Harriot, Thomas, Mss. 6782

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              <s xml:space="preserve">[
                <emph style="bf">Commentary:</emph>
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              <s xml:space="preserve"> Across the top of the page are the terms of a geometric progression with multiplier
                <math>
                  <mstyle>
                    <mfrac>
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                      <mrow>
                        <mi>b</mi>
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              . </s>
              <lb/>
              <s xml:space="preserve"> The rest of the page contains a table of successive squares of the number that may be interpreted as
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                    <mo>.</mo>
                    <mn>9</mn>
                    <mn>9</mn>
                    <mn>9</mn>
                    <mn>9</mn>
                    <mn>9</mn>
                    <mn>9</mn>
                    <mn>9</mn>
                    <mn>9</mn>
                    <mn>9</mn>
                    <mn>9</mn>
                    <mn>8</mn>
                    <mn>8</mn>
                    <mn>7</mn>
                    <mn>7</mn>
                  </mstyle>
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              . Selected powers are then added to give
                <math>
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                    <mo>.</mo>
                    <mn>9</mn>
                    <mn>9</mn>
                    <mn>9</mn>
                    <mn>9</mn>
                    <mn>9</mn>
                    <mn>9</mn>
                    <mn>9</mn>
                    <mn>9</mn>
                    <mn>9</mn>
                    <mn>9</mn>
                    <mn>8</mn>
                    <mn>8</mn>
                    <mn>7</mn>
                    <mrow>
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                        <mn>7</mn>
                        <mrow>
                          <mn>2</mn>
                          <mn>5</mn>
                          <mn>9</mn>
                          <mn>2</mn>
                          <mn>0</mn>
                          <mn>0</mn>
                          <mn>0</mn>
                          <mn>0</mn>
                        </mrow>
                      </msup>
                    </mrow>
                  </mstyle>
                </math>
              . A calculation on the following page, Add MS 6782
                <ref target="http://echo.mpiwg-berlin.mpg.de/ECHOdocuViewSB?url=/mpiwg/online/permanent/library/HSPGZ0AE&start=20&viewMode=image&pn=25"> f. </ref>
              , shows that
                <math>
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                    <mn>2</mn>
                    <mn>5</mn>
                    <mn>9</mn>
                    <mn>2</mn>
                    <mn>0</mn>
                    <mn>0</mn>
                    <mn>0</mn>
                    <mn>0</mn>
                    <mo>=</mo>
                    <mn>2</mn>
                    <mo>×</mo>
                    <mn>6</mn>
                    <mrow>
                      <msup>
                        <mn>0</mn>
                        <mn>4</mn>
                      </msup>
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              , that is, the number of half-fifths of a degree in a minute (where a degree is subdivided in the traditional way into minutes, seconds, thirds, fourths, and fifths by successive divisions by 60). </s>
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              <s xml:space="preserve"> The entries in the table are calculated in the subsequent pages labelled c.2 to c.7;
                <ref target="http://echo.mpiwg-berlin.mpg.de/content/scientific_revolution/harriot/maps/7.2.4.2_series_a_to_f.pt"> 'Spirals, series </ref>
              . </s>
              <s xml:space="preserve">]</s>
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              <math>
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                  <mi>m</mi>
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            in charta
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            [
              <emph style="bf">Commentary: </emph>
            Sheet ca.1 is HMC MS 240.v
              <ref target="http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/mpiwg/online/permanent/library/928CQY8W/pageimg&start=30&viewMode=image&pn=37&mode=imagepath"> f. 419 </ref>
            . </s>
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