
              <lb/>
            the Appeaarance H I, likewiſe paſſes through
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            the Extremity of the given Line; </s>
            <s xml:id="echoid-s1804" xml:space="preserve">and </s>
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