Harriot, Thomas, Mss. 6782

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491 (246) 		492
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            <p>
              <s xml:space="preserve">[
                <emph style="bf">Commentary:</emph>
              </s>
            </p>
            <p>
              <s xml:space="preserve"> Here Harriot calculates the square root of 4489, the cube root of 300763, the fourth root of 20151121, and the sixth root of 1350125107, demonstrating that the answer is 67 in each case. This is the analysis, or taking apart, of what has been constructed on Add MS 6782
                <ref target="http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/library/HSPGZ0AE&start=550&viewMode=image&pn=556"> f. </ref>
              .
                <lb/>
              Maurolico's treatment of cube roots begins on page 110 of
                <emph style="it">Arithmeticorum libri duo</emph>
                <ref id="maurolico_1575" target="http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/mpiwg/online/permanent/library/XFWC6D23/pageimg&start=421&viewMode=images&pn=430&mode=imagepath"> (Maurolico 1575, </ref>
              . </s>
              <s xml:space="preserve">]</s>
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            <s xml:space="preserve"> Inde:
              <math>
                <mstyle>
                  <mi>d</mi>
                  <mi>d</mi>
                  <mi>d</mi>
                  <mo>=</mo>
                  <mi>b</mi>
                  <mi>b</mi>
                  <mi>b</mi>
                  <mo>+</mo>
                  <mn>3</mn>
                  <mi>d</mi>
                  <mi>b</mi>
                  <mi>c</mi>
                  <mo>+</mo>
                  <mi>c</mi>
                  <mi>c</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
              <lb/>
            ut Maurolicus et nos in alia charta
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Whence
              <math>
                <mstyle>
                  <mi>d</mi>
                  <mi>d</mi>
                  <mi>d</mi>
                  <mo>=</mo>
                  <mi>b</mi>
                  <mi>b</mi>
                  <mi>b</mi>
                  <mo>+</mo>
                  <mn>3</mn>
                  <mi>d</mi>
                  <mi>b</mi>
                  <mi>c</mi>
                  <mo>+</mo>
                  <mi>c</mi>
                  <mi>c</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
            , as in Maurolicus and as I have demonstrated in another sheet.
              <lb/>
            [
              <emph style="bf">Commentary: </emph>
            This note shows an alternative method of calculation, attributed to Maurolico, in which
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mo>+</mo>
                  <mi>c</mi>
                </mstyle>
              </math>
            is replaced by
              <math>
                <mstyle>
                  <mi>d</mi>
                </mstyle>
              </math>
            . An asterisk against the note directs the reader to Maurolico's method of calculation, on the right. </s>
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            <s xml:space="preserve"> Maurolicus
              <lb/>
            </s>
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