Harriot, Thomas, Mss. 6784

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611 (306) 		612
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page |< < (363) of 862 > >|
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      <text xml:lang="eng" type="free">
        <div type="section" level="1" n="1">
          <pb file="add_6784_f363" o="363" n="725"/>
          <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"> In this folio Harriot repeats statements that are to be found in
                <emph style="it">Variorum responsorum</emph>
              , Chapter XVII
                <ref id="viete_1595d" target="http://www.e-rara.ch/zut/content/pageview/2684267"> (Viète 1595d, Chapter </ref>
              .
                <lb/>
              Harriot's letters
                <math>
                  <mstyle>
                    <mi>M</mi>
                  </mstyle>
                </math>
              ,
                <math>
                  <mstyle>
                    <mi>m</mi>
                  </mstyle>
                </math>
              ,
                <math>
                  <mstyle>
                    <mi>o</mi>
                  </mstyle>
                </math>
              ,
                <emph style="st">M</emph>
              ,
                <emph style="st">m</emph>
              correspond to Viete's
                <math>
                  <mstyle>
                    <mi>D</mi>
                  </mstyle>
                </math>
              ,
                <math>
                  <mstyle>
                    <mi>X</mi>
                  </mstyle>
                </math>
              ,
                <math>
                  <mstyle>
                    <mi>F</mi>
                  </mstyle>
                </math>
              ,
                <math>
                  <mstyle>
                    <mi>D</mi>
                  </mstyle>
                </math>
              ,
                <math>
                  <mstyle>
                    <mi>B</mi>
                  </mstyle>
                </math>
              .
                <lb/>
              Harriot's final comments refer to the final sentence of Viete's penultimate paragraph (1646, 398):
                <lb/>
                <foreign xml:lang="lat"> Et ut differentia terminorum rationis ad terminorum rationis majorem, ita maxima ad compositam ex ombnibus plus cremento.</foreign>
                <lb/>
                <lb/>
              [
                <emph style="bf">Translation: </emph>
              As the difference in the terms of the ratio is to the greater term of the ratio, so is the the greatest term of the progression to the sum plus an increment.</s>
              <s xml:space="preserve">]</s>
            </p>
          </div>
          <head xml:space="preserve" xml:lang="lat"> 3.) De progressione geometrica. (ut Vieta in var:
            <lb/>
          [
            <emph style="bf">Translation: </emph>
          On geometric progressions (as Viete in
            <emph style="it">Variorum responsorum</emph>
          ) </head>
          <p xml:lang="lat">
            <s xml:space="preserve">
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            ]</s>
            <s xml:space="preserve">
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve">
              <emph style="st">m</emph>
            . minor terminus
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Let
              <emph style="st">m</emph>
            be the lesser terms of the ratio. </s>
            <lb/>
            <s xml:space="preserve">
              <emph style="st">M</emph>
            . Maior terminus
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Let
              <emph style="st">M</emph>
            be the greater terms of the ratio. </s>
            <lb/>
            <s xml:space="preserve">
              <math>
                <mstyle>
                  <mi>M</mi>
                </mstyle>
              </math>
            . maximus terminus
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Let
              <math>
                <mstyle>
                  <mi>M</mi>
                </mstyle>
              </math>
            be the greatest term of the progression. </s>
            <lb/>
            <s xml:space="preserve">
              <math>
                <mstyle>
                  <mi>m</mi>
                </mstyle>
              </math>
            . minimus terminus
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Let
              <math>
                <mstyle>
                  <mi>M</mi>
                </mstyle>
              </math>
            be the least term of the progression. </s>
            <lb/>
            <s xml:space="preserve">
              <math>
                <mstyle>
                  <mi>o</mi>
                </mstyle>
              </math>
            . omnes, id est summa
              <lb/>
            [
              <emph style="bf">Translation: </emph>
              <math>
                <mstyle>
                  <mi>o</mi>
                </mstyle>
              </math>
            is all, that is the sum of all. </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> ita Vieta post δεδόμενα
              <lb/>
            in respons: pag.
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            thus Viete after δεδόμενα
              <emph style="it">Variorum Responsorum</emph>
            page 29. </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> apud Vieta dicitur
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            in Viete this is said to be the ]</s>
          </p>
        </div>
      </text>
    </echo>
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