Gravesande, Willem Jacob 's, An essay on perspective

Table of Notes

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            <emph style="sc">Theorem</emph>
          I.</head>
          <p style="it">
            <s xml:id="echoid-s269" xml:space="preserve">4. </s>
            <s xml:id="echoid-s270" xml:space="preserve">The Repreſentation of a Line Parallel to the
              <lb/>
              <note position="left" xlink:label="note-0024-01" xlink:href="note-0024-01a" xml:space="preserve">Fig. 3.</note>
            perſpective Plane, is parallel to the Line whereof it is
              <lb/>
            the Repreſentation.</s>
            <s xml:id="echoid-s271" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s272" xml:space="preserve">Let A B be a Line Parallel to the perſpective
              <lb/>
            Plane; </s>
            <s xml:id="echoid-s273" xml:space="preserve">we are to prove that a b its Repreſentati-
              <lb/>
            on is Parallel thereto.</s>
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          <p>
            <s xml:id="echoid-s275" xml:space="preserve">Theſe two Lines A B and a b, will never
              <lb/>
            meet each other, becauſe a b is in the perſpective
              <lb/>
            Plane, and A B is ſuppoſed parallel to the ſaid
              <lb/>
            Plane. </s>
            <s xml:id="echoid-s276" xml:space="preserve">But they are alſo in one and the ſame
              <lb/>
            Plane, becauſe a b is the Interſection of the per-
              <lb/>
            ſpective Plane, and the Plane O A B, paſſing
              <lb/>
            through the Eye and the Line A B; </s>
            <s xml:id="echoid-s277" xml:space="preserve">and there-
              <lb/>
            fore they are parallel between themſelves: </s>
            <s xml:id="echoid-s278" xml:space="preserve">Which
              <lb/>
            was to be demonſtrated.</s>
            <s xml:id="echoid-s279" xml:space="preserve"/>
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            <emph style="sc">Corollary</emph>
          I.</head>
          <p style="it">
            <s xml:id="echoid-s280" xml:space="preserve">5. </s>
            <s xml:id="echoid-s281" xml:space="preserve">The Appearance of a Line, parallel to the baſe
              <lb/>
            Line, is alſo parallel to the ſaid baſe Line.</s>
            <s xml:id="echoid-s282" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s283" xml:space="preserve">For the baſe Line, and the Repreſentation
              <lb/>
            being parallel to the ſame Line, are parallel to
              <lb/>
            one another.</s>
            <s xml:id="echoid-s284" xml:space="preserve"/>
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        <div xml:id="echoid-div31" type="section" level="1" n="12">
          <head xml:id="echoid-head14" xml:space="preserve">
            <emph style="sc">Corollary</emph>
          II.</head>
          <p style="it">
            <s xml:id="echoid-s285" xml:space="preserve">6. </s>
            <s xml:id="echoid-s286" xml:space="preserve">The Repreſentation of a Line parallel to the
              <lb/>
            vertical Line, is parallel to the ſaid vertical Line, and
              <lb/>
            conſequently perpendicular to the baſe Line. </s>
            <s xml:id="echoid-s287" xml:space="preserve">This
              <lb/>
            is demonſtrated as in the laſt Corollary.</s>
            <s xml:id="echoid-s288" xml:space="preserve"/>
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          <head xml:id="echoid-head15" xml:space="preserve">
            <emph style="sc">Corollary</emph>
          III.</head>
          <p style="it">
            <s xml:id="echoid-s289" xml:space="preserve">7. </s>
            <s xml:id="echoid-s290" xml:space="preserve">The Appearances of Lines parallel to the per-
              <lb/>
            ſpective Plane, and equally inclin’d the ſame Way </s>
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Impressum