Harriot, Thomas, Mss. 6786

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          <pb file="add_6786_f453v" o="453v" n="906"/>
          <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
                <emph style="it">Variorum responsorum liber VIII</emph>
              , Chapter 17
                <ref id="Viete_1593d" target="http://www.e-rara.ch/zut/content/pageview/2684267"> (Viete 1593d, Chapter </ref>
              . </s>
              <lb/>
              <quote xml:lang="lat">
                <s xml:space="preserve"> Theorema.
                  <lb/>
                Si fuerint magnitudines continue proportionales: erit ut terminus rationis major ad terminum rationis minorem, ita differentia compositæ ex ombinbus & minimæ ad differentiam compositæ ex omnibus & </s>
              </quote>
              <lb/>
              <quote>
                <s xml:space="preserve"> If there are magnitudes in continued proportion, then the ratio of the greatest term to the least will be as the difference between the sum of all and the minimum to the difference between the sum of all and the maximum.</s>
              </quote>
              <lb/>
              <s xml:space="preserve"> Harriot's notation here is the same as </s>
              <s xml:space="preserve">]</s>
            </p>
          </div>
          <head xml:space="preserve" xml:lang="lat"> In Cap. 17. Resp. pag. Vieta
            <lb/>
          [
            <emph style="bf">Translation: </emph>
          From Chapter 17, Responsorum, page 29, ]</head>
          <p xml:lang="lat">
            <s xml:space="preserve"> Si fuerint magnitudines continue proportionales: Erit ut terminus
              <lb/>
            rationis major ad terminum rationis minorem; ita differentia
              <lb/>
            compositæ ex ombinbus et minimæ ad differentiam compositæ ex
              <lb/>
            omnibus et
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            If there are magnitudes in continued proportion, then the ratio of the greatest term to the least will be as the difference between the sum of all and the minimum to the difference between the sum of all and the maximum.</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Sit maxima.
              <math>
                <mstyle>
                  <mi>D</mi>
                </mstyle>
              </math>
            .
              <lb/>
            minima.
              <math>
                <mstyle>
                  <mi>X</mi>
                </mstyle>
              </math>
            .
              <lb/>
            composita ex omnibus.
              <math>
                <mstyle>
                  <mi>F</mi>
                </mstyle>
              </math>
              <lb/>
            ratio Maioris ad minore.
              <math>
                <mstyle>
                  <mi>D</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>B</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Let the greatest be
              <math>
                <mstyle>
                  <mi>D</mi>
                </mstyle>
              </math>
            ,
              <lb/>
            the least
              <math>
                <mstyle>
                  <mi>X</mi>
                </mstyle>
              </math>
            ,
              <lb/>
            the sum of all
              <math>
                <mstyle>
                  <mi>F</mi>
                </mstyle>
              </math>
            ,
              <lb/>
            the ratio of a greater to the lesser
              <math>
                <mstyle>
                  <mi>D</mi>
                  <mo>:</mo>
                  <mi>B</mi>
                </mstyle>
              </math>
            . </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Alius sic: si fuerint magnitudes continue proportionales:
              <lb/>
            ut prima ad secundam: ita omnes antecedentes ad omnes
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Otherwise thusL if there are magnitudes in continued proportion, as the first is to the second, so are all the antecedents to all the consequents.</s>
          </p>
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      </text>
    </echo>
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