Harriot, Thomas, Mss. 6782

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512 (256v)
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page |< < (254) of 1011 > >|
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            <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>z</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>
                    <mrow>
                      <msup>
                        <mi>x</mi>
                        <mn>2</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>
                  </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 three further tables for
                <math>
                  <mstyle>
                    <mn>1</mn>
                    <mi>C</mi>
                    <mo>+</mo>
                    <mn>2</mn>
                    <mi>z</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>
                    <mn>2</mn>
                    <mrow>
                      <msup>
                        <mi>x</mi>
                        <mn>2</mn>
                      </msup>
                    </mrow>
                    <mo>+</mo>
                    <mn>3</mn>
                    <mi>x</mi>
                  </mstyle>
                </math>
              ),
                <math>
                  <mstyle>
                    <mn>1</mn>
                    <mi>C</mi>
                    <mo>+</mo>
                    <mn>3</mn>
                    <mi>z</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>
                    <mn>3</mn>
                    <mrow>
                      <msup>
                        <mi>x</mi>
                        <mn>2</mn>
                      </msup>
                    </mrow>
                    <mo>+</mo>
                    <mn>2</mn>
                    <mi>x</mi>
                  </mstyle>
                </math>
              ), and
                <math>
                  <mstyle>
                    <mn>1</mn>
                    <mi>C</mi>
                    <mo>+</mo>
                    <mn>4</mn>
                    <mi>z</mi>
                    <mo>+</mo>
                    <mn>5</mn>
                    <mi>r</mi>
                  </mstyle>
                </math>
              (
                <math>
                  <mstyle>
                    <mrow>
                      <msup>
                        <mi>x</mi>
                        <mn>3</mn>
                      </msup>
                    </mrow>
                    <mo>+</mo>
                    <mn>4</mn>
                    <mrow>
                      <msup>
                        <mi>x</mi>
                        <mn>2</mn>
                      </msup>
                    </mrow>
                    <mo>+</mo>
                    <mn>5</mn>
                    <mi>x</mi>
                  </mstyle>
                </math>
              ). </s>
              <s xml:space="preserve">]</s>
            </p>
          </div>
        </div>
      </text>
    </echo>
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