Gravesande, Willem Jacob 's, An essay on perspective

Table of contents

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[121.] Problem I.
[122.] Problem II.
[123.] Operation.
[124.] Demonstration.
[125.] Remark.
[126.] Problem III.
[127.] Method II.
[128.] Operation.
[129.] Demonstration.
[130.] Method III.
[131.] Operation.
[132.] Demonstration.
[133.] Remark.
[134.] Problem IV.
[135.] Problem V.
[136.] Operation.
[137.] Demonstration.
[138.] Problem VI.
[139.] Method II.
[140.] Operation.
[141.] Demonstration.
[142.] Method III.
[143.] CHAP. VI.
[144.] Prob. I.
[145.] Prob. II.
[146.] Demonstration.
[147.] Corollary.
[148.] Method II.
[149.] Operation,
[150.] Demonstration.
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            fore the Point X is the Repreſentation of the
              <lb/>
            ſaid Extremity.</s>
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        <div xml:id="echoid-div279" type="section" level="1" n="147">
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            <emph style="sc">Corollary</emph>
          .</head>
          <p>
            <s xml:id="echoid-s1806" xml:space="preserve">94. </s>
            <s xml:id="echoid-s1807" xml:space="preserve">It is manifeſt from hence, that when the
              <lb/>
            Perſpective of a Line, perpendicular to the
              <lb/>
            Geometrical Plane is once found, it is eaſy af-
              <lb/>
            terwards to find the Repreſentations of any Per-
              <lb/>
            pendiculars of the ſame Length as that.</s>
            <s xml:id="echoid-s1808" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div280" type="section" level="1" n="148">
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            <emph style="sc">Method</emph>
          II.</head>
          <p style="it">
            <s xml:id="echoid-s1809" xml:space="preserve">The Perſpective Plane being conſider’d as the Geo-
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            metrical Plane.</s>
            <s xml:id="echoid-s1810" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s1811" xml:space="preserve">95. </s>
            <s xml:id="echoid-s1812" xml:space="preserve">Let T (as in Fig. </s>
            <s xml:id="echoid-s1813" xml:space="preserve">51.) </s>
            <s xml:id="echoid-s1814" xml:space="preserve">be the accidental
              <lb/>
              <note position="right" xlink:label="note-0139-01" xlink:href="note-0139-01a" xml:space="preserve">Fig. 53.</note>
            Point of perpendicular Lines to the Geometri-
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            cal Plane; </s>
            <s xml:id="echoid-s1815" xml:space="preserve">H I the Arc of a Circle, whoſe Cen-
              <lb/>
            ter is T, and ſemidiameter the Eye’s Diſtance
              <lb/>
            from the perſpective Plane: </s>
            <s xml:id="echoid-s1816" xml:space="preserve">Alſo let a be the
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            Point where the Perpendicular, whoſe Appear-
              <lb/>
            ance is ſought, meets the perſpective Plane, and
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            B C the Length of this Perpendicular.</s>
            <s xml:id="echoid-s1817" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div282" type="section" level="1" n="149">
          <head xml:id="echoid-head155" xml:space="preserve">
            <emph style="sc">Operation</emph>
          ,</head>
          <p>
            <s xml:id="echoid-s1818" xml:space="preserve">About the Point a, as a Center, and with the
              <lb/>
            Semidiameter B C, deſcribe the Circle L F, and
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            draw the Line I L, or H F, touching each of the
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            Circles H I, and F L; </s>
            <s xml:id="echoid-s1819" xml:space="preserve">and then a X or a x, is
              <lb/>
            the Appearance ſought, viz. </s>
            <s xml:id="echoid-s1820" xml:space="preserve">a X, when the Per-
              <lb/>
            pendicular is above that Surface of the per-
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            ſpective Plane next to the Eye, and a x, when
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            the Perpendicular is on the oppoſite Side.</s>
            <s xml:id="echoid-s1821" xml:space="preserve"/>
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        <div xml:id="echoid-div283" type="section" level="1" n="150">
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            <emph style="sc">Demonstration</emph>
          .</head>
          <p>
            <s xml:id="echoid-s1822" xml:space="preserve">Draw the Radii a F, a L, T I, T H, to the
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            Points of Contact F, L, I, and H. </s>
            <s xml:id="echoid-s1823" xml:space="preserve">Then </s>
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