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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          <p>
            <s xml:id="echoid-s1597" xml:space="preserve">
              <pb o="67" file="0121" n="139" rhead="on PERSPECTIVE."/>
            Line T B X; </s>
            <s xml:id="echoid-s1598" xml:space="preserve">which interſect in the Point X,
              <lb/>
            by a Perpendicular to the Baſe Line, in the
              <lb/>
            Point G; </s>
            <s xml:id="echoid-s1599" xml:space="preserve">and then the Point X is the Appear-
              <lb/>
            ance ſought.</s>
            <s xml:id="echoid-s1600" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div235" type="section" level="1" n="124">
          <head xml:id="echoid-head130" xml:space="preserve">
            <emph style="sc">Demonstration</emph>
          .</head>
          <p>
            <s xml:id="echoid-s1601" xml:space="preserve">In Fig. </s>
            <s xml:id="echoid-s1602" xml:space="preserve">44. </s>
            <s xml:id="echoid-s1603" xml:space="preserve">where V, S, T, and H, repreſent
              <lb/>
            the ſame Points as thoſe that are denoted with
              <lb/>
            the ſame Letters in this Figure; </s>
            <s xml:id="echoid-s1604" xml:space="preserve">we have,
              <lb/>
            </s>
          </p>
          <p>
            <s xml:id="echoid-s1605" xml:space="preserve">T H: </s>
            <s xml:id="echoid-s1606" xml:space="preserve">H S:</s>
            <s xml:id="echoid-s1607" xml:space="preserve">: T V: </s>
            <s xml:id="echoid-s1608" xml:space="preserve">V O.</s>
            <s xml:id="echoid-s1609" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1610" xml:space="preserve">Compon. </s>
            <s xml:id="echoid-s1611" xml:space="preserve">and altern.</s>
            <s xml:id="echoid-s1612" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1613" xml:space="preserve">T H: </s>
            <s xml:id="echoid-s1614" xml:space="preserve">T V:</s>
            <s xml:id="echoid-s1615" xml:space="preserve">: T H + H S: </s>
            <s xml:id="echoid-s1616" xml:space="preserve">T V + V O.</s>
            <s xml:id="echoid-s1617" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1618" xml:space="preserve">This being apply’d to Fig. </s>
            <s xml:id="echoid-s1619" xml:space="preserve">45. </s>
            <s xml:id="echoid-s1620" xml:space="preserve">and it will be,
              <lb/>
            T H: </s>
            <s xml:id="echoid-s1621" xml:space="preserve">T V:</s>
            <s xml:id="echoid-s1622" xml:space="preserve">: T S: </s>
            <s xml:id="echoid-s1623" xml:space="preserve">T V + V O.</s>
            <s xml:id="echoid-s1624" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1625" xml:space="preserve">If now T X be continued, till it cuts the Ho-
              <lb/>
            rizontal Line in F; </s>
            <s xml:id="echoid-s1626" xml:space="preserve">we ſhall have,</s>
          </p>
          <p>
            <s xml:id="echoid-s1627" xml:space="preserve">T H: </s>
            <s xml:id="echoid-s1628" xml:space="preserve">T V:</s>
            <s xml:id="echoid-s1629" xml:space="preserve">: T B: </s>
            <s xml:id="echoid-s1630" xml:space="preserve">T F.</s>
            <s xml:id="echoid-s1631" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1632" xml:space="preserve">And conſequently,</s>
          </p>
          <p>
            <s xml:id="echoid-s1633" xml:space="preserve">T B: </s>
            <s xml:id="echoid-s1634" xml:space="preserve">T F:</s>
            <s xml:id="echoid-s1635" xml:space="preserve">: T S: </s>
            <s xml:id="echoid-s1636" xml:space="preserve">T V + V O.</s>
            <s xml:id="echoid-s1637" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1638" xml:space="preserve">Whence it follows, that if a Line be drawn
              <lb/>
            ſrom the Eye, to the Point F, it will be paral-
              <lb/>
            lel to S B A. </s>
            <s xml:id="echoid-s1639" xml:space="preserve">Therefore the Perſpective
              <note symbol="*" position="right" xlink:label="note-0121-01" xlink:href="note-0121-01a" xml:space="preserve">13.</note>
            B A, is a Part of B X; </s>
            <s xml:id="echoid-s1640" xml:space="preserve">and ſo the Repreſenta-
              <lb/>
            tion of A is in the ſaid Line. </s>
            <s xml:id="echoid-s1641" xml:space="preserve">The Perſpective
              <lb/>
            of a Line perpendicular to the Geometrical
              <lb/>
            Plane, in the Point A, paſſes thro’ the Perſpe-
              <lb/>
            ctive of the Point A, and thro’ the Point T ;</s>
            <s xml:id="echoid-s1642" xml:space="preserve">
              <note symbol="*" position="right" xlink:label="note-0121-02" xlink:href="note-0121-02a" xml:space="preserve">13, 14.</note>
            therefore it is a Part of T X. </s>
            <s xml:id="echoid-s1643" xml:space="preserve">But the given Point
              <lb/>
            is in the aſoreſaid Perpendicular: </s>
            <s xml:id="echoid-s1644" xml:space="preserve">And ſo its Per-
              <lb/>
            ſpective is in T X.</s>
            <s xml:id="echoid-s1645" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1646" xml:space="preserve">Again; </s>
            <s xml:id="echoid-s1647" xml:space="preserve">it is otherwiſe manifeſt, that the Per-
              <lb/>
            ſpective of C L, is a Part of C X; </s>
            <s xml:id="echoid-s1648" xml:space="preserve">and
              <note symbol="*" position="right" xlink:label="note-0121-03" xlink:href="note-0121-03a" xml:space="preserve">41.</note>
            quently, the Appearance of L is in this Line.
              <lb/>
            </s>
            <s xml:id="echoid-s1649" xml:space="preserve">Now, if a Line be ſuppos’d to be drawn from
              <lb/>
            the Point L, thro’ the propos’d Point, it will be
              <lb/>
            parallel to the Vertical Line; </s>
            <s xml:id="echoid-s1650" xml:space="preserve">and ſo its
              <note symbol="*" position="right" xlink:label="note-0121-04" xlink:href="note-0121-04a" xml:space="preserve">6.</note>
            ſpective is parallel to the Baſe Line. </s>
            <s xml:id="echoid-s1651" xml:space="preserve">And </s>
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