Harriot, Thomas, Mss. 6782

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491 (246) 		492
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            <p>
              <s xml:space="preserve">[
                <emph style="bf">Commentary:</emph>
              </s>
            </p>
            <p>
              <s xml:space="preserve"> This page contains an analysis of Proposition 1 from Book XIII of Euclid's
                <emph style="it">Elements</emph>
              : </s>
              <lb/>
              <quote>
                <s xml:space="preserve">
                  <ref target="http://aleph0.clarku.edu/~djoyce/java/elements/bookXIII/propXIII1.html"/>
                If a straight line is cut in extreme and mean ratio, then the square on the greater segment added to the half of the whole is five times the square on the half. </s>
              </quote>
              <lb/>
              <s xml:space="preserve"> The left hand column gives the 'analysis' or 'resolution' of the problem, beginning from the final statement and working backwards to discover what conditions must hold.
                <lb/>
              The right hand column gives the 'synthesis' or 'composition', beginning from the given conditions and working forward to the proof of the proposition.</s>
              <s xml:space="preserve">]</s>
            </p>
          </div>
          <head xml:space="preserve" xml:lang="lat"> Euclid: lib:
            <lb/>
          [
            <emph style="bf">Translation: </emph>
          Euclid Book ]</head>
          <p xml:lang="lat">
            <s xml:space="preserve"> prop. 1.
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Proposition 1, ]</s>
            <lb/>
            <s xml:space="preserve"> sit
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
            secta extra: & med.
              <lb/>
            in puncto
              <math>
                <mstyle>
                  <mi>c</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Let
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
            be cut in extrme and mean ratio in point
              <math>
                <mstyle>
                  <mi>c</mi>
                </mstyle>
              </math>
            . </s>
            <lb/>
            <s xml:space="preserve"> dico
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            I say ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve">
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            ]</s>
            <lb/>
            <s xml:space="preserve">[…]</s>
            <lb/>
            <s xml:space="preserve"> Est igitur
              <lb/>
            est
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Therefore it is so; for it is ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve">
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            ]</s>
            <lb/>
            <s xml:space="preserve">[…]</s>
            <lb/>
            <s xml:space="preserve"> Quod demonstrare
              <lb/>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Which was to be ]</s>
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Impressum