Harriot, Thomas, Mss. 6785

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page |< < (141v) of 882 > >|
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            <p>
              <s xml:space="preserve">[
                <emph style="bf">Commentary:</emph>
              </s>
            </p>
            <p>
              <s xml:space="preserve"> The reference on this page is to Stevin's
                <emph style="it">L'arithmétique ... aussi l'algebre</emph>
                <ref id="stevin_1585a"> (Stevin </ref>
              , page 289. </s>
              <s xml:space="preserve">]</s>
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          <p>
            <s xml:space="preserve"> The Theorem of this proposition </s>
            <lb/>
            <s xml:space="preserve"> If the summe of the second & third be double: & unto that double
              <lb/>
            added the half of the first magnitude: & betwixt that aggregate
              <lb/>
            & half of the first magnitude be gotten a meane proportionall:
              <lb/>
            & from that meane proportionall be taken the sayd half of the
              <lb/>
            first magnitude: The remayne is the second </s>
          </p>
          <p>
            <s xml:space="preserve"> The theorem is found by resolving of an æquation
              <lb/>
            which was the second sorte in Stevin pag. 289; & then after by composition
              <lb/>
            I made the problem above on the other </s>
          </p>
          <p>
            <s xml:space="preserve"> The worke to bring it to an æquation is this.
              <lb/>
            Let the second be
              <math>
                <mstyle>
                  <mn>1</mn>
                  <mi>a</mi>
                </mstyle>
              </math>
            . then the third must be
              <math>
                <mstyle>
                  <mn>1</mn>
                  <mn>5</mn>
                  <mo>-</mo>
                  <mn>1</mn>
                  <mi>a</mi>
                </mstyle>
              </math>
            .
              <lb/>
            </s>
          </p>
          <p>
            <s xml:space="preserve"> per species
              <lb/>
            it is done
              <lb/>
            in the next
              <lb/>
            </s>
          </p>
          <p>
            <s xml:space="preserve"> So that if it be considered the absolutes wilbe always the
              <lb/>
              <emph style="super">the oblong made of</emph>
            the summe of the second &
              <emph style="super">and the first magnitude:</emph>
            & the nomber of roots wilbe always so many
              <lb/>
            as therebe unites in the </s>
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