Gravesande, Willem Jacob 's, An essay on perspective

Table of handwritten notes

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        <div xml:id="echoid-div144" type="section" level="1" n="78">
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          <p>
            <s xml:id="echoid-s1052" xml:space="preserve">Now we have proved, that F G is the half of
              <lb/>
            F B, therefore G N is likewiſe equal to the half
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            of B L, and conſequently equal to the Height
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            of the ſuppoſed Perpendicular.</s>
            <s xml:id="echoid-s1053" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1054" xml:space="preserve">Again, the ſimilar Triangles F G N and F a I
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            give</s>
          </p>
          <p style="it">
            <s xml:id="echoid-s1055" xml:space="preserve">F G : </s>
            <s xml:id="echoid-s1056" xml:space="preserve">F a : </s>
            <s xml:id="echoid-s1057" xml:space="preserve">: </s>
            <s xml:id="echoid-s1058" xml:space="preserve">G N : </s>
            <s xml:id="echoid-s1059" xml:space="preserve">a I.</s>
            <s xml:id="echoid-s1060" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1061" xml:space="preserve">But F G : </s>
            <s xml:id="echoid-s1062" xml:space="preserve">F a : </s>
            <s xml:id="echoid-s1063" xml:space="preserve">: </s>
            <s xml:id="echoid-s1064" xml:space="preserve">G D : </s>
            <s xml:id="echoid-s1065" xml:space="preserve">a H; </s>
            <s xml:id="echoid-s1066" xml:space="preserve">becauſe the Tri-
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            angles F G D and F a H are ſimilar.</s>
            <s xml:id="echoid-s1067" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1068" xml:space="preserve">Whence</s>
          </p>
          <p style="it">
            <s xml:id="echoid-s1069" xml:space="preserve">G N : </s>
            <s xml:id="echoid-s1070" xml:space="preserve">a I : </s>
            <s xml:id="echoid-s1071" xml:space="preserve">: </s>
            <s xml:id="echoid-s1072" xml:space="preserve">G D : </s>
            <s xml:id="echoid-s1073" xml:space="preserve">a H.</s>
            <s xml:id="echoid-s1074" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1075" xml:space="preserve">Now becauſe G N has been proved to be e-
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            qual to the Perpendicular, whoſe Perſpective is
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            requir’d and D G is ſuppoſed equal to that Per-
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            pendicular; </s>
            <s xml:id="echoid-s1076" xml:space="preserve">it follows, that G N and G D are
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            equal; </s>
            <s xml:id="echoid-s1077" xml:space="preserve">and therefore a I and a H are alſo equal.
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            </s>
            <s xml:id="echoid-s1078" xml:space="preserve">Q E D.</s>
            <s xml:id="echoid-s1079" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div146" type="section" level="1" n="79">
          <head xml:id="echoid-head85" xml:space="preserve">
            <emph style="sc">Scholium</emph>
          .</head>
          <p>
            <s xml:id="echoid-s1080" xml:space="preserve">I might have aſſumed C P equal to the Perpen-
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            dicular, and uſed the Points C and P inſtead of
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            B and L. </s>
            <s xml:id="echoid-s1081" xml:space="preserve">But uſing the ſaid Points B and L is
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            better: </s>
            <s xml:id="echoid-s1082" xml:space="preserve">For when the Points C and P are uſed,
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            the Horizontal Line muſt almoſt always be con-
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            tinued, that ſo a Line drawn through the Points
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            c and a may cut it; </s>
            <s xml:id="echoid-s1083" xml:space="preserve">moreover this Interſection
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            will ſometimes be at an infinite Diſtance; </s>
            <s xml:id="echoid-s1084" xml:space="preserve">where-
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            as in uſing the Point B, M N can never be
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            greater than thrice the Breadth of the Deſign to
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            be drawn.</s>
            <s xml:id="echoid-s1085" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div147" type="section" level="1" n="80">
          <head xml:id="echoid-head86" xml:space="preserve">
            <emph style="sc">Corollary</emph>
          .</head>
          <p>
            <s xml:id="echoid-s1086" xml:space="preserve">The ſixth Problem may be ſolv’d by this;
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            </s>
            <s xml:id="echoid-s1087" xml:space="preserve">for a Point elevated above the Geometrical
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            Plane, may be conceived as the Extremity of a
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            Perpendicular to the Geometrical Plane.</s>
            <s xml:id="echoid-s1088" xml:space="preserve"/>
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