Harriot, Thomas, Mss. 6785

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              <s xml:space="preserve">[
                <emph style="bf">Commentary:</emph>
              </s>
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            <p>
              <s xml:space="preserve"> This page gives the three standard cases of quadratic (
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              ,
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              , and
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              ), and shows how they relate to divisions of a line into given ratios. The first case is the subject of Propositions IX and XII from Viète's
                <emph style="it">Effectionum geometricarum canonica recensio</emph>
                <ref id="Viete_1593b" target="http://www.e-rara.ch/zut/content/pageview/2684102"> (Viète 1593b, Props 9, </ref>
              .
                <lb/>
              The second case is the subject of Propositions X and XIII.
                <lb/>
              The third case is the subject of Proposition
                <ref id="Viete_1593b" target="http://www.e-rara.ch/zut/content/pageview/2684102"> (Viète 1593b, Props 10, </ref>
              .
                <lb/>
              Note on this page two different words used for demonstrating the nature of an equation: 'exegesis' when the equation is written in general notation, but 'effectio' when it is represented by a geometric </s>
              <s xml:space="preserve">]</s>
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          <head xml:space="preserve" xml:lang="lat"> De
            <lb/>
          [
            <emph style="bf">Translation: </emph>
          On ]</head>
          <p xml:lang="">
            <s xml:space="preserve"> extrema et
              <lb/>
            media
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            extreme and mean ]</s>
          </p>
          <p xml:lang="">
            <s xml:space="preserve"> De exegesi per species
              <lb/>
            et per effectiones arith.
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            On showing [the solution] in general form and by arithmetic or geometric construction.</s>
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