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_f056" o="56" n="111"/>
          <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 VIII from
                <emph style="it">Apollonius Gallus</emph>
                <emph style="it">Apollonius Gallus</emph>
                <ref id="Viete_1600a" target="http://www.e-rara.ch/zut/content/pageview/2684203"> (Viete 1600a, Prob </ref>
              . </s>
              <lb/>
              <quote xml:lang="lat">
                <s xml:space="preserve"> Problema VIII.
                  <lb/>
                Datis duobus punctis, & circulo, per data duo puncta circulum describere, qui datum </s>
              </quote>
              <lb/>
              <quote>
                <s xml:space="preserve"> VIII. Given two points and a circle, through the two given points describe a circle that touches the given </s>
              </quote>
              <s xml:space="preserve">]</s>
            </p>
          </div>
          <head xml:space="preserve" xml:lang="lat"> Apoll: Gallus. prