Harriot, Thomas, Mss. 6784

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            <p>
              <s xml:space="preserve">[
                <emph style="bf">Commentary:</emph>
              </s>
            </p>
            <p>
              <s xml:space="preserve"> The problem pursued in this and many other folios in Add MS 6784 is 'the determinate section', as set out in Pappus,
                <emph style="it">Mathematicae collectiones</emph>
              , Book 7. In Commandino's edition of 1588, the problem is stated on page 159
                <ref id="pappus_1588"> (Pappus </ref>
              . </s>
              <lb/>
              <quote xml:lang="lat">
                <s xml:space="preserve"> Data infinitam rectam lineam vno puncta secare, ita vt interiectarum linearum ad data ipsius puncta, vel unius quadratum, vel rectangulum duabus contentum datam proportionem habeat, vel ad rectangulum contentum vna ipsarum interiecta, & alia extra data, vel duabus interiectis contentum punctis ad vtrasque partes </s>
              </quote>
              <lb/>
              <quote>
                <s xml:space="preserve"> Given an infinite line, to cut it in a single point so that the square of one of the lines to given points on it, or the rectangle of two of them, will have a given ratio either to a rectangle either of one of the cut off lines and another given line, or of two cut off lines to points given on either </s>
              </quote>
              <lb/>
              <s xml:space="preserve"> In the first problem on this page, for example, Harriot requires the position of the point
                <math>
                  <mstyle>
                    <mi>o</mi>
                  </mstyle>
                </math>
              so that
                <math>
                  <mstyle>
                    <mi>a</mi>
                    <mi>a</mi>
                    <mo>:</mo>
                    <mi>x</mi>
                    <mo maxsize="1">(</mo>
                    <mi>b</mi>
                    <mo>-</mo>
                    <mi>a</mi>
                    <mo maxsize="1">)</mo>
                    <mo>=</mo>
                    <mi>r</mi>
                    <mo>:</mo>
                    <mi>s</mi>
                  </mstyle>
                </math>
              , where
                <math>
                  <mstyle>
                    <mi>x</mi>
                  </mstyle>
                </math>
              is the length of some given line, and
                <math>
                  <mstyle>
                    <mi>r</mi>
                    <mo>:</mo>
                    <mi>s</mi>
                  </mstyle>
                </math>
              is a given ratio. </s>
              <s xml:space="preserve">]</s>
            </p>
          </div>
          <head xml:space="preserve" xml:lang="lat"> 1.) De determinata
            <lb/>
          [
            <emph style="bf">Translation: </emph>
          On a determinate ]</head>
          <p xml:lang="lat">
            <s xml:space="preserve"> prob.
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Problem ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> epit.
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Epitagmis ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> epit.
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Epitagmis ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve">
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            ]</s>
          </p>
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