Harriot, Thomas, Mss. 6787

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          <pb file="add_6787_f032" o="32" n="63"/>
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            <p>
              <s xml:space="preserve">[
                <emph style="bf">Commentary:</emph>
              </s>
            </p>
            <p>
              <s xml:space="preserve"> This page continues Harriot's work from Add MS
                <ref target="http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/library/MAH52R5E&start=60&viewMode=image&pn=61"> f. </ref>
              , on Viète's statement of 'Syntomon'
                <ref id="Viete_1593d" target="http://www.e-rara.ch/zut/content/pageview/2684281"> (Viete 1593d, Chapter 19, Prop </ref>
              . </s>
              <s xml:space="preserve">]</s>
            </p>
          </div>
          <head xml:space="preserve" xml:lang="lat"> 2)
            <lb/>
          [
            <emph style="bf">Translation: </emph>
          2) ]</head>
          <p xml:lang="lat">
            <s xml:space="preserve"> primus casus. quando
              <math>
                <mstyle>
                  <mi>c</mi>
                  <mi>b</mi>
                  <mo>+</mo>
                  <mi>b</mi>
                  <mi>a</mi>
                  <mo>≤</mo>
                  <mn>9</mn>
                  <mn>0</mn>
                </mstyle>
              </math>
            .
              <lb/>
            Ponatur
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            First case, when
              <math>
                <mstyle>
                  <mi>c</mi>
                  <mi>b</mi>
                  <mo>+</mo>
                  <mi>b</mi>
                  <mi>a</mi>
                  <mo>≤</mo>
                  <mn>9</mn>
                  <mn>0</mn>
                </mstyle>
              </math>
            .
              <lb/>
            There is put the ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> sit
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
            maior arcus
              <lb/>
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
            minor
              <lb/>
            sit
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>d</mi>
                  <mo>=</mo>
                  <mi>a</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
              <lb/>
            ideo
              <math>
                <mstyle>
                  <mi>d</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
            differentia
              <math>
                <mstyle>
                  <mo>=</mo>
                  <mi>b</mi>
                  <mi>c</mi>
                  <mo>-</mo>
                  <mi>a</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
            .
              <lb/>
            sit etiam,
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>c</mi>
                  <mo>+</mo>
                  <mi>a</mi>
                  <mi>c</mi>
                  <mo>≤</mo>
                  <mn>9</mn>
                  <mn>0</mn>
                </mstyle>
              </math>
            : pro 1
              <emph style="super">o</emph>
            casu.
              <lb/>
            Dico quod
              <lb/>
            vel sub hæc
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Let
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
            be the greater arc,
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
            the lesser, and let
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>d</mi>
                  <mo>=</mo>
                  <mi>a</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
            .
              <lb/>
            Therefore
              <math>
                <mstyle>
                  <mi>d</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
            is the difference
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>c</mi>
                  <mo>-</mo>
                  <mi>a</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
            .
              <lb/>
            Let also
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>c</mi>
                  <mo>+</mo>
                  <mi>a</mi>
                  <mi>c</mi>
                  <mo>≤</mo>
                  <mn>9</mn>
                  <mn>0</mn>
                </mstyle>
              </math>
            for the first case.
              <lb/>
            I say that:
              <lb/>
            Or in this general ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> nota
              <lb/>
            complementum differentiæ
              <lb/>
            complementum
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Note.
              <lb/>
            Complement of the difference.
              <lb/>
            Complement of the ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Secundus casus est quando
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>c</mi>
                  <mo>+</mo>
                  <mi>a</mi>
                  <mi>b</mi>
                  <mo>≥</mo>
                  <mn>9</mn>
                  <mn>0</mn>
                </mstyle>
              </math>
            .
              <lb/>
            […]
              <lb/>
            Quod etiam demonstrandum
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            The second case is when
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>c</mi>
                  <mo>+</mo>
                  <mi>a</mi>
                  <mi>b</mi>
                  <mo>≥</mo>
                  <mn>9</mn>
                  <mn>0</mn>
                </mstyle>
              </math>
            .
              <lb/>
              <lb/>
            Which was also to be ]</s>
          </p>
        </div>
      </text>
    </echo>
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