Gravesande, Willem Jacob 's, An essay on perspective

Table of contents

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[171.] Problem V.
[172.] Remarks.
[173.] CHAP. VIII. Of mechanically ſhortning the Operations of Perſpective. 1. WHEN the perſpective Plane is ſup-pos’d perpendicular or upright. Problem I.
[174.] Operation.
[175.] Method II.
[176.] Prob. II.
[177.] Operation.
[178.] Method II.
[179.] Method III.
[180.] The Demonſtration of the two laſt Ways.
[181.] II. When the Perſpective Plane is inclined. Prob. III.
[182.] Prob. IV.
[183.] Remarks.
[184.] III. When the Perſpective Plane is Parallel or Horizontal. Prob. V.
[185.] Operation.
[186.] Demonstration.
[187.] Remarks.
[188.] Prob. VI.
[189.] Demonstration.
[190.] Prob. VII.
[191.] CHAP. IX.
[192.] Prob. I. 122. To draw Vertical Dials.
[193.] Demonstration.
[194.] Remark.
[195.] Prob. II. 123. To draw inclining Dials.
[196.] The Uſe of the Camera Obscura in Deſigning. Advertisement.
[197.] The Uſe of the Camera Obscura in Deſigning. Definition.
[198.] Theorem I.
[199.] Theorem II.
[200.] The Deſcription of the Firſt Machine.
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        <div xml:id="echoid-div320" type="section" level="1" n="173">
          <p>
            <s xml:id="echoid-s2015" xml:space="preserve">
              <pb o="88" file="0154" n="178" rhead="An ESSAY on"/>
            ner, that right Lines drawn along one of its Sides,
              <lb/>
            may paſs through the Point G. </s>
            <s xml:id="echoid-s2016" xml:space="preserve">This being done,
              <lb/>
            faſten one End of a Thread, put through the Eye
              <lb/>
            of a Needle B, in the Point F; </s>
            <s xml:id="echoid-s2017" xml:space="preserve">and then put the
              <lb/>
            ſaid Thread about a Pin faſten’d in the Point O;
              <lb/>
            </s>
            <s xml:id="echoid-s2018" xml:space="preserve">ſo that when the Thread is uſing, it may be al-
              <lb/>
            ways kept tight by means of a Plummet fix’d to
              <lb/>
            its other End, and freely hanging under the Tube. </s>
            <s xml:id="echoid-s2019" xml:space="preserve">
              <lb/>
            Note, The aforeſaid Needle onght to be Braſs or
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            Silver, ſharp at both Ends, and having its Eye
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            pretty near one of them.</s>
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        <div xml:id="echoid-div322" type="section" level="1" n="174">
          <head xml:id="echoid-head186" xml:space="preserve">
            <emph style="sc">Operation</emph>
          .</head>
          <p>
            <s xml:id="echoid-s2021" xml:space="preserve">Let A be a Point of the Figure to be thrown
              <lb/>
            into Perſpective. </s>
            <s xml:id="echoid-s2022" xml:space="preserve">Now place that of the two
              <lb/>
            Points of the Needle, which is nigheſt to the
              <lb/>
            Eye thereof, upon the ſaid Point A, and move
              <lb/>
            the Ruler G E, until it cuts the Thread A F, in
              <lb/>
            the Point E, wherein the ſaid Thread cuts the
              <lb/>
            Baſe Line; </s>
            <s xml:id="echoid-s2023" xml:space="preserve">and then the Point a, wherein the
              <lb/>
            Ruler cuts the Thread A O, is the Point ſought,
              <lb/>
            and it may be marked with that Point of the
              <lb/>
            Needle fartheſt diſtant from its Eye, having firſt
              <lb/>
            preſſed the Ruler down upon the Paper and Thread,
              <lb/>
            that ſo the Plummet may not make the Thread
              <lb/>
            ſlip. </s>
            <s xml:id="echoid-s2024" xml:space="preserve">And in this manner may any Number of
              <lb/>
            Points be found. </s>
            <s xml:id="echoid-s2025" xml:space="preserve">This is demonſtrated in N. </s>
            <s xml:id="echoid-s2026" xml:space="preserve">32.
              <lb/>
            </s>
            <s xml:id="echoid-s2027" xml:space="preserve">Sometimes it is more convenient to uſe the fol-
              <lb/>
            lowing Method.</s>
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        <div xml:id="echoid-div323" type="section" level="1" n="175">
          <head xml:id="echoid-head187" xml:space="preserve">
            <emph style="sc">Method</emph>
          II.</head>
          <p>
            <s xml:id="echoid-s2029" xml:space="preserve">110. </s>
            <s xml:id="echoid-s2030" xml:space="preserve">Let O be the Eye, H E the Baſe Line,
              <lb/>
              <note position="left" xlink:label="note-0154-01" xlink:href="note-0154-01a" xml:space="preserve">Fig. 61.</note>
            and F I the Geometrical Line. </s>
            <s xml:id="echoid-s2031" xml:space="preserve">Take a Ruler
              <lb/>
            M N, having two Threads equal in Length
              <lb/>
            faſten’d to it, and about O as a Center, and </s>
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