Harriot, Thomas, Mss. 6785

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page |< < (205) of 882 > >|
    <echo version="1.0RC">
      <text xml:lang="eng" type="free">
        <div type="section" level="1" n="1">
          <pb file="add_6785_f205" o="205" n="409"/>
          <div type="page_commentary" level="0" n="0">
            <p>
              <s xml:space="preserve">[
                <emph style="bf">Commentary:</emph>
              </s>
            </p>
            <p>
              <s xml:space="preserve"> The reference at the top of this page is to Zetetic IV.1 from
                <emph style="it">Zeteticorum libri quinque</emph>
                <ref id="Viete 1593a" target="http://www.e-rara.ch/zut/content/pageview/2683942"> (Viète 1593a, Zet </ref>
              . </s>
              <lb/>
              <quote xml:lang="lat">
                <s xml:space="preserve"> Zeteticum I
                  <lb/>
                Invenire numero duo quadrata, aequalia dato </s>
              </quote>
              <lb/>
              <quote>
                <s xml:space="preserve"> To find in numbers, two squares equal to a given </s>
              </quote>
              <lb/>
              <s xml:space="preserve"> Harriot's pagination indicates that this page follows Add MS
                <ref target="http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/library/KN1CRTZ2/&start=410&viewMode=image&pn=413"> f. </ref>
              , but now
                <math>
                  <mstyle>
                    <mi>c</mi>
                  </mstyle>
                </math>
              and
                <math>
                  <mstyle>
                    <mi>d</mi>
                  </mstyle>
                </math>
              have been replaced by
                <math>
                  <mstyle>
                    <mi>s</mi>
                  </mstyle>
                </math>
              and
                <math>
                  <mstyle>
                    <mi>r</mi>
                  </mstyle>
                </math>
              .
                <lb/>
              In the second half of the page, Harriot addresses the problem posed in Zeteticum IV.1: to divide a square into two other squares. This is also Problem II.8 in the
                <emph style="it">Arithmetica</emph>
              of Diophantus
                <ref id="diophantus_1575" target="http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/mpiwg/online/permanent/library/W770Y3H9/&start=51&viewMode=images&pn=56"> (Diophantus 1575, </ref>
              . Viète referred to the working by Diophantus, but Harriot refers only to Viète.
                <lb/>
              Following Viète, Harriot denoted the side of the given square by
                <math>
                  <mstyle>
                    <mi>b</mi>
                  </mstyle>
                </math>
              , the side of the first unknown square by
                <math>
                  <mstyle>
                    <mi>a</mi>
                  </mstyle>
                </math>
              , and the side of the other by
                <math>
                  <mstyle>
                    <mi>b</mi>
                    <mo>-</mo>
                    <mfrac>
                      <mrow>
                        <mi>s</mi>
                        <mi>a</mi>
                      </mrow>
                      <mrow>
                        <mi>r</mi>
                      </mrow>
                    </mfrac>
                  </mstyle>
                </math>
              . The side of the second square is thus found to be
                <math>
                  <mstyle>
                    <mfrac>
                      <mrow>
                        <mi>b</mi>
                        <mi>r</mi>
                        <mi>r</mi>
                        <mo>-</mo>
                        <mi>b</mi>
                        <mi>s</mi>
                        <mi>s</mi>
                      </mrow>
                      <mrow>
                        <mi>r</mi>
                        <mi>r</mi>
                        <mo>+</mo>
                        <mi>s</mi>
                        <mi>s</mi>
                      </mrow>
                    </mfrac>
                  </mstyle>
                </math>
              . In the 1591 edition of Viète's
                <emph style="it">Zetetica</emph>
              , there is a switch between
                <math>
                  <mstyle>
                    <mi>R</mi>
                  </mstyle>
                </math>
              and
                <math>
                  <mstyle>
                    <mi>S</mi>
                  </mstyle>
                </math>
              at this point, so that the second side is given as
                <math>
                  <mstyle>
                    <mfrac>
                      <mrow>
                        <mrow>
                          <msup>
                            <mi>S</mi>
                            <mn>2</mn>
                          </msup>
                        </mrow>
                        <mi>B</mi>
                        <mo>-</mo>
                        <mrow>
                          <msup>
                            <mi>R</mi>
                            <mn>2</mn>
                          </msup>
                        </mrow>
                        <mi>B</mi>
                      </mrow>
                      <mrow>
                        <mrow>
                          <msup>
                            <mi>S</mi>
                            <mn>2</mn>
                          </msup>
                        </mrow>
                        <mo>+</mo>
                        <mrow>
                          <msup>
                            <mi>R</mi>
                            <mn>2</mn>
                          </msup>
                        </mrow>
                      </mrow>
                    </mfrac>
                  </mstyle>
                </math>
              . This is the error Harriot refers to. It was corrected in the 1646 edition of Viète's collected works, the
                <emph style="it">Opera mathematica</emph>
                <ref id="viete_1646"> (Viète </ref>
              . </s>
              <s xml:space="preserve">]</s>
            </p>
          </div>
          <head xml:space="preserve" xml:lang="lat"> 2.) Zet. lib. 4.
            <lb/>
          [
            <emph style="bf">Translation: </emph>
          Zetetica, Book IV, Zeteticum ]</head>
          <p xml:lang="lat">
            <s xml:space="preserve"> Dividere
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
            in
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            To divide
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
            into two [squares]. ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> latus 2
              <emph style="super">i</emph>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            the side of the second
              <emph style="it">square</emph>
            </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Contra Vieta, igitur emendandus
              <lb/>
            vide chartam
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Contrary to Viete, therefore to be amended
              <lb/>
            see sheet ]
              <lb/>
            [
              <emph style="bf">Commentary: </emph>
            Sheet 3 is Add MS
              <ref target="http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/library/KN1CRTZ2/&start=400&viewMode=image&pn=407"> f. </ref>
            . </s>
          </p>
        </div>
      </text>
    </echo>
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