Harriot, Thomas, Mss. 6785

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          <pb file="add_6785_f013" o="13" n="25"/>
          <div type="page_commentary" level="0" n="0">
            <p>
              <s xml:space="preserve">[
                <emph style="bf">Commentary:</emph>
              </s>
            </p>
            <p>
              <s xml:space="preserve"> This page refers to Propositions I.21 and III.52 of Apollonius, as edited by Commandino
                <emph style="it">Conicorum libri quattuor</emph>
                <ref id="apollonius_1566"> (Apollonius </ref>
              . </s>
              <lb/>
              <quote>
                <s xml:space="preserve"> I.21 If in a hyperbola or ellipse or circumference of a circle straight lines are dropped as ordinates to the diameter, the square on them will be to the areas contained by the straight lines cut off by them beginning from the ends of the transverse side of the figure, as the upright side of the figure is to the transverse, and to each other as the areas contained by the straight lines cut off, as we have </s>
              </quote>
              <lb/>
              <quote>
                <s xml:space="preserve"> III.52 If in an ellipse a rectangle equal to the fourth part of the figure is applied from both sides to the major axis and deficient by a square figure, and from the points resulting from the application straight lines are deflected to the line of the section, then they will be equal to the axis.</s>
              </quote>
              <s xml:space="preserve">]</s>
            </p>
          </div>
          <p xml:lang="lat">
            <s xml:space="preserve"> per 21, p.
              <lb/>
            1. lib.
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            by Proposition 21 of Book I of ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve">
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> figura
              <lb/>
            vel
              <math>
                <mstyle>
                  <mfrac>
                    <mrow>
                      <mn>1</mn>
                    </mrow>
                    <mrow>
                      <mn>4</mn>
                    </mrow>
                  </mfrac>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            figure
              <lb/>
            or
              <math>
                <mstyle>
                  <mfrac>
                    <mrow>
                      <mn>1</mn>
                    </mrow>
                    <mrow>
                      <mn>4</mn>
                    </mrow>
                  </mfrac>
                </mstyle>
              </math>
            of the figure </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> fiat […] vel
              <math>
                <mstyle>
                  <mfrac>
                    <mrow>
                      <mn>1</mn>
                    </mrow>
                    <mrow>
                      <mn>4</mn>
                    </mrow>
                  </mfrac>
                </mstyle>
              </math>
            figura
              <lb/>
            ut sequitur
              <lb/>
            ponatur:
              <math>
                <mstyle>
                  <mi>D</mi>
                  <mi>W</mi>
                </mstyle>
              </math>
            dari
              <lb/>
            […] centro igitur
              <math>
                <mstyle>
                  <mi>g</mi>
                </mstyle>
              </math>
            , intervallo ad
              <math>
                <mstyle>
                  <mi>p</mi>
                </mstyle>
              </math>
              <lb/>
            periferia agatur secabit
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            in
              <math>
                <mstyle>
                  <mi>w</mi>
                </mstyle>
              </math>
              <lb/>
            Ergo
              <math>
                <mstyle>
                  <mi>w</mi>
                </mstyle>
              </math>
            est centroides per 52. p. 3.
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Let or
              <math>
                <mstyle>
                  <mfrac>
                    <mrow>
                      <mn>1</mn>
                    </mrow>
                    <mrow>
                      <mn>4</mn>
                    </mrow>
                  </mfrac>
                </mstyle>
              </math>
            of the figure, as follows.
              <lb/>
            Put
              <math>
                <mstyle>
                  <mi>D</mi>
                  <mi>W</mi>
                </mstyle>
              </math>
            to be given
              <lb/>
            Therefore the centre is
              <math>
                <mstyle>
                  <mi>g</mi>
                </mstyle>
              </math>
            , the interval taken to
              <math>
                <mstyle>
                  <mi>p</mi>
                </mstyle>
              </math>
            the periphery will therefore cut
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            in
              <math>
                <mstyle>
                  <mi>w</mi>
                </mstyle>
              </math>
            .
              <lb/>
            Therefore
              <math>
                <mstyle>
                  <mi>w</mi>
                </mstyle>
              </math>
            is the centroid by Proposition 52 of Book 3 of Apollonius. </s>
          </p>
        </div>
      </text>
    </echo>
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