Harriot, Thomas, Mss. 6787

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page |< < (58) of 1155 > >|
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            <p>
              <s xml:space="preserve">[
                <emph style="bf">Commentary:</emph>
              </s>
            </p>
            <p>
              <s xml:space="preserve"> On the left is a table of 'pretend' sines with constant third difference 81.
                <lb/>
              The final row of the tables is 7240, 600, 405, 81.
                <lb/>
              The task is to interpolate the table with two new entries between each existing entry, using the formulae calculated in the previous sheets.
                <lb/>
                <math>
                  <mstyle>
                    <mi>n</mi>
                    <mo>=</mo>
                    <mn>3</mn>
                  </mstyle>
                </math>
              by hypothesis.
                <lb/>
              Thus the constant difference in the interpolated table will be
                <math>
                  <mstyle>
                    <mfrac>
                      <mrow>
                        <mn>8</mn>
                        <mn>1</mn>
                      </mrow>
                      <mrow>
                        <mn>2</mn>
                        <mn>7</mn>
                      </mrow>
                    </mfrac>
                    <mo>=</mo>
                    <mn>3</mn>
                  </mstyle>
                </math>
              .
                <lb/>
              Further calculations give
                <math>
                  <mstyle>
                    <mi>p</mi>
                    <mo>=</mo>
                    <mn>4</mn>
                    <mn>5</mn>
                  </mstyle>
                </math>
              and
                <math>
                  <mstyle>
                    <mrow>
                      <msup>
                        <mi>p</mi>
                        <mn>2</mn>
                      </msup>
                    </mrow>
                  </mstyle>
                </math>
              for the first new entries after the row beginning 6640. </s>
              <s xml:space="preserve">]</s>
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            <s xml:space="preserve">
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            ]</s>
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          <p xml:lang="lat">
            <s xml:space="preserve">
              <math>
                <mstyle>
                  <mi>n</mi>
                  <mo>=</mo>
                  <mn>3</mn>
                </mstyle>
              </math>
            per hypothesi numero dividendum
              <lb/>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
              <math>
                <mstyle>
                  <mi>n</mi>
                  <mo>=</mo>
                  <mn>3</mn>
                </mstyle>
              </math>
            by hypothesis, the number of parts to be divided. </s>
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Impressum