Harriot, Thomas, Mss. 6786

List of thumbnails

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761
761 (381) 		762
762 (381v)
763
763 (382) 		764
764 (382v)
765
765 (383) 		766
766 (383v)
767
767 (384) 		768
768 (384v)
769
769 (385) 		770
770 (385v)
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page |< < (417) of 1122 > >|
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            <p>
              <s xml:space="preserve">[
                <emph style="bf">Commentary:</emph>
              </s>
            </p>
            <p>
              <s xml:space="preserve"> The numbers in the table at the top of the page are, from left to right: units, lengths, triangular numbers, triangular-pyramidal numbers, and so on.
                <lb/>
              The table in the centre of the page repeats the first and third columns from the table at the top, but now the triangular numbers are written in multiplicative form, thus,
                <math>
                  <mstyle>
                    <mn>6</mn>
                    <mo>=</mo>
                    <mfrac>
                      <mrow>
                        <mn>3</mn>
                        <mo>×</mo>
                        <mn>4</mn>
                      </mrow>
                      <mrow>
                        <mn>1</mn>
                        <mo>×</mo>
                        <mn>2</mn>
                      </mrow>
                    </mfrac>
                  </mstyle>
                </math>
              .
                <lb/>
              The third table gives all the rows in multiplicative form, thus in the seventh
                <math>
                  <mstyle>
                    <mn>8</mn>
                    <mn>4</mn>
                    <mo>=</mo>
                    <mfrac>
                      <mrow>
                        <mn>7</mn>
                        <mo>×</mo>
                        <mn>8</mn>
                        <mo>×</mo>
                        <mn>9</mn>
                      </mrow>
                      <mrow>
                        <mn>1</mn>
                        <mo>×</mo>
                        <mn>2</mn>
                        <mo>×</mo>
                        <mn>3</mn>
                      </mrow>
                    </mfrac>
                  </mstyle>
                </math>
              .
                <lb/>
              The final row gives general formulae for the
                <math>
                  <mstyle>
                    <mi>n</mi>
                  </mstyle>
                </math>
              th row.
                <lb/>
              See also page 1 of the 'Magisteria' (Add MS
                <ref target="http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/library/HSPGZ0AE&start=210&viewMode=image&pn=215"> f. </ref>
              ), for which this is possibly a draft. </s>
              <s xml:space="preserve">]</s>
            </p>
          </div>
          <head xml:space="preserve" xml:lang="lat"> De numeris </head>
        </div>
      </text>
    </echo>
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