Harriot, Thomas, Mss. 6784

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    <echo version="1.0RC">
      <text xml:lang="eng" type="free">
        <div type="section" level="1" n="1">
          <pb file="add_6784_f091" o="91" n="181"/>
          <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 'the cutting-off of an area', as set out in Pappus,
                <emph style="it">Mathematicae collectiones</emph>
                <ref id="pappus_1588"> (Pappus </ref>
              , Book 7. For a statement of the problem see Add MS 6784
                <ref target="http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/library/XT0KZ8QC/&start=30&viewMode=image&pn=37"> f. </ref>
              . </s>
              <s xml:space="preserve">]</s>
            </p>
          </div>
          <head xml:space="preserve" xml:lang="lat"> 1. problematis de spatij resectione 4
            <emph style="super">a</emph>
          demonstratione et
            <lb/>
          [
            <emph style="bf">Translation: </emph>
          Problems of cutting off of an area, demonstration and most ]</head>
          <p xml:lang="lat">
            <s xml:space="preserve"> Quatuor possunt esse
              <lb/>
            resectiones ab uno
              <lb/>
            puncto dato et duabus
              <lb/>
            solummodo lineis datis;
              <lb/>
            secundum quantitatem
              <lb/>
            spatij dati
              <lb/>
            aliquando tres:
              <lb/>
            semper
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            There are four possible sections from one given point and just two given lines, according to the size of the given area; sometimes three, always two.</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Exegesis.
              <lb/>
            producetur
              <math>
                <mstyle>
                  <mi>A</mi>
                  <mi>C</mi>
                </mstyle>
              </math>
            usque ad
              <math>
                <mstyle>
                  <mi>L</mi>
                </mstyle>
              </math>
            et fiat
              <lb/>
              <math>
                <mstyle>
                  <mi>C</mi>
                  <mi>L</mi>
                </mstyle>
              </math>
            æqualis
              <math>
                <mstyle>
                  <mi>D</mi>
                  <mi>E</mi>
                </mstyle>
              </math>
            cui etiam sit æqualis
              <lb/>
            sit
              <math>
                <mstyle>
                  <mi>A</mi>
                  <mi>M</mi>
                </mstyle>
              </math>
            . Around
              <math>
                <mstyle>
                  <mi>M</mi>
                </mstyle>
              </math>
            intervallo
              <math>
                <mstyle>
                  <mi>A</mi>
                  <mi>L</mi>
                </mstyle>
              </math>
              <lb/>
            agatur periferia
              <math>
                <mstyle>
                  <mi>F</mi>
                  <mi>Z</mi>
                  <mi>O</mi>
                </mstyle>
              </math>
            .
              <lb/>
            Ab
              <math>
                <mstyle>
                  <mi>E</mi>
                </mstyle>
              </math>
            puncto, per
              <math>
                <mstyle>
                  <mi>O</mi>
                </mstyle>
              </math>
            et
              <math>
                <mstyle>
                  <mi>F</mi>
                </mstyle>
              </math>
            Ducatur rectæ
              <lb/>
              <math>
                <mstyle>
                  <mi>E</mi>
                  <mi>F</mi>
                </mstyle>
              </math>
            et
              <math>
                <mstyle>
                  <mi>E</mi>
                  <mi>W</mi>
                </mstyle>
              </math>
            .
              <lb/>
            Dico
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Exegesis.
