Harriot, Thomas, Mss. 6785

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461 (231) 		462
462 (231v)
463
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            <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. 6 of
                <emph style="it">Zeteticorum libri quinque</emph>
                <ref id="Viete 1593a" target="http://www.e-rara.ch/zut/content/pageview/2683947"> (Viète 1593a, Zet </ref>
              . This is also Proposition II.10 from 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=59"> (Diophantus 1575, </ref>
              , but Harriot refers only to Viète's version of it. </s>
              <lb/>
              <quote xml:lang="lat">
                <s xml:space="preserve"> Zeteticum VI
                  <lb/>
                Invenire numero duo quadrata, distantia dato </s>
              </quote>
              <lb/>
              <quote>
                <s xml:space="preserve"> To find in numbers two squares having a given difference between </s>
              </quote>
              <lb/>
              <s xml:space="preserve"> Viète used the letter
                <math>
                  <mstyle>
                    <mi>B</mi>
                  </mstyle>
                </math>
              for the given difference. Harriot followed Viète's working but in his own lower-case notation. The 1591 edition of the
                <emph style="it">Zetetica</emph>
              at one point mistakenly gives 'maior' instead of 'minor'. This is the error that Harriot points out. It was corrected in the 1646 edition of Viète's
                <emph style="it">Opera mathematica</emph>
              . </s>
              <s xml:space="preserve">]</s>
            </p>
          </div>
          <head xml:space="preserve" xml:lang="lat"> Zet. lib. 4.
            <lb/>
          [
            <emph style="bf">Translation: </emph>
          Zetetica, Book IV, Zeteticum ]</head>
          <p xml:lang="lat">
            <s xml:space="preserve"> Invenire duo quadrata
              <lb/>
            distantia data
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            To find two squares a given distance ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> et ut differentia vel
              <lb/>
            summa laterum sit æqualis,
              <math>
                <mstyle>
                  <mi>d</mi>
                </mstyle>
              </math>
              <lb/>
            dato
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            and so that the difference or sum of the sides is equal to
              <math>
                <mstyle>
                  <mi>d</mi>
                </mstyle>
              </math>
            , a given number. </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Sit datum intervallum
              <math>
                <mstyle>
                  <mi>r</mi>
                  <mi>s</mi>
                </mstyle>
              </math>
              <lb/>
            et intelligatur pro quadrato basis
              <lb/>
            Et sit differentia inter hypotenusum
              <lb/>
            et perpendiculum quælibet quantitas
              <math>
                <mstyle>
                  <mi>d</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Let the given interval be
              <math>
                <mstyle>
                  <mi>r</mi>
                  <mi>s</mi>
                </mstyle>
              </math>
            , and it is understood to be the square of the base; And let the difference between the hypotenuse and the perpendicular be any quantity. </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Menda in
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Wrong in ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Ergo latera
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Therefore the sides of the ]</s>
          </p>
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Impressum