Gravesande, Willem Jacob 's, An essay on perspective

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          <p>
            <s xml:id="echoid-s1725" xml:space="preserve">
              <pb o="72" file="0128" n="147" rhead="An ESSAY"/>
            draw S N perpendicular to the ſaid Line A B,
              <lb/>
            cutting the Baſe Line in N, and draw the Line
              <lb/>
            N D. </s>
            <s xml:id="echoid-s1726" xml:space="preserve">Then about the Point D, as a Center, and
              <lb/>
            with the Radius D O, deſcribe the Circular Arc
              <lb/>
            O o: </s>
            <s xml:id="echoid-s1727" xml:space="preserve">And about N, as a Center, with the Radius
              <lb/>
            N S, draw the Circular Arc S s. </s>
            <s xml:id="echoid-s1728" xml:space="preserve">This being done,
              <lb/>
            draw the Line s o touching the ſaid two Arcs,
              <lb/>
            and the Line D o perpendicular to s o. </s>
            <s xml:id="echoid-s1729" xml:space="preserve">Then
              <lb/>
            draw o F, making an Angle with o D, equal to
              <lb/>
            the Angle of the Inclination of the Lines given,
              <lb/>
            and cutting N D continued in F: </s>
            <s xml:id="echoid-s1730" xml:space="preserve">Now I ſay F
              <lb/>
            is the Accidental Point ſought when the Lines
              <lb/>
            do not incline towards the Perſpective Plane:
              <lb/>
            </s>
            <s xml:id="echoid-s1731" xml:space="preserve">But if they do, o F muſt be drawn below o D.</s>
            <s xml:id="echoid-s1732" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div262" type="section" level="1" n="137">
          <head xml:id="echoid-head143" xml:space="preserve">
            <emph style="sc">Demonstration</emph>
          .</head>
          <p>
            <s xml:id="echoid-s1733" xml:space="preserve">If a Plane be ſuppoſed to paſs thro’ the Eye
              <lb/>
            parallel to theinclin’d Lines; </s>
            <s xml:id="echoid-s1734" xml:space="preserve">the common Secti-
              <lb/>
            ons of this Plane, and the Horizontal and Geo-
              <lb/>
            metrical Planes, will be O D and S N. </s>
            <s xml:id="echoid-s1735" xml:space="preserve">It is
              <lb/>
            now manifeſt, that if a Line be drawn in the
              <lb/>
            ſaid Plane, below the Horizontal Plane, when
              <lb/>
            the Lines incline towards the perſpective Plane,
              <lb/>
            and above it when they incline the other way,
              <lb/>
            making an Angle with O D equal to the Angle
              <lb/>
            of Inclination of the propoſed Lines; </s>
            <s xml:id="echoid-s1736" xml:space="preserve">I ſay it is
              <lb/>
            manifeſt, that the ſaid Line will be parallel to
              <lb/>
            the propoſed Lines, and will meet the
              <note symbol="*" position="left" xlink:label="note-0128-01" xlink:href="note-0128-01a" xml:space="preserve">13, 14.</note>
            ctive Plane in the Accidental Point ſought. </s>
            <s xml:id="echoid-s1737" xml:space="preserve">If
              <lb/>
            now the before ſuppoſed Plane be conceiv’d to
              <lb/>
            turn about the Line N D, the Eye, and the
              <lb/>
            Station Point in the ſaid Plain, will then meet
              <lb/>
            the perſpective Plane in the Points o and s; </s>
            <s xml:id="echoid-s1738" xml:space="preserve">for
              <lb/>
            the Lines D o and N s are equal to D O and N S,
              <lb/>
            and form right Angles with the Line s o joyning
              <lb/>
            their Extremities. </s>
            <s xml:id="echoid-s1739" xml:space="preserve">Now the two Points s and o
              <lb/>
            anſwer to the Situation of the Eye and </s>
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