Harriot, Thomas, Mss. 6786

List of thumbnails

< >
861
861 (431) 		862
862 (431v)
863
863 (432) 		864
864 (432v)
865
865 (433) 		866
866 (433v)
867
867 (434) 		868
868 (434v)
869
869 (435) 		870
870 (435v)
< >
page |< < (457) of 1122 > >|
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      <text xml:lang="eng" type="free">
        <div type="section" level="1" n="1">
          <pb file="add_6786_f457" o="457" n="913"/>
          <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"> Powers of
                <math>
                  <mstyle>
                    <mo maxsize="1">(</mo>
                    <mi>b</mi>
                    <mo>+</mo>
                    <mi>c</mi>
                    <mo maxsize="1">)</mo>
                  </mstyle>
                </math>
              up to
                <math>
                  <mstyle>
                    <mo maxsize="1">(</mo>
                    <mi>b</mi>
                    <mo>+</mo>
                    <mi>c</mi>
                    <mrow>
                      <msup>
                        <mo maxsize="1">)</mo>
                        <mn>5</mn>
                      </msup>
                    </mrow>
                  </mstyle>
                </math>
              . Each power is calculated from the previous one by multiplication.
                <lb/>
              Note the use of cossist
                <math>
                  <mstyle>
                    <mi>r</mi>
                  </mstyle>
                </math>
              for a first power,
                <math>
                  <mstyle>
                    <mi>z</mi>
                  </mstyle>
                </math>
              for a square,
                <math>
                  <mstyle>
                    <mi>c</mi>
                  </mstyle>
                </math>
              for a cube,
                <math>
                  <mstyle>
                    <mi>z</mi>
                    <mi>z</mi>
                  </mstyle>
                </math>
              for a square-suare or fourth power,
                <math>
                  <mstyle>
                    <mo>ßß</mo>
                  </mstyle>
                </math>
              for a sursolid or fifth power.
                <lb/>
              Below the main table is a list of the final sums, including the sixth power (
                <math>
                  <mstyle>
                    <mi>z</mi>
                    <mi>c</mi>
                  </mstyle>
                </math>
              ), which has not been calculated on this page but which can be deduced from the pattern for the previous cases.
                <lb/>
              For a similar table see Add MS
                <ref target="http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/library/HSPGZ0AE&start=550&viewMode=image&pn=552"> f. </ref>
              .
                <lb/>
              This table underpins the method of root extraction taught by Francois Viete in
                <emph style="it">De numerosa potestatum resolutione</emph>
              (1600). </s>
              <s xml:space="preserve">]</s>
            </p>
          </div>
          <p xml:lang="lat">
            <s xml:space="preserve"> species figuratorum
              <lb/>
            ex binomia
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            terms of figurate numbers from binomial ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> (sunt canones pro
              <lb/>
            extractione
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            (these are the canons for the extraction of ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> (Demptis numeris sunt species
              <lb/>
            continue proportionalium,
              <lb/>
            in minimis terminis
              <lb/>
            ut
              <math>
                <mstyle>
                  <mi>b</mi>
                </mstyle>
              </math>
            , ad
              <math>
                <mstyle>
                  <mi>c</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            (Without the numbers, the terms are in continual proportion, in the ratio expressed in lowest terms as
              <math>
                <mstyle>
                  <mi>b</mi>
                </mstyle>
              </math>
            to
              <math>
                <mstyle>
                  <mi>c</mi>
                </mstyle>
              </math>
            ). </s>
          </p>
        </div>
      </text>
    </echo>
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