Gravesande, Willem Jacob 's, An essay on perspective

Table of contents

< >
[151.] Remarks.
Page: 162 (78)
[152.] Method III.
Page: 163 (79)
[153.] Operation.
Page: 163 (79)
[154.] Demonstration.
Page: 163 (79)
[155.] H I: T H:: a X: a T.
Page: 164 (80)
[156.] Prob. III.
Page: 164 (80)
[157.] Operation.
Page: 164 (80)
[158.] Demonstration.
Page: 164 (80)
[159.] Prob. IV.
Page: 165 (81)
[160.] Method II.
Page: 165 (81)
[161.] Operation.
Page: 165 (81)
[162.] Method III.
Page: 165 (81)
[163.] Remarks.
Page: 166 (82)
[164.] CHAP. VII. Of Shadows.
Page: 166 (82)
[165.] Of Solar Shadows. Problem I.
Page: 167 (83)
[166.] Operation.
Page: 168 (84)
[167.] Proe. II.
Page: 168 (84)
[168.] Remarks.
Page: 168 (84)
[169.] Problem III.
Page: 172 (85)
[170.] Of the Shadows of a ſmall Light. Prob. IV.
Page: 173 (86)
[171.] Problem V.
Page: 173 (86)
[172.] Remarks.
Page: 177 (87)
[173.] CHAP. VIII. Of mechanically ſhortning the Operations of Perſpective. 1. WHEN the perſpective Plane is ſup-pos’d perpendicular or upright. Problem I.
Page: 177 (87)
[174.] Operation.
Page: 178 (88)
[175.] Method II.
Page: 178 (88)
[176.] Prob. II.
Page: 182 (89)
[177.] Operation.
Page: 182 (89)
[178.] Method II.
Page: 183 (90)
[179.] Method III.
Page: 183 (90)
[180.] The Demonſtration of the two laſt Ways.
Page: 184 (91)
< >
page |< < (73) of 237 > >|
    <echo version="1.0RC">
      <text xml:lang="en" type="free">
        <div xml:id="echoid-div262" type="section" level="1" n="137">
          <p>
            <s xml:id="echoid-s1739" xml:space="preserve">
              <pb o="73" file="0131" n="151" rhead="on PERSPECTIVE."/>
            Point in reſpect to each other, in the before ſup-
              <lb/>
            poſed Plane. </s>
            <s xml:id="echoid-s1740" xml:space="preserve">Therefore the Line o F anſwers
              <lb/>
            @kewiſe to the Line in the ſaid Plane imagined
              <lb/>
            to be parallel to the propoſed Lines; </s>
            <s xml:id="echoid-s1741" xml:space="preserve">and con-
              <lb/>
            ſequently the Point F, is that wherein the
              <lb/>
            ſaid Parallel meets the Perſpective Plane; </s>
            <s xml:id="echoid-s1742" xml:space="preserve">and
              <lb/>
            therefore it is the accidental Point ſought.</s>
            <s xml:id="echoid-s1743" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1744" xml:space="preserve">Note, Iſ the accidental Point T of Perpendi-
              <lb/>
            culars to the Geometrical Plane be found, the
              <lb/>
            Operation of this Problem may be ſhorten’d, in
              <lb/>
            drawing the Line T D, which will neceſſarily
              <lb/>
            paſs thro’ the Point N, and then the Point o will
              <lb/>
            be found by the Interſection of the Arc O o,
              <lb/>
            and a Semi-circle, whoſe Diameter is T D.</s>
            <s xml:id="echoid-s1745" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div264" type="section" level="1" n="138">
          <head xml:id="echoid-head144" xml:space="preserve">
            <emph style="sc">Problem</emph>
          VI.</head>
          <p style="it">
            <s xml:id="echoid-s1746" xml:space="preserve">89. </s>
            <s xml:id="echoid-s1747" xml:space="preserve">To find the Perſpective of one or more Lines
              <lb/>
            inclin’d to the Geometrical Plane.</s>
            <s xml:id="echoid-s1748" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1749" xml:space="preserve">Let A be the Foot of a Line inclin’d to the
              <lb/>
              <note position="right" xlink:label="note-0131-01" xlink:href="note-0131-01a" xml:space="preserve">Fig. 48.</note>
            Geometrical Plane, and a its Repreſentation.
              <lb/>
            </s>
            <s xml:id="echoid-s1750" xml:space="preserve">Now determine, by Means of the Triangle C P E
              <lb/>
            according to the Manner lay’d down for
              <note symbol="*" position="right" xlink:label="note-0131-02" xlink:href="note-0131-02a" xml:space="preserve">69.</note>
            Perſpective Plane when ſuppoſed perpendicular,
              <lb/>
            the Length A B of the Direction of the propoſed
              <lb/>
            Line. </s>
            <s xml:id="echoid-s1751" xml:space="preserve">This being done, find the Point X the
              <note symbol="*" position="right" xlink:label="note-0131-03" xlink:href="note-0131-03a" xml:space="preserve">82.</note>
            ſpective of a Point above the Geometrical Plane
              <lb/>
            by the Length of P E; </s>
            <s xml:id="echoid-s1752" xml:space="preserve">and then a X will be the
              <lb/>
            Perſpective ſought.</s>
            <s xml:id="echoid-s1753" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div266" type="section" level="1" n="139">
          <head xml:id="echoid-head145" xml:space="preserve">
            <emph style="sc">Method</emph>
          II.</head>
          <p style="it">
            <s xml:id="echoid-s1754" xml:space="preserve">90. </s>
            <s xml:id="echoid-s1755" xml:space="preserve">To ſolve this Problem by the Accidental Points
              <lb/>
            of inclined Lines, and their Directions.</s>
            <s xml:id="echoid-s1756" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1757" xml:space="preserve">Let AB be the Direction of an inclin’d Line; </s>
            <s xml:id="echoid-s1758" xml:space="preserve">D
              <lb/>
              <note position="right" xlink:label="note-0131-04" xlink:href="note-0131-04a" xml:space="preserve">Fig. 48.</note>
            the Accidental Point of the Directions, & </s>
            <s xml:id="echoid-s1759" xml:space="preserve">F that </s>
          </p>
        </div>
      </text>
    </echo>
Impressum