Harriot, Thomas, Mss. 6783

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page |< < (57v) of 852 > >|
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            <s xml:space="preserve"> sit æquationis forma data:
              <lb/>
              <math>
                <mstyle>
                  <mi>x</mi>
                  <mi>x</mi>
                  <mi>x</mi>
                  <mi>z</mi>
                  <mo>=</mo>
                  <mo>+</mo>
                  <mi>f</mi>
                  <mi>f</mi>
                  <mi>g</mi>
                  <mi>a</mi>
                  <mo>+</mo>
                  <mi>c</mi>
                  <mi>d</mi>
                  <mi>a</mi>
                  <mi>a</mi>
                  <mo>+</mo>
                  <mn>4</mn>
                  <mi>r</mi>
                  <mi>a</mi>
                  <mi>a</mi>
                  <mi>a</mi>
                  <mo>-</mo>
                  <mi>a</mi>
                  <mi>a</mi>
                  <mi>a</mi>
                  <mi>a</mi>
                </mstyle>
              </math>
            .
              <lb/>
            quæ quatuor radicum potis est: oportet invenire
              <lb/>
            æquationem sub eadem froma
              <emph style="st">quæ</emph>
              <emph style="super">ut</emph>
            habeat
              <emph style="super">radices</emph>
            duas.
              <lb/>
            Quoniam potestas est negativa non feret unicam vel tres
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Let the equation be in the given form
              <lb/>
              <math>
                <mstyle>
                  <mi>x</mi>
                  <mi>x</mi>
                  <mi>x</mi>
                  <mi>z</mi>
                  <mo>=</mo>
                  <mo>+</mo>
                  <mi>f</mi>
                  <mi>f</mi>
                  <mi>g</mi>
                  <mi>a</mi>
                  <mo>+</mo>
                  <mi>c</mi>
                  <mi>d</mi>
                  <mi>a</mi>
                  <mi>a</mi>
                  <mo>+</mo>
                  <mn>4</mn>
                  <mi>r</mi>
                  <mi>a</mi>
                  <mi>a</mi>
                  <mi>a</mi>
                  <mo>-</mo>
                  <mi>a</mi>
                  <mi>a</mi>
                  <mi>a</mi>
                  <mi>a</mi>
                </mstyle>
              </math>
            .
              <lb/>
            which may have four roots; it is required to find an equation of the same form that has only two roots. Because the highest power is negative, if cannot have one or ]</s>
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