Harriot, Thomas, Mss. 6786

List of thumbnails

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691
691 (346) 		692
692 (346v)
693
693 (347) 		694
694 (347v)
695
695 (348) 		696
696 (348v)
697
697 (349) 		698
698 (349v)
699
699 (350) 		700
700 (350v)
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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>
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    </echo>
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