Harriot, Thomas, Mss. 6782

List of thumbnails

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741
741 (370v) 		742
742 (371)
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743 (371v) 		744
744 (372)
745
745 (372v) 		746
746 (373)
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747 (373v) 		748
748 (374)
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749 (374v) 		750
750 (375)
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    <echo version="1.0RC">
      <text xml:lang="eng" type="free">
        <div type="bundle" level="1" n="1">
          <pb file="add_6782_f318" o="318" n="636"/>
          <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>8</mn>
                    <mi>a</mi>
                    <mi>a</mi>
                    <mo>+</mo>
                    <mn>9</mn>
                    <mn>5</mn>
                    <mi>a</mi>
                    <mo>=</mo>
                    <mn>1</mn>
                    <mn>2</mn>
                    <mn>6</mn>
                  </mstyle>
                </math>
              , which has roots 2, 7, 9. 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>
              . </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>c</mi>
                  <mi>c</mi>
                  <mo>-</mo>
                  <mn>9</mn>
                  <mi>c</mi>
                  <mi>d</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 the ]</s>
            <lb/>
            <s xml:space="preserve">
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            less ]</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>
            <lb/>
            <s xml:space="preserve">
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> medium et maximum latus
              <lb/>
            excedunt.
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mo>-</mo>
                  <mi>d</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            medium and maximum sides ]</s>
            <lb/>
            <s xml:space="preserve"> sit unus vel alter excessu,
              <math>
                <mstyle>
                  <mi>e</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            let one or other excess be
              <math>
                <mstyle>
                  <mi>e</mi>
                </mstyle>
              </math>
            </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> erit
              <math>
                <mstyle>
                  <mi>e</mi>
                  <mo>=</mo>
                  <mi>d</mi>
                </mstyle>
              </math>
            , excessus medij 1. adde
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mo>-</mo>
                  <mi>d</mi>
                </mstyle>
              </math>
            erit:
              <math>
                <mstyle>
                  <mi>b</mi>
                </mstyle>
              </math>
            medium.
              <lb/>
            erit
              <math>
                <mstyle>
                  <mi>e</mi>
                  <mo>=</mo>
                  <mn>3</mn>
                  <mi>c</mi>
                  <mo>-</mo>
                  <mn>2</mn>
                  <mi>d</mi>
                </mstyle>
              </math>
            , excessus maximi 3. adde
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mo>-</mo>
                  <mi>d</mi>
                </mstyle>
              </math>
            erit:
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mo>+</mo>
                  <mn>3</mn>
                  <mi>c</mi>
                  <mo>-</mo>
                  <mn>2</mn>
                  <mi>d</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            if
              <math>
                <mstyle>
                  <mi>e</mi>
                  <mo>=</mo>
                  <mi>d</mi>
                </mstyle>
              </math>
            , the excess of the medium, add
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mo>-</mo>
                  <mi>d</mi>
                </mstyle>
              </math>
            , then
              <math>
                <mstyle>
                  <mi>b</mi>
                </mstyle>
              </math>
            will be the medium;
              <lb/>
            if
              <math>
                <mstyle>
                  <mi>e</mi>
                  <mo>=</mo>
                  <mn>3</mn>
                  <mi>c</mi>
                  <mo>-</mo>
                  <mn>2</mn>
                  <mi>d</mi>
                </mstyle>
              </math>
            , the excess of the maximum, add
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mo>-</mo>
                  <mi>d</mi>
                </mstyle>
              </math>
            , then
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mo>+</mo>
                  <mn>3</mn>
                  <mi>c</mi>
                  <mo>-</mo>
                  <mn>3</mn>
                  <mi>d</mi>
                </mstyle>
              </math>
            will be the maximum; </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve">
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            ]</s>
            <lb/>
            <s xml:space="preserve">
              <math>
                <mstyle>
                  <mn>3</mn>
                  <mi>c</mi>
                </mstyle>
              </math>
            in
              <math>
                <mstyle>
                  <mn>2</mn>
                  <mi>d</mi>
                </mstyle>
              </math>
              <lb/>
            in coeff
              <lb/>
            [
              <emph style="bf">Translation: </emph>
              <math>
                <mstyle>
                  <mn>3</mn>
                  <mi>c</mi>
                </mstyle>
              </math>
            times
              <math>
                <mstyle>
                  <mn>2</mn>
                  <mi>d</mi>
                </mstyle>
              </math>
            times the plane coefficient </s>
            <lb/>
            <s xml:space="preserve"> cubus
              <math>
                <mstyle>
                  <mn>3</mn>
                  <mi>c</mi>
                  <mo>-</mo>
                  <mn>2</mn>
                  <mi>d</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            The cube of
              <math>
                <mstyle>
                  <mn>3</mn>
                  <mi>c</mi>
                  <mo>-</mo>
                  <mn>2</mn>
                  <mi>d</mi>
                </mstyle>
              </math>
            </s>
            <lb/>
            <s xml:space="preserve">
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Operationes sunt
              <lb/>
            in dorso
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            The working is on the back of ]
              <lb/>
            [
              <emph style="bf">Commentary: </emph>
            The back of sheet D.1 is Add MS
              <ref target="http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/library/HSPGZ0AE&start=630&viewMode=image&pn=633"> f. </ref>
            . </s>
          </p>
        </div>
      </text>
    </echo>
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