Harriot, Thomas, Mss. 6786

List of thumbnails

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851
851 (426) 		852
852 (426v)
853
853 (427) 		854
854 (427v)
855
855 (428) 		856
856 (428v)
857
857 (429) 		858
858 (429v)
859
859 (430) 		860
860 (430v)
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page |< < (417) of 1122 > >|
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          <pb file="add_6786_f417" o="417" n="833"/>
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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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