Harriot, Thomas, Mss. 6784

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      <text xml:lang="eng" type="free">
        <div type="section" level="1" n="1">
          <pb file="add_6784_f216" o="216" n="431"/>
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            <p>
              <s xml:space="preserve">[
                <emph style="bf">Commentary:</emph>
              </s>
            </p>
            <p>
              <s xml:space="preserve"> Square roots of binomes of the fifth and sixth kind by the general rule derived in Add MS 6788
                <ref target="http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/library/AYB35Z4D/&start=20&viewMode=image&pn=29"> f. </ref>
              (and elsewhere). Here Harriot works with two types of fifth binome, (
                <math>
                  <mstyle>
                    <msqrt>
                      <mrow>
                        <mi>b</mi>
                        <mi>b</mi>
                        <mo>+</mo>
                        <mi>c</mi>
                        <mi>c</mi>
                      </mrow>
                    </msqrt>
                    <mo>+</mo>
                    <mi>b</mi>
                  </mstyle>
                </math>
              and
                <math>
                  <mstyle>
                    <msqrt>
                      <mrow>
                        <mi>b</mi>
                        <mi>b</mi>
                        <mo>+</mo>
                        <mi>c</mi>
                        <mi>d</mi>
                      </mrow>
                    </msqrt>
                    <mo>+</mo>
                    <mi>b</mi>
                  </mstyle>
                </math>
              ), according to whether the difference between the squares of the two terms is a square or not. Elsewhere he refers to these as bin.
                <math>
                  <mstyle>
                    <mn>5</mn>
                    <mo>"</mo>
                  </mstyle>
                </math>
              and bin.
                <math>
                  <mstyle>
                    <mn>5</mn>
                    <mo/>
                  </mstyle>
                </math>
              .
                <lb/>
              Similarly he distinguishes two types of sixth (
                <math>
                  <mstyle>
                    <msqrt>
                      <mrow>
                        <mi>b</mi>
                        <mi>c</mi>
                        <mo>+</mo>
                        <mi>d</mi>
                        <mi>d</mi>
                      </mrow>
                    </msqrt>
                    <mo>+</mo>
                    <msqrt>
                      <mrow>
                        <mi>b</mi>
                        <mi>c</mi>
                      </mrow>
                    </msqrt>
                    <mi>b</mi>
                  </mstyle>
                </math>
              and
                <math>
                  <mstyle>
                    <msqrt>
                      <mrow>
                        <mi>b</mi>
                        <mi>c</mi>
                        <mo>+</mo>
                        <mi>d</mi>
                        <mi>f</mi>
                      </mrow>
                    </msqrt>
                    <mo>+</mo>
                    <msqrt>
                      <mrow>
                        <mi>b</mi>
                        <mi>c</mi>
                      </mrow>
                    </msqrt>
                  </mstyle>
                </math>
              ). Elsewhere he refers to these as bin.
                <math>
                  <mstyle>
                    <mn>6</mn>
                    <mo>"</mo>
                  </mstyle>
                </math>
              and bin.
                <math>
                  <mstyle>
                    <mn>6</mn>
                    <mo/>
                  </mstyle>
                </math>
              .
                <lb/>
              In all cases the roots are </s>
              <s xml:space="preserve">]</s>
            </p>
          </div>
        </div>
      </text>
    </echo>
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