Harriot, Thomas, Mss. 6787

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page |< < (398v) of 1155 > >|
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      <text xml:lang="eng" type="free">
        <div type="section" level="1" n="1">
          <pb file="add_6787_f398v" o="398v" n="795"/>
          <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 on this page is to Viète's
                <emph style="it">Variorum de rebus mathematicis responsorum liber VIII</emph>
                <ref id="Viete_1593d" target="http://www.e-rara.ch/zut/content/pageview/2684235"> (Viete 1593d, Chapter </ref>
              . Viète investigated the properties of the quadratrix in Chapter VII. Harriot's diagram is the same as Viète's. </s>
              <s xml:space="preserve">]</s>
            </p>
          </div>
          <head xml:space="preserve" xml:lang="lat"> Vieta resp. pag. 12. lin: 9, De
            <lb/>
          [
            <emph style="bf">Translation: </emph>
          Viète, Responsorum, page 12, line 9, On the ]</head>
          <p xml:lang="lat">
            <s xml:space="preserve"> Sit:
              <math>
                <mstyle>
                  <mi>B</mi>
                  <mi>C</mi>
                  <mo>,</mo>
                  <mi>A</mi>
                  <mi>B</mi>
                  <mo>:</mo>
                  <mi>A</mi>
                  <mi>B</mi>
                  <mo>,</mo>
                  <mi>A</mi>
                  <mi>E</mi>
                </mstyle>
              </math>
            .
              <lb/>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Let
              <math>
                <mstyle>
                  <mi>B</mi>
                  <mi>C</mi>
                  <mo>:</mo>
                  <mi>A</mi>
                  <mi>B</mi>
                  <mo>=</mo>
                  <mi>A</mi>
                  <mi>B</mi>
                  <mo>:</mo>
                  <mi>A</mi>
                  <mi>E</mi>
                </mstyle>
              </math>
            .
              <lb/>
            </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Sit
              <math>
                <mstyle>
                  <mi>A</mi>
                  <mi>E</mi>
                </mstyle>
              </math>
            maior,
              <math>
                <mstyle>
                  <mi>A</mi>
                  <mi>D</mi>
                </mstyle>
              </math>
              <lb/>
            […]
              <lb/>
            Ergo
              <math>
                <mstyle>
                  <mi>F</mi>
                  <mi>H</mi>
                  <mo>=</mo>
                  <mi>F</mi>
                  <mi>E</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Let
              <math>
                <mstyle>
                  <mi>A</mi>
                  <mi>E</mi>
                </mstyle>
              </math>
            be greater than
              <math>
                <mstyle>
                  <mi>A</mi>
                  <mi>D</mi>
                </mstyle>
              </math>
            .
              <lb/>
              <lb/>
            Therefore
              <math>
                <mstyle>
                  <mi>F</mi>
                  <mi>H</mi>
                  <mo>=</mo>
                  <mi>F</mi>
                  <mi>E</mi>
                </mstyle>
              </math>
            , absurd </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Sit
              <math>
                <mstyle>
                  <mi>A</mi>
                  <mi>E</mi>
                </mstyle>
              </math>
            minor,
              <math>
                <mstyle>
                  <mi>A</mi>
                  <mi>D</mi>
                </mstyle>
              </math>
              <lb/>
            […]
              <lb/>
            Ergo
              <math>
                <mstyle>
                  <mi>H</mi>
                  <mi>E</mi>
                  <mo>=</mo>
                  <mi>F</mi>
                  <mi>E</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Let
              <math>
                <mstyle>
                  <mi>A</mi>
                  <mi>E</mi>
                </mstyle>
              </math>
            be less than
              <math>
                <mstyle>
                  <mi>A</mi>
                  <mi>D</mi>
                </mstyle>
              </math>
            .
              <lb/>
              <lb/>
            Therefore
              <math>
                <mstyle>
                  <mi>H</mi>
                  <mi>E</mi>
                  <mo>=</mo>
                  <mi>F</mi>
                  <mi>E</mi>
                </mstyle>
              </math>
            , absurd </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Et inde:
              <math>
                <mstyle>
                  <mi>B</mi>
                  <mi>C</mi>
                  <mo>,</mo>
                  <mi>A</mi>
                  <mi>B</mi>
                  <mo>:</mo>
                  <mi>A</mi>
                  <mi>B</mi>
                  <mo>,</mo>
                  <mi>B</mi>
                  <mi>D</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            And hence
              <math>
                <mstyle>
                  <mi>B</mi>
                  <mi>C</mi>
                  <mo>:</mo>
                  <mi>A</mi>
                  <mi>B</mi>
                  <mo>=</mo>
                  <mi>A</mi>
                  <mi>B</mi>
                  <mo>:</mo>
                  <mi>B</mi>
                  <mi>D</mi>
                </mstyle>
              </math>
            , which was sought. </s>
          </p>
        </div>
      </text>
    </echo>
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