Harriot, Thomas, Mss. 6782

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            <p>
              <s xml:space="preserve">[
                <emph style="bf">Commentary:</emph>
              </s>
            </p>
            <p>
              <s xml:space="preserve"> An examination of the equation
                <math>
                  <mstyle>
                    <mi>a</mi>
                    <mi>a</mi>
                    <mi>a</mi>
                    <mo>-</mo>
                    <mn>6</mn>
                    <mi>a</mi>
                    <mi>a</mi>
                    <mo>+</mo>
                    <mn>1</mn>
                    <mn>2</mn>
                    <mi>a</mi>
                    <mo>=</mo>
                    <mn>8</mn>
                  </mstyle>
                </math>
              , which has roots 2, 2, 2. This is one of several equations with multiple roots treated by Viète in
                <emph style="it">De potestatum numerosa resolutione</emph>
                <ref id="viete_1600b"> (Viète </ref>
              . Harriot solved it in full on Add MS 6783
                <ref target="http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/library/VWXURW4V&start=370&viewMode=image&pn=373"> f. </ref>
              , and refers to it again in Add MS 6783
                <ref target="http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/library/VWXURW4V&start=370&viewMode=image&pn=375"> f. </ref>
              . </s>
              <s xml:space="preserve">]</s>
            </p>
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          <p xml:lang="lat">
            <s xml:space="preserve"> Triens coeff: long:
              <math>
                <mstyle>
                  <mi>b</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            A third of the longitudinal ]</s>
            <lb/>
            <s xml:space="preserve"> Triplum quadrat:
              <math>
                <mstyle>
                  <mn>3</mn>
                  <mi>b</mi>
                  <mi>b</mi>
                  <mo>=</mo>
                  <mn>3</mn>
                  <mi>b</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
            coeff.
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Three times the square is
              <math>
                <mstyle>
                  <mn>3</mn>
                  <mi>b</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
            , the plane coefficient. </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Duplus cubus e triente.
              <math>
                <mstyle>
                  <mn>2</mn>
                  <mi>b</mi>
                  <mi>b</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Twice the cube of the ]</s>
            <lb/>
            <s xml:space="preserve">
              <math>
                <mstyle>
                  <mi>b</mi>
                </mstyle>
              </math>
              <lb/>
            in coeff:
              <lb/>
            [
              <emph style="bf">Translation: </emph>
              <math>
                <mstyle>
                  <mi>b</mi>
                </mstyle>
              </math>
            times the plane coefficient </s>
            <lb/>
            <s xml:space="preserve"> Tria latera
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Therefore the three sides ]</s>
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