Harriot, Thomas, Mss. 6787

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              <s xml:space="preserve">[
                <emph style="bf">Commentary:</emph>
              </s>
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            <p>
              <s xml:space="preserve"> Formulae for the entries in a table that has been interpolated to
                <math>
                  <mstyle>
                    <mi>n</mi>
                  </mstyle>
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              times its original length; for full details see Harriot's
                <ref target="http://echo.mpiwg-berlin.mpg.de/content/scientific_revolution/harriot/maps/3.9.1_magisteria.pt"> 'Magisteria </ref>
              .
                <lb/>
              The third difference is constant,
                <math>
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                    <mi>e</mi>
                    <mi>n</mi>
                    <mi>n</mi>
                    <mi>n</mi>
                  </mstyle>
                </math>
              .
                <lb/>
              The second differences begin with
                <math>
                  <mstyle>
                    <mi>p</mi>
                  </mstyle>
                </math>
              , the first differences begin with
                <math>
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                    <mrow>
                      <msup>
                        <mi>p</mi>
                        <mn>2</mn>
                      </msup>
                    </mrow>
                  </mstyle>
                </math>
              ; these are superscripts, not powers.
                <lb/>
              The differences alternately increase and decrease, as in a table of sines.
                <lb/>
              Values are calculated for
                <math>
                  <mstyle>
                    <mi>n</mi>
                  </mstyle>
                </math>
              th,
                <math>
                  <mstyle>
                    <mn>2</mn>
                    <mi>n</mi>
                  </mstyle>
                </math>
              th,
                <math>
                  <mstyle>
                    <mn>3</mn>
                    <mi>n</mi>
                  </mstyle>
                </math>
              th entries using the result obtained on Add MS 6787
                <ref target="http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/library/MAH52R5E&start=110&viewMode=image&pn=111"> f. </ref>
              . </s>
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