Harriot, Thomas, Mss. 6784

List of thumbnails

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521
521 (261) 		522
522 (261v)
523
523 (262) 		524
524 (262v)
525
525 (263) 		526
526 (263v)
527
527 (264) 		528
528 (264v)
529
529 (265) 		530
530 (265v)
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page |< < (291) of 862 > >|
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          <pb file="add_6784_f291" o="291" n="581"/>
          <div type="page_commentary" level="0" n="0">
            <p>
              <s xml:space="preserve">[
                <emph style="bf">Commentary:</emph>
              </s>
            </p>
            <p>
              <s xml:space="preserve"> The problem pursued in this and many other folios in Add MS 6784 is that of 'inclination' or 'neusis', as set out in Pappus,
                <emph style="it">Mathematicae collectiones</emph>
                <ref id="pappus_1588"> (Pappus </ref>
              , Book 7. In Commandino's edition of 1588, the problem is stated on page 163v. </s>
              <lb/>
              <quote xml:lang="lat">
                <s xml:space="preserve"> Duabus lineis positione datis inter ipsas ponere rectam lineam magnitudine datam, quæ ad datum punctum </s>
              </quote>
              <lb/>
              <quote>
                <s xml:space="preserve"> Given two lines in position, place between them a line of given magnitude, which relates to a given </s>
              </quote>
              <s xml:space="preserve">]</s>
            </p>
          </div>
          <head xml:space="preserve" xml:lang="lat"> De inclinationibus. prop.
            <lb/>
          [
            <emph style="bf">Translation: </emph>
          On neusis, proposition ]</head>
          <p xml:lang="lat">
            <s xml:space="preserve"> Sit semicirculus
              <math>
                <mstyle>
                  <mi>A</mi>
                  <mi>D</mi>
                  <mi>B</mi>
                </mstyle>
              </math>
            .
              <math>
                <mstyle>
                  <mi>B</mi>
                  <mi>C</mi>
                </mstyle>
              </math>
            perpendicularis
              <lb/>
            ad
              <math>
                <mstyle>
                  <mi>A</mi>
                  <mi>B</mi>
                </mstyle>
              </math>
            . A puncto
              <math>
                <mstyle>
                  <mi>A</mi>
                </mstyle>
              </math>
            ducere rectam ad
              <math>
                <mstyle>
                  <mi>C</mi>
                </mstyle>
              </math>
            ut
              <lb/>
              <math>
                <mstyle>
                  <mi>D</mi>
                  <mi>C</mi>
                </mstyle>
              </math>
            sit æqualis
              <math>
                <mstyle>
                  <mi>H</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Let there be a semicircle
              <math>
                <mstyle>
                  <mi>A</mi>
                  <mi>D</mi>
                  <mi>B</mi>
                </mstyle>
              </math>
            . The line
              <math>
                <mstyle>
                  <mi>B</mi>
                  <mi>C</mi>
                </mstyle>
              </math>
            is perpendicular to
              <math>
                <mstyle>
                  <mi>A</mi>
                  <mi>B</mi>
                </mstyle>
              </math>
            . From the point
              <math>
                <mstyle>
                  <mi>A</mi>
                </mstyle>
              </math>
            , draw a line to
              <math>
                <mstyle>
                  <mi>C</mi>
                </mstyle>
              </math>
            so that
              <math>
                <mstyle>
                  <mi>D</mi>
                  <mi>C</mi>
                </mstyle>
              </math>
            is equal to
              <math>
                <mstyle>
                  <mi>H</mi>
                </mstyle>
              </math>
            . </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Nota pro effectionibus.
              <lb/>
            Effectio huius æquationis est in altera
              <lb/>
            charta, per quam data (
              <math>
                <mstyle>
                  <mi>a</mi>
                </mstyle>
              </math>
            ), dabitur etiam
              <lb/>
            (
              <math>
                <mstyle>
                  <mi>a</mi>
                </mstyle>
              </math>
            ) superioris æquationis; quam est linea
              <math>
                <mstyle>
                  <mi>B</mi>
                  <mi>C</mi>
                </mstyle>
              </math>
            .
              <lb/>
            scilicet negativæ æquationis
              <lb/>
            sed affirmativæ
              <math>
                <mstyle>
                  <mi>B</mi>
                  <mi>D</mi>
                </mstyle>
              </math>
            est (
              <math>
                <mstyle>
                  <mi>a</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Note for the consitructions.
              <lb/>
            The construction of this equation is in another sheet, by which given (
              <math>
                <mstyle>
                  <mi>a</mi>
                </mstyle>
              </math>
            ), there is also given (
              <math>
                <mstyle>
                  <mi>a</mi>
                </mstyle>
              </math>
            ) in the above equation; which is the linoe
              <math>
                <mstyle>
                  <mi>B</mi>
                  <mi>C</mi>
                </mstyle>
              </math>
            ; of course, (
              <math>
                <mstyle>
                  <mi>a</mi>
                </mstyle>
              </math>
            ) is of a negative equation but an affirmative
              <math>
                <mstyle>
                  <mi>B</mi>
                  <mi>D</mi>
                </mstyle>
              </math>
            . </s>
          </p>
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