Harriot, Thomas, Mss. 6785

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691
691 (346) 		692
692 (346v)
693
693 (347) 		694
694 (347v)
695
695 (348) 		696
696 (348v)
697
697 (349) 		698
698 (349v)
699
699 (350) 		700
700 (350v)
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page |< < (392v) of 882 > >|
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              <s xml:space="preserve">[
                <emph style="bf">Commentary:</emph>
              </s>
            </p>
            <p>
              <s xml:space="preserve"> The text at the top of the page uses Stevin's notation, 5(2), for example, for what we would now write as
                <math>
                  <mstyle>
                    <mn>5</mn>
                    <mrow>
                      <msup>
                        <mi>x</mi>
                        <mn>2</mn>
                      </msup>
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              .
                <lb/>
              At the bottom of the page are two references to Stevin's
                <emph style="it">L'arithmétique ... aussi l'algebre</emph>
                <ref id="stevin_1585a"> (Stevin </ref>
              , pages 289 and 293. On page 289 Stevin deals with equations of the form: square = number – roots. On page 293 he deals with the form: square = roots – number. Stevin's example is 1(2) = 6(1) – 5 (in modern notation
                <math>
                  <mstyle>
                    <mrow>
                      <msup>
                        <mi>x</mi>
                        <mn>2</mn>
                      </msup>
                    </mrow>
                    <mo>=</mo>
                    <mn>6</mn>
                    <mi>x</mi>
                    <mo>-</mo>
                    <mn>5</mn>
                  </mstyle>
                </math>
              ), which has two real roots, 1 and 5. Harriot's example
                <math>
                  <mstyle>
                    <mn>1</mn>
                    <mi>z</mi>
                    <mo>=</mo>
                    <mn>2</mn>
                    <mi>r</mi>
                    <mo>-</mo>
                    <mn>5</mn>
                  </mstyle>
                </math>
              (in modern notation
                <math>
                  <mstyle>
                    <mrow>
                      <msup>
                        <mi>x</mi>
                        <mn>2</mn>
                      </msup>
                    </mrow>
                    <mo>=</mo>
                    <mn>2</mn>
                    <mi>x</mi>
                    <mo>-</mo>
                    <mn>5</mn>
                  </mstyle>
                </math>
              ) has no real roots. The annotation 'W.W.' is presumably a reference to Harriot's friend Walter Warner. </s>
              <s xml:space="preserve">]</s>
            </p>
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          <p xml:lang="lat">
            <s xml:space="preserve"> to find a number which being multiplied by 3. & the product mulltiplied into it self
              <lb/>
            may be equal to the first number multiplied by it self,
              <emph style="st">after</emph>
            and the product by </s>
            <lb/>
            <s xml:space="preserve"> Suppose the number 1(1) to be multiplied by 3 to be 3(1) which multiplied into it self makes </s>
            <lb/>
            <s xml:space="preserve"> after, multiplie the first supposed number being 1(1) into it self which is 1(2) and the same
              <lb/>
            1(2) multiplie by 5 the product shalbe 5(2) which must be equal to 9(2) which
              <lb/>
            equation is </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve">
              <math>
                <mstyle>
                  <mn>1</mn>
                  <mi>z</mi>
                  <mo>=</mo>
                  <mn>7</mn>
                  <mo>-</mo>
                  <mn>8</mn>
                  <mi>r</mi>
                </mstyle>
              </math>
            . 289. </s>
            <lb/>
            <s xml:space="preserve">
              <math>
                <mstyle>
                  <mn>1</mn>
                  <mi>z</mi>
                  <mo>=</mo>
                  <mn>2</mn>
                  <mi>r</mi>
                  <mo>-</mo>
                  <mn>5</mn>
                </mstyle>
              </math>
            imposib. W.W. </s>
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