Harriot, Thomas, Mss. 6786

List of thumbnails

< >
951
951 (476) 		952
952 (476v)
953
953 (477) 		954
954 (477v)
955
955 (478) 		956
956 (478v)
957
957 (479) 		958
958 (479v)
959
959 (480) 		960
960 (480v)
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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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