Harriot, Thomas, Mss. 6785

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      <text xml:lang="eng" type="free">
        <div type="section" level="1" n="1">
          <pb file="add_6785_f100" o="100" n="199"/>
          <head xml:space="preserve"> B. Quædam Notatu digna de tribus
            <lb/>
          [
            <emph style="bf">Translation: </emph>
          A certain useful note on three ]</head>
          <p xml:lang="lat">
            <s xml:space="preserve"> Hinc facilior modus indagandi tertium lateris
              <lb/>
            trianguli rectanguli quam vulgaris: silicet
              <lb/>
            cum circa rectum, [???] datis.
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Here is an easier way of investigating the third side of a right-angled triangle, as is common, as around a right angle, [???] given. </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Hinc etiam corollarium apud Vieta manifestis
              <lb/>
              <emph style="st">[???]</emph>
            scilicet. Quantum differentia dimidia
              <lb/>
            inter
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
            et
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
            erit unitas, talium
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>b</mi>
                  <mo>-</mo>
                  <mn>1</mn>
                </mstyle>
              </math>
            . vel
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>c</mi>
                  <mo>+</mo>
                  <mn>1</mn>
                </mstyle>
              </math>
              <lb/>
            erit dimidium quadrati
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Here also is a corollary obvious in Viète. Namely. The quantity of half the difference between
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
            and
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
            will be a unit, so that
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>b</mi>
                  <mo>-</mo>
                  <mn>1</mn>
                </mstyle>
              </math>
            or
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>c</mi>
                  <mo>+</mo>
                  <mn>1</mn>
                </mstyle>
              </math>
            will be half the square of
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
            . </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Si latus
              <math>
                <mstyle>
                  <mi>c</mi>
                </mstyle>
              </math>
            sit ignota melius est operare secundi
              <lb/>
            formam in resolutio, quam in
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            If the side
              <math>
                <mstyle>
                  <mi>c</mi>
                </mstyle>
              </math>
            is unkonwn, it is better to operate the form in the solution, as in the equation. </s>
          </p>
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