Harriot, Thomas, Mss. 6782

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491
491 (246) 		492
492 (246v)
493
493 (247) 		494
494 (247v)
495
495 (248) 		496
496 (248v)
497
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498 (249v)
499
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500 (250v)
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          <pb file="add_6782_f315v" o="315v" n="631"/>
          <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"> An examination of the equation
                <math>
                  <mstyle>
                    <mi>a</mi>
                    <mi>a</mi>
                    <mi>a</mi>
                    <mo>-</mo>
                    <mn>1</mn>
                    <mn>2</mn>
                    <mi>a</mi>
                    <mi>a</mi>
                    <mo>+</mo>
                    <mn>2</mn>
                    <mn>9</mn>
                    <mi>a</mi>
                    <mo>=</mo>
                    <mn>1</mn>
                    <mn>8</mn>
                  </mstyle>
                </math>
              , which has roots 1, 2, 9. This is one of several equations with multiple roots treated by Viète in
                <emph style="it">De numerosa potestatum resolutione</emph>
              . 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>
              . </s>
              <s xml:space="preserve">]</s>
            </p>
          </div>
          <head xml:space="preserve"/>
          <p xml:lang="lat">
            <s xml:space="preserve"> Triens coefficientis longituidnis.
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mo>+</mo>
                  <mi>d</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            A third of the longitudinal ]</s>
            <lb/>
            <s xml:space="preserve"> Triplum quadratum.
              <math>
                <mstyle>
                  <mn>3</mn>
                  <mi>b</mi>
                  <mi>b</mi>
                  <mo>+</mo>
                  <mn>6</mn>
                  <mi>b</mi>
                  <mi>d</mi>
                  <mo>+</mo>
                  <mn>3</mn>
                  <mi>d</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Three times the ]</s>
            <lb/>
            <s xml:space="preserve"> maius est coefficientibus planis
              <lb/>
            per
              <math>
                <mstyle>
                  <mn>3</mn>
                  <mi>d</mi>
                  <mi>d</mi>
                  <mo>+</mo>
                  <mn>9</mn>
                  <mi>d</mi>
                  <mi>c</mi>
                  <mo>+</mo>
                  <mn>9</mn>
                  <mi>c</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            greater than the plane coefficient ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Duplus cubus e triente.
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mo>+</mo>
                  <mi>d</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Twice the cube of a third of
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mo>+</mo>
                  <mi>d</mi>
                </mstyle>
              </math>
            </s>
            <lb/>
            <s xml:space="preserve">
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            greater ]</s>
            <lb/>
            <s xml:space="preserve">
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mo>+</mo>
                  <mi>d</mi>
                </mstyle>
              </math>
              <lb/>
            in coefficientibus
              <lb/>
            [
              <emph style="bf">Translation: </emph>
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mo>+</mo>
                  <mi>d</mi>
                </mstyle>
              </math>
            times the plane coefficient </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Excessus maximi laterus supra
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mo>+</mo>
                  <mi>d</mi>
                </mstyle>
              </math>
            fit
              <math>
                <mstyle>
                  <mi>e</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            The excess of the greatest side over
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mo>+</mo>
                  <mi>d</mi>
                </mstyle>
              </math>
            is
              <math>
                <mstyle>
                  <mi>e</mi>
                </mstyle>
              </math>
            </s>
            <lb/>
            <s xml:space="preserve"> reliqua duo sunt minora
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mo>+</mo>
                  <mi>d</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            the two remaining are less than
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mo>+</mo>
                  <mi>d</mi>
                </mstyle>
              </math>
            </s>
            <lb/>
            <s xml:space="preserve"> maxium latus
              <lb/>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            the greatest side will ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Examinatio. Vide Charta
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Examination. See sheet ]
              <lb/>
            [
              <emph style="bf">Commentary: </emph>
            Sheet B is Add MS
              <ref target="http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/library/HSPGZ0AE&start=620&viewMode=image&pn=628"> f. </ref>
            . </s>
            <lb/>
            <s xml:space="preserve">
              <math>
                <mstyle>
                  <mi>e</mi>
                </mstyle>
              </math>
            in
              <lb/>
            coefficientia
              <lb/>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
              <math>
                <mstyle>
                  <mi>e</mi>
                </mstyle>
              </math>
            times the plane coefficient </s>
            <lb/>
            <s xml:space="preserve">
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Nota. Vide K in
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Note. See K in ]
              <lb/>
            [
              <emph style="bf">Commentary: </emph>
            Sheet D.1 is Add MS
              <ref target="http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/library/HSPGZ0AE&start=630&viewMode=image&pn=632"> f. </ref>
            . </s>
          </p>
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