Gravesande, Willem Jacob 's, An essay on perspective

Table of contents

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[181.] II. When the Perſpective Plane is inclined. Prob. III.
Page: 185 (92)
[182.] Prob. IV.
Page: 185 (92)
[183.] Remarks.
Page: 185 (92)
[184.] III. When the Perſpective Plane is Parallel or Horizontal. Prob. V.
Page: 189 (93)
[185.] Operation.
Page: 189 (93)
[186.] Demonstration.
Page: 190 (94)
[187.] Remarks.
Page: 190 (94)
[188.] Prob. VI.
Page: 190 (94)
[189.] Demonstration.
Page: 191 (95)
[190.] Prob. VII.
Page: 192 (96)
[191.] CHAP. IX.
Page: 199 (97)
[192.] Prob. I. 122. To draw Vertical Dials.
Page: 200 (98)
[193.] Demonstration.
Page: 201 (99)
[194.] Remark.
Page: 201 (99)
[195.] Prob. II. 123. To draw inclining Dials.
Page: 201 (99)
[196.] The Uſe of the Camera Obscura in Deſigning. Advertisement.
Page: 206 (101)
[197.] The Uſe of the Camera Obscura in Deſigning. Definition.
Page: 208 (103)
[198.] Theorem I.
Page: 208 (103)
[199.] Theorem II.
Page: 209 (104)
[200.] The Deſcription of the Firſt Machine.
Page: 209 (104)
[201.] Remarks.
Page: 212 (107)
[202.] Uſe of the Machine. Problem I.
Page: 212 (107)
[203.] Demonstration. Concerning the before-mention’d Inclination of the Mirrours.
Page: 214 (109)
[204.] Prob. II.
Page: 215 (110)
[205.] Prop. III.
Page: 218 (113)
[206.] Problem IV.
Page: 219 (114)
[207.] As the Machine’s Height above the Table, leſs the Glaſs’s focal Length, is to
Page: 219 (114)
[208.] The Height of the Machine above the Table; So is The Glaſſes focal Length, to the Diſtance of the Figure from the Glaſs.
Page: 220 (115)
[209.] 37 Remarks concerning the Repreſentation of Per-ſons Faces.
Page: 220 (115)
[210.] A Deſcription of the Second Machine.
Page: 222 (117)
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          <p>
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              <pb o="91" file="0159" n="184" rhead="on PERSPECTIVE."/>
            in the Perpendicular R S, continued equal to R S,
              <lb/>
            and draw f i parallel to the Baſe Line, in which
              <lb/>
            take the Point f in E I, the ſame as F in F I ; </s>
            <s xml:id="echoid-s2069" xml:space="preserve">
              <note symbol="*" position="right" xlink:label="note-0159-01" xlink:href="note-0159-01a" xml:space="preserve">110.</note>
            if the Threads which before were faſten’d in F,
              <lb/>
            being placed in f, and by uſing them thus faſten’d,
              <lb/>
            as likewiſe S Q for a Baſe Line, the Repreſen-
              <lb/>
            tations of the Feet of the Perpendiculars be
              <lb/>
            found , you will have the Repreſentations
              <note symbol="*" position="right" xlink:label="note-0159-02" xlink:href="note-0159-02a" xml:space="preserve">110.</note>
            their Extremities.</s>
            <s xml:id="echoid-s2070" xml:space="preserve"/>
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        <div xml:id="echoid-div332" type="section" level="1" n="180">
          <head xml:id="echoid-head192" style="it" xml:space="preserve">The Demonſtration of the two laſt Ways.</head>
          <p>
            <s xml:id="echoid-s2071" xml:space="preserve">114. </s>
            <s xml:id="echoid-s2072" xml:space="preserve">If a Plane be imagined to paſs through
              <lb/>
              <note position="right" xlink:label="note-0159-03" xlink:href="note-0159-03a" xml:space="preserve">Fig. 60,
                <lb/>
              and 61.</note>
            the Extremities of the equal Perpendiculars, it
              <lb/>
            will be parallel to the Geometrical Plane, and
              <lb/>
            will meet the perſpective Plane in S Q; </s>
            <s xml:id="echoid-s2073" xml:space="preserve">becauſe
              <lb/>
            R S is equal to the ſaid Perpendiculars: </s>
            <s xml:id="echoid-s2074" xml:space="preserve">Moreover,
              <lb/>
            the Extremities of theſe Perpendiculars form a
              <lb/>
            Figure in this ſuppoſed Plane, ſimilar to that
              <lb/>
            which their Feet form in the Geometrical Plane;
              <lb/>
            </s>
            <s xml:id="echoid-s2075" xml:space="preserve">and the ſaid Figure hath the ſame Situation with
              <lb/>
            regard to the Line Q S, as that on the Geome-
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            trical Plane hath in reſpect of H R: </s>
            <s xml:id="echoid-s2076" xml:space="preserve">And conſe-
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            quently, if the Figure in the Geometrical Plane
              <lb/>
            be ſo raiſed up, that it hath the ſame Reſpect to
              <lb/>
            Q S, as it had to H R, and if the Appearances
              <lb/>
            of the Feet of the propoſed Perpendiculars be
              <lb/>
            found, the Repreſentations of their Extremties
              <lb/>
            will be had. </s>
            <s xml:id="echoid-s2077" xml:space="preserve">But the before ſuppoſed Tranſpo-
              <lb/>
            ſition of the Figure in the Geometrical Plane,
              <lb/>
            gives it the requiſite Situation with regard to
              <lb/>
            Q S, and the Repreſentation of the Figure
              <lb/>
            conſider’d in this new Geometrical Plane is
              <lb/>
            found ; </s>
            <s xml:id="echoid-s2078" xml:space="preserve">becauſe S Q, is taken for the Baſe
              <note symbol="*" position="right" xlink:label="note-0159-04" xlink:href="note-0159-04a" xml:space="preserve">32, 39.</note>
            O f (Fig. </s>
            <s xml:id="echoid-s2079" xml:space="preserve">60.) </s>
            <s xml:id="echoid-s2080" xml:space="preserve">equal to the Height of the Eye
              <lb/>
            above this Plane, and fi (Fig. </s>
            <s xml:id="echoid-s2081" xml:space="preserve">61.) </s>
            <s xml:id="echoid-s2082" xml:space="preserve">is the Geo-
              <lb/>
            metrical Line in the ſaid Plane.</s>
            <s xml:id="echoid-s2083" xml:space="preserve"/>
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