Gravesande, Willem Jacob 's, An essay on perspective

Table of Notes

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          <p>
            <s xml:id="echoid-s2133" xml:space="preserve">
              <pb o="95" file="0165" n="191" rhead="on PERSPECTIVE."/>
            lar drawn from the Eye to the Geometrical
              <lb/>
            Plane, meets the ſaid Plane; </s>
            <s xml:id="echoid-s2134" xml:space="preserve">and T the Per-
              <lb/>
            ſpective of that Point, found by the aforegoing
              <lb/>
            Problem. </s>
            <s xml:id="echoid-s2135" xml:space="preserve">Now make F L and C R, equal to the
              <lb/>
            Length of the given Lines; </s>
            <s xml:id="echoid-s2136" xml:space="preserve">and about the
              <lb/>
            Points R and S, as Centers, with the Radius
              <lb/>
            M N or P Q, deſcribe two Arcs cutting the
              <lb/>
            Perpendiculars H D and G H, in the Points
              <lb/>
            X and S: </s>
            <s xml:id="echoid-s2137" xml:space="preserve">Then fix the Extremities of the
              <lb/>
            Threads, which before were faſten’d to the
              <lb/>
            Points F and E, to the Points L and S; </s>
            <s xml:id="echoid-s2138" xml:space="preserve">and alſo
              <lb/>
            the Extremities of thoſe two Threads, which
              <lb/>
            were before faſten’d to the Points C and D, in
              <lb/>
            the Points R and X: </s>
            <s xml:id="echoid-s2139" xml:space="preserve">Then moving the two
              <lb/>
            Rulers, until the Threads S P and X M, croſs
              <lb/>
            each other in the Point T, mark the Point O,
              <lb/>
            wherein the two other Threads croſs one another,
              <lb/>
            through which, and the Point B, draw the
              <lb/>
            indefinite Line B O V: </s>
            <s xml:id="echoid-s2140" xml:space="preserve">this being done, tranſ-
              <lb/>
            poſe the Lines of the Geometrical Plane, ſo that
              <lb/>
            the Point B, coincides with the Point O, and
              <lb/>
            the Line B O, with O V. </s>
            <s xml:id="echoid-s2141" xml:space="preserve">And by the precedent
              <lb/>
            Problem, find the Appearances of the Feet of
              <lb/>
            the Perpendiculars, and you will have the Re-
              <lb/>
            preſentations of their Extremities.</s>
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        <div xml:id="echoid-div347" type="section" level="1" n="189">
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            <emph style="sc">Demonstration</emph>
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          <p>
            <s xml:id="echoid-s2143" xml:space="preserve">If a Plane be ſuppoſed to paſs through the
              <lb/>
            Extremities of the Perpendiculars, it will be
              <lb/>
            parallel to the Geometrical Plane, and conſe-
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            quently, likewiſe to the perſpective Plane, be-
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            cauſe all the Perpendiculars are ſuppoſed equal.
              <lb/>
            </s>
            <s xml:id="echoid-s2144" xml:space="preserve">But the Figure formed by the Extremities of
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            the Perpendiculars in the ſaid Plane, is ſimilar
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            and equal to that form’d by their Feet in the
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            Geometrical Plane: </s>
            <s xml:id="echoid-s2145" xml:space="preserve">and therefore, the </s>
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