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_f295" o="295" n="589"/>
          <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"> Appoll. Gall. problema. 9.
            <lb/>
          Casus.
            <lb/>
          [
            <emph style="bf">Translation: </emph>
          Apollonius Gallus, Problem IX, case ]</head>
          <p xml:lang="lat">
            <s xml:space="preserve"> In isto casu:
              <lb/>
            Si punctum datum
              <math>
                <mstyle>
                  <mi>I</mi>
                </mstyle>
              </math>
            sit extra
              <lb/>
            circulum circa
              <math>
                <mstyle>
                  <mi>A</mi>
                  <mi>H</mi>
                </mstyle>
              </math>
            , et intra
              <lb/>
            tangentes ad partes
              <math>
                <mstyle>
                  <mi>A</mi>
                </mstyle>
              </math>
            :
              <lb/>
            vel extra eundem circulum et
              <lb/>
            intra tangentes ad partes
              <math>
                <mstyle>
                  <mi>H</mi>
                </mstyle>
              </math>
            .
              <math>
                <mstyle>
                  <mi>M</mi>
                </mstyle>
              </math>
            .
              <lb/>
            Duo circuli possunt
              <lb/>
            tangere duos
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            In this case, if the point
              <math>
                <mstyle>
                  <mi>I</mi>
                </mstyle>
              </math>
            is outside the circle around
              <math>
                <mstyle>
                  <mi>A</mi>
                  <mi>H</mi>
                </mstyle>
              </math>
            , and inside the tangents on the side of
              <math>
                <mstyle>
                  <mi>A</mi>
                </mstyle>
              </math>
            , or outside the same circle and inside the tangents on the sides of
              <math>
                <mstyle>
                  <mi>H</mi>
                </mstyle>
              </math>
            and
              <math>
                <mstyle>
                  <mi>M</mi>
                </mstyle>
              </math>
            , then two circles can touch the two given. </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Punctum non dabiter in circulis
              <lb/>
              <math>
                <mstyle>
                  <mi>A</mi>
                  <mi>D</mi>
                </mstyle>
              </math>
            et
              <math>
                <mstyle>
                  <mi>E</mi>
                  <mi>H</mi>
                </mstyle>
              </math>
            , neque in spatio intra
              <lb/>
            illos circulos vidilicet
              <math>
                <mstyle>
                  <mi>D</mi>
                  <mi>E</mi>
                </mstyle>
              </math>
              <lb/>
            et intra tangentes.
              <lb/>
            Alias utercunque: et unus tantum
              <lb/>
            circulus tangens describitur nisi in
              <lb/>
            locis supra
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            The point will not be given in the circles
              <math>
                <mstyle>
                  <mi>A</mi>
                  <mi>D</mi>
                </mstyle>
              </math>
            and
              <math>
                <mstyle>
                  <mi>E</mi>
                  <mi>H</mi>
                </mstyle>
              </math>
            , nor in the space inside those circles, namely
              <math>
                <mstyle>
                  <mi>D</mi>
                  <mi>E</mi>
                </mstyle>
              </math>
            , and inside the tangents. Any other way, and one such tangent circle will be described unless in the places delineated above. </s>
          </p>
        </div>
      </text>
    </echo>
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