Harriot, Thomas, Mss. 6787

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page |< < (304) of 1155 > >|
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            <p>
              <s xml:space="preserve">[
                <emph style="bf">Commentary:</emph>
              </s>
            </p>
            <p>
              <s xml:space="preserve"> Here Harriot creates further Pythagorean triples, not necessarily all integers.
                <lb/>
              In the first few lines, for example, he multiplies 21 by
                <math>
                  <mstyle>
                    <mfrac>
                      <mrow>
                        <mn>5</mn>
                      </mrow>
                      <mrow>
                        <mn>4</mn>
                      </mrow>
                    </mfrac>
                  </mstyle>
                </math>
              ,
                <math>
                  <mstyle>
                    <mfrac>
                      <mrow>
                        <mn>3</mn>
                      </mrow>
                      <mrow>
                        <mn>4</mn>
                      </mrow>
                    </mfrac>
                  </mstyle>
                </math>
              , and
                <math>
                  <mstyle>
                    <mfrac>
                      <mrow>
                        <mn>4</mn>
                      </mrow>
                      <mrow>
                        <mn>4</mn>
                      </mrow>
                    </mfrac>
                  </mstyle>
                </math>
              to obtain (
                <math>
                  <mstyle>
                    <mfrac>
                      <mrow>
                        <mn>1</mn>
                        <mn>0</mn>
                        <mn>5</mn>
                      </mrow>
                      <mrow>
                        <mn>4</mn>
                      </mrow>
                    </mfrac>
                  </mstyle>
                </math>
              ,
                <math>
                  <mstyle>
                    <mfrac>
                      <mrow>
                        <mn>6</mn>
                        <mn>3</mn>
                      </mrow>
                      <mrow>
                        <mn>4</mn>
                      </mrow>
                    </mfrac>
                  </mstyle>
                </math>
              ,
                <math>
                  <mstyle>
                    <mfrac>
                      <mrow>
                        <mn>8</mn>
                        <mn>4</mn>
                      </mrow>
                      <mrow>
                        <mn>4</mn>
                      </mrow>
                    </mfrac>
                  </mstyle>
                </math>
              ) or (
                <math>
                  <mstyle>
                    <mrow>
                      <mn>2</mn>
                      <mn>6</mn>
                      <mfrac>
                        <mrow>
                          <mn>1</mn>
                        </mrow>
                        <mrow>
                          <mn>4</mn>
                        </mrow>
                      </mfrac>
                    </mrow>
                  </mstyle>
                </math>
              ,
                <math>
                  <mstyle>
                    <mrow>
                      <mn>1</mn>
                      <mn>5</mn>
                      <mfrac>
                        <mrow>
                          <mn>3</mn>
                        </mrow>
                        <mrow>
                          <mn>4</mn>
                        </mrow>
                      </mfrac>
                    </mrow>
                  </mstyle>
                </math>
              ,
                <math>
                  <mstyle>
                    <mn>2</mn>
                    <mn>1</mn>
                  </mstyle>
                </math>
              ). </s>
              <s xml:space="preserve">]</s>
            </p>
          </div>
        </div>
      </text>
    </echo>
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