Harriot, Thomas, Mss. 6784

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              <s xml:space="preserve">[
                <emph style="bf">Commentary:</emph>
              </s>
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              <s xml:space="preserve"> This page summarizes in shorthand some rules that are written out in full in Harriot's treatise on cubic equations, on Add MS 6782
                <ref target="http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/library/XT0KZ8QC/&start=840&viewMode=image&pn=847"> f. </ref>
              .
                <lb/>
              The abbreviations 'co:l' and 'co:pl' stand for 'longitudinal coefficient' and 'plane coefficient' respectively. In an equation of the form
                <math>
                  <mstyle>
                    <mi>a</mi>
                    <mi>a</mi>
                    <mi>a</mi>
                    <mo>-</mo>
                    <mi>b</mi>
                    <mi>a</mi>
                    <mi>a</mi>
                    <mo>+</mo>
                    <mi>c</mi>
                    <mi>c</mi>
                    <mi>a</mi>
                    <mo>=</mo>
                    <mi>d</mi>
                    <mi>d</mi>
                    <mi>f</mi>
                  </mstyle>
                </math>
              , the longitudinal coefficient is
                <math>
                  <mstyle>
                    <mi>b</mi>
                  </mstyle>
                </math>
              and the plane coefficient is
                <math>
                  <mstyle>
                    <mi>c</mi>
                    <mi>c</mi>
                  </mstyle>
                </math>
              . Below the diagram Harriot has set out the different conditions under which such an equation can have three real roots, not necessarily distinct. The same sets of roots are also listed in Add MS 6783
                <ref target="http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/library/VWXURW4V&start=560&viewMode=image&pn=561"> f. </ref>
              .
                <lb/>
              The relevant equations are worked in full in sheets marked C, D, E, F, G (Add MS 6782
                <ref target="http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/library/HSPGZ0AE&start=630&viewMode=image&pn=630"> f. </ref>
              ,
                <ref target="http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/library/HSPGZ0AE&start=630&viewMode=image&pn=631"> f. </ref>
              ,
                <ref target="http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/library/HSPGZ0AE&start=630&viewMode=image&pn=634"> f. </ref>
              ,
                <ref target="http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/library/HSPGZ0AE&start=630&viewMode=image&pn=636"> f. </ref>
              ,
                <ref target="http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/library/HSPGZ0AE&start=630&viewMode=image&pn=638"> f. </ref>
              ), and also in Add MS 6783
                <ref target="http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/library/VWXURW4V&start=360&viewMode=image&pn=369"> f. </ref>
              .
                <lb/>
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