Harriot, Thomas, Mss. 6782

List of thumbnails

< >
381
381 (191) 		382
382 (191v)
383
383 (192) 		384
384 (192v)
385
385 (193) 		386
386 (193v)
387
387 (194) 		388
388 (194v)
389
389 (195) 		390
390 (195v)
< >
page |< < (246) of 1011 > >|
    <echo version="1.0RC">
      <text xml:lang="eng" type="free">
        <div type="bundle" level="1" n="1">
          <pb file="add_6782_f246" o="246" n="491"/>
          <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"> The table at the top of the page shows the polynomial
                <math>
                  <mstyle>
                    <mn>1</mn>
                    <mi>C</mi>
                    <mo>+</mo>
                    <mn>1</mn>
                    <mi>r</mi>
                  </mstyle>
                </math>
              (in modern notation
                <math>
                  <mstyle>
                    <mrow>
                      <msup>
                        <mi>x</mi>
                        <mn>3</mn>
                      </msup>
                    </mrow>
                    <mo>+</mo>
                    <mi>x</mi>
                  </mstyle>
                </math>
              ) evaluated for
                <math>
                  <mstyle>
                    <mi>r</mi>
                    <mo>=</mo>
                    <mn>1</mn>
                    <mo>,</mo>
                    <mn>2</mn>
                    <mo>,</mo>
                    <mn>3</mn>
                    <mo>,</mo>
                    <mn>4</mn>
                    <mo>,</mo>
                    <mn>5</mn>
                    <mo>.</mo>
                  </mstyle>
                </math>
              To the right are columns of successive differences as far as the constant difference 6. </s>
              <s xml:space="preserve">]</s>
            </p>
            <p>
              <s xml:space="preserve"> Below that are two further tables, for
                <math>
                  <mstyle>
                    <mn>1</mn>
                    <mi>C</mi>
                    <mo>+</mo>
                    <mn>2</mn>
                    <mi>r</mi>
                  </mstyle>
                </math>
              (
                <math>
                  <mstyle>
                    <mrow>
                      <msup>
                        <mi>x</mi>
                        <mn>3</mn>
                      </msup>
                    </mrow>
                    <mo>+</mo>
                    <mi>x</mi>
                  </mstyle>
                </math>
              ) and
                <math>
                  <mstyle>
                    <mn>1</mn>
                    <mi>C</mi>
                    <mo>+</mo>
                    <mn>3</mn>
                    <mi>r</mi>
                  </mstyle>
                </math>
              (
                <math>
                  <mstyle>
                    <mrow>
                      <msup>
                        <mi>x</mi>
                        <mn>3</mn>
                      </msup>
                    </mrow>
                    <mo>+</mo>
                    <mi>x</mi>
                  </mstyle>
                </math>
              ). The last one is extrapolated upwards to include values for
                <math>
                  <mstyle>
                    <mi>r</mi>
                    <mo>=</mo>
                    <mn>0</mn>
                    <mo>,</mo>
                    <mo>-</mo>
                    <mn>1</mn>
                    <mo>,</mo>
                    <mo>-</mo>
                    <mn>2</mn>
                  </mstyle>
                </math>
              . </s>
              <s xml:space="preserve">]</s>
            </p>
            <p>
              <s xml:space="preserve"> At the bottom of the page are formulae for the
                <math>
                  <mstyle>
                    <mi>n</mi>
                  </mstyle>
                </math>
              th entries columns 0 to 4 of a table generated from a constant difference
                <math>
                  <mstyle>
                    <mi>e</mi>
                  </mstyle>
                </math>
              in column 0. </s>
              <s xml:space="preserve">]</s>
            </p>
          </div>
        </div>
      </text>
    </echo>
Impressum