Harriot, Thomas, Mss. 6785

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page |< < (53) of 882 > >|
    <echo version="1.0RC">
      <text xml:lang="eng" type="free">
        <div type="section" level="1" n="1">
          <pb file="add_6785_f053" o="53" n="105"/>
          <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 VI from
                <emph style="it">Apollonius Gallus</emph>
                <ref id="Viete_1600a" target="http://www.e-rara.ch/zut/content/pageview/2684201"> (Viete 1600a, Prob </ref>
              , noting cases that were missed by Viète. </s>
              <lb/>
              <quote xml:lang="lat">
                <s xml:space="preserve"> Problema VI.
                  <lb/>
                Datis puncto, linea recta, & circulo, per datum punctam describere circulum, quem data linea recta & datus circulus </s>
              </quote>
              <lb/>
              <quote>
                <s xml:space="preserve"> VI. Given a point, a line, and a circle, through the given point describe a circle that touches the given line and the given circle.</s>
              </quote>
              <s xml:space="preserve">]</s>
            </p>
          </div>
          <head xml:space="preserve" xml:lang="lat"> (. – o) Apoll: Gallus. prob.
            <lb/>
          [
            <emph style="bf">Translation: </emph>
          Apollonius Gallus, Problem ]</head>
          <p xml:lang="lat">
            <s xml:space="preserve"> alius casus:
              <lb/>
            a Vieta
              <lb/>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            another case, missed by ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Data.
              <lb/>
            punctum,
              <math>
                <mstyle>
                  <mi>a</mi>
                </mstyle>
              </math>
              <lb/>
            linea
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
              <lb/>
            circulum
              <math>
                <mstyle>
                  <mi>d</mi>
                  <mi>e</mi>
                  <mi>f</mi>
                </mstyle>
              </math>
              <lb/>
            Quæsitum.
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>b</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
            .
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Given:
              <lb/>
            the point
              <math>
                <mstyle>
                  <mi>a</mi>
                </mstyle>
              </math>
            ,
              <lb/>
            the line
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
            ,
              <lb/>
            the circle
              <math>
                <mstyle>
                  <mi>d</mi>
                  <mi>e</mi>
                  <mi>f</mi>
                </mstyle>
              </math>
            .
              <lb/>
            Sought: the circle
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>b</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
            . </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Casus
              <lb/>
            1.
              <math>
                <mstyle>
                  <mi>c</mi>
                  <mi>f</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            . Vieta.
              <lb/>
            2.
              <math>
                <mstyle>
                  <mi>c</mi>
                  <mi>d</mi>
                  <mi>f</mi>
                </mstyle>
              </math>
            .
              <lb/>
            3.
              <math>
                <mstyle>
                  <mi>d</mi>
                  <mi>c</mi>
                  <mi>f</mi>
                </mstyle>
              </math>
            .
              <lb/>
            4.
              <math>
                <mstyle>
                  <mi>d</mi>
                  <mi>c</mi>
                  <mi>f</mi>
                </mstyle>
              </math>
            .
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Cases:
              <lb/>
            1.
              <math>
                <mstyle>
                  <mi>c</mi>
                  <mi>f</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            , in Viète.
              <lb/>
            2.
              <math>
                <mstyle>
                  <mi>c</mi>
                  <mi>d</mi>
                  <mi>f</mi>
                </mstyle>
              </math>
            .
              <lb/>
            3.
              <math>
                <mstyle>
                  <mi>d</mi>
                  <mi>c</mi>
                  <mi>f</mi>
                </mstyle>
              </math>
            .
              <lb/>
            4.
              <math>
                <mstyle>
                  <mi>d</mi>
                  <mi>c</mi>
                  <mi>f</mi>
                </mstyle>
              </math>
            , in Viète. </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> alter casus:
              <lb/>
            a Vieta
              <lb/>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            another case missed by ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> In tribus prioribus
              <lb/>
            casibus
              <lb/>
            punctum (
              <math>
                <mstyle>
                  <mi>a</mi>
                </mstyle>
              </math>
            ) datum, est extra
              <lb/>
            datum circulum, et
              <math>
                <mstyle>
                  <mi>d</mi>
                </mstyle>
              </math>
            punctum
              <lb/>
            est ad easdem partes lineæ datæ.
              <lb/>
            cum (
              <math>
                <mstyle>
                  <mi>a</mi>
                </mstyle>
              </math>
            ) puncto seu cum circulo
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            In the three previous cases, the point
              <math>
                <mstyle>
                  <mi>a</mi>
                </mstyle>
              </math>
            is outside the given circle, and the point
              <math>
                <mstyle>
                  <mi>d</mi>
                </mstyle>
              </math>
            is on the same side of the given line as the point
              <math>
                <mstyle>
                  <mi>a</mi>
                </mstyle>
              </math>
            or as the given circle. </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> In 4
              <emph style="super">o</emph>
            casu, punctum (
              <math>
                <mstyle>
                  <mi>a</mi>
                </mstyle>
              </math>
            ) datum
              <lb/>
            est intra datum circulum
              <lb/>
            et
              <math>
                <mstyle>
                  <mi>d</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>a</mi>
                </mstyle>
              </math>
            , sunt ad partes
              <lb/>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            In the 4th case, the given point
              <math>
                <mstyle>
                  <mi>a</mi>
                </mstyle>
              </math>
            is inside the given circle, and
              <math>
                <mstyle>
                  <mi>d</mi>
                </mstyle>
              </math>
            and
              <math>
                <mstyle>
                  <mi>a</mi>
                </mstyle>
              </math>
            are on opposite sides. </s>
          </p>
        </div>
      </text>
    </echo>
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