Harriot, Thomas, Mss. 6785

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page |< < (55) of 882 > >|
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          <pb file="add_6785_f055" o="55" n="109"/>
          <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"> On this page, Harriot examines Problem IX from
                <emph style="it">Apollonius Gallus</emph>
                <ref id="Viete_1600a" target="http://www.e-rara.ch/zut/content/pageview/2684205"> (Viete 1600a, Prob </ref>
              . </s>
              <lb/>
              <quote xml:lang="lat">
                <s xml:space="preserve"> Problema IX.
                  <lb/>
                Datis duobus circulis, & puncto, per datum punctum circulum describere quem duo dati circuli contingat.</s>
              </quote>
              <lb/>
              <quote>
                <s xml:space="preserve"> IX. Given two circles and a point, through the given point describe a circle that touches the two given </s>
              </quote>
              <s xml:space="preserve">]</s>
            </p>
          </div>
          <head xml:space="preserve" xml:lang="lat"> .oo) Apoll: Gall. prob. 9. de casibus
            <lb/>
            <lb/>
          [
            <emph style="bf">Translation: </emph>
          Apollonius Gallus, Problem IX, on impossible ]</head>
          <p xml:lang="lat">
            <s xml:space="preserve"> Duobus datis
              <lb/>
            circulis et
              <lb/>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            From two given circles and a ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Si tertius tangetur
              <lb/>
            a datis, intra:
              <lb/>
            punctum non dabitur in
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>b</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
              <lb/>
            neque in spatio
              <math>
                <mstyle>
                  <mi>g</mi>
                  <mi>k</mi>
                  <mi>l</mi>
                  <mi>h</mi>
                </mstyle>
              </math>
            .
              <lb/>
            extra:
              <lb/>
            punctum non dabitur
              <lb/>
            in spatio
              <math>
                <mstyle>
                  <mi>f</mi>
                  <mi>g</mi>
                  <mi>h</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>k</mi>
                  <mi>c</mi>
                  <mi>l</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            If the third is touched by the given one, internally, then the point may not be in
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>b</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
            nor in
              <math>
                <mstyle>
                  <mi>g</mi>
                  <mi>k</mi>
                  <mi>l</mi>
                  <mi>h</mi>
                </mstyle>
              </math>
            ; if extrenally, the point may not be in the spaces
              <math>
                <mstyle>
                  <mi>f</mi>
                  <mi>g</mi>
                  <mi>h</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            or
              <math>
                <mstyle>
                  <mi>k</mi>
                  <mi>c</mi>
                  <mi>l</mi>
                </mstyle>
              </math>
            . </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Extra et intra:
              <lb/>
            punctum non dabitur
              <lb/>
            in spatio
              <math>
                <mstyle>
                  <mi>f</mi>
                  <mi>g</mi>
                  <mi>h</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>k</mi>
                  <mi>c</mi>
                  <mi>l</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Outside or inside, the point may not be in the spaces
              <math>
                <mstyle>
                  <mi>f</mi>
                  <mi>g</mi>
                  <mi>h</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            or
              <math>
                <mstyle>
                  <mi>k</mi>
                  <mi>c</mi>
                  <mi>l</mi>
                </mstyle>
              </math>
            . </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Si unus datorum includat
              <lb/>
            alterum circulum:
              <lb/>
            punctum non dabitur
              <lb/>
            extra maiorem circuli
              <lb/>
            vel intra
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            If one of the given circles includes the other circle, the point may not be outside the larger circle nor inside the smaller circle.</s>
          </p>
        </div>
      </text>
    </echo>
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