              <lb/>
            Let
              <math>
                <mstyle>
                  <mi>A</mi>
                  <mi>C</mi>
                </mstyle>
              </math>
            be extended as far as
              <math>
                <mstyle>
                  <mi>L</mi>
                </mstyle>
              </math>
            and make
              <math>
                <mstyle>
                  <mi>C</mi>
                  <mi>L</mi>
                </mstyle>
              </math>
            equal to
              <math>
                <mstyle>
                  <mi>D</mi>
                  <mi>E</mi>
                </mstyle>
              </math>
            to which
              <math>
                <mstyle>
                  <mi>A</mi>
                  <mi>M</mi>
                </mstyle>
              </math>
            is also equal. Around
              <math>
                <mstyle>
                  <mi>M</mi>
                </mstyle>
              </math>
            with radius
              <math>
                <mstyle>
                  <mi>A</mi>
                  <mi>L</mi>
                </mstyle>
              </math>
            there is constructed the circumference
              <math>
                <mstyle>
                  <mi>F</mi>
                  <mi>Z</mi>
                  <mi>O</mi>
                </mstyle>
              </math>
            . From the point
              <math>
                <mstyle>
                  <mi>E</mi>
                </mstyle>
              </math>
            , through
              <math>
                <mstyle>
                  <mi>O</mi>
                </mstyle>
              </math>
            and
              <math>
                <mstyle>
                  <mi>F</mi>
                </mstyle>
              </math>
            there are drawn the lines
              <math>
                <mstyle>
                  <mi>E</mi>
                  <mi>F</mi>
                </mstyle>
              </math>
            and
              <math>
                <mstyle>
                  <mi>E</mi>
                  <mi>W</mi>
                </mstyle>
              </math>
            .
              <lb/>
            I say ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Poristice et inde
              <lb/>
            synthesis manifesta The poristic, and hence the synthesis, is obvious.</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Si
              <math>
                <mstyle>
                  <mi>D</mi>
                  <mi>E</mi>
                </mstyle>
              </math>
            sit æqualis
              <math>
                <mstyle>
                  <mi>D</mi>
                  <mi>C</mi>
                </mstyle>
              </math>
              <lb/>
            tum:
              <lb/>
              <math>
                <mstyle>
                  <mi>C</mi>
                  <mi>O</mi>
                  <mo>=</mo>
                  <mi>C</mi>
                  <mi>G</mi>
                </mstyle>
              </math>
              <lb/>
            Nam
              <math>
                <mstyle>
                  <mi>C</mi>
                  <mi>L</mi>
                  <mi>E</mi>
                  <mi>D</mi>
                </mstyle>
              </math>
            erit quadratum
              <lb/>
            et punctum
              <math>
                <mstyle>
                  <mi>E</mi>
                </mstyle>
              </math>
            [???]
              <lb/>
            [???].
              <lb/>
            Sit
              <math>
                <mstyle>
                  <mi>D</mi>
                  <mi>E</mi>
                </mstyle>
              </math>
            sit maior
              <math>
                <mstyle>
                  <mi>D</mi>
                  <mi>C</mi>
                </mstyle>
              </math>
            . tum
              <lb/>
              <math>
                <mstyle>
                  <mi>F</mi>
                  <mi>C</mi>
                </mstyle>
              </math>
            est maximum secta [???]
              <lb/>
            et
              <math>
                <mstyle>
                  <mi>C</mi>
                  <mi>G</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            If
              <math>
                <mstyle>
                  <mi>D</mi>
                  <mi>E</mi>
                </mstyle>
              </math>
            is equal to
              <math>
                <mstyle>
                  <mi>D</mi>
                  <mi>C</mi>
                </mstyle>
              </math>
            , then
              <math>
                <mstyle>
                  <mi>C</mi>
                  <mi>O</mi>
                  <mo>=</mo>
                  <mi>C</mi>
                  <mi>G</mi>
                </mstyle>
              </math>
            .
              <lb/>
            For
              <math>
                <mstyle>
                  <mi>C</mi>
                  <mi>L</mi>
                  <mi>E</mi>
                  <mi>D</mi>
                </mstyle>
              </math>
            will be a square, and the point
              <math>
                <mstyle>
                  <mi>E</mi>
                </mstyle>
              </math>
            [???].
              <lb/>
            If
              <math>
                <mstyle>
                  <mi>D</mi>
                  <mi>E</mi>
                </mstyle>
              </math>
            is greater than
              <math>
                <mstyle>
                  <mi>D</mi>
                  <mi>C</mi>
                </mstyle>
              </math>
            , then
              <math>
                <mstyle>
                  <mi>F</mi>
                  <mi>C</mi>
                </mstyle>
              </math>
            is the maximum segment and
              <math>
                <mstyle>
                  <mi>C</mi>
                  <mi>G</mi>
                </mstyle>
              </math>
            the minimum. </s>
          </p>
        </div>
      </text>
    </echo>
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