Harriot, Thomas, Mss. 6785

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page |< < (83) of 882 > >|
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      <text xml:lang="eng" type="free">
        <div type="section" level="1" n="1">
          <pb file="add_6785_f083" o="83" n="165"/>
          <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"> A generalization of Pascal’s triangle,showing the results of multiplication by
                <math>
                  <mstyle>
                    <mi>a</mi>
                  </mstyle>
                </math>
              and by 3 (see also Add MS 6782
                <ref target="http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/library/HSPGZ0AE&start=320&viewMode=image&pn=329"> f. </ref>
              ).
                <lb/>
              Note that in the third table, the entry
                <math>
                  <mstyle>
                    <mfrac>
                      <mrow>
                        <mn>3</mn>
                        <mn>4</mn>
                        <mo>,</mo>
                        <mi>a</mi>
                      </mrow>
                      <mrow>
                        <mn>1</mn>
                        <mn>2</mn>
                      </mrow>
                    </mfrac>
                  </mstyle>
                </math>
              on the diagonal, for example, is to be read as
                <math>
                  <mstyle>
                    <mfrac>
                      <mrow>
                        <mn>3</mn>
                        <mo>×</mo>
                        <mn>4</mn>
                        <mi>a</mi>
                      </mrow>
                      <mrow>
                        <mn>1</mn>
                        <mo>×</mo>
                        <mn>2</mn>
                      </mrow>
                    </mfrac>
                  </mstyle>
                </math>
              and similarly for the other entries.
                <lb/>
              In the lower part of the page are general formulae for the rows, similar to those that Harriot derived elsewhere for the standard version of Pascal's triangle.
                <lb/>
              See also page 2 of the 'Magisteria' (Add MS
                <ref target="http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/library/HSPGZ0AE&start=210&viewMode=image&pn=217"> f. </ref>
              ).
                <lb/>
              </s>
              <s xml:space="preserve">]</s>
            </p>
          </div>
          <p xml:lang="lat">
            <s xml:space="preserve"> Æquipollentia ex utraque
              <lb/>
            parte diagonalis perse
              <lb/>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Equality (or symmetry) on either side of the diagonal is shown by ]</s>
          </p>
        </div>
      </text>
    </echo>
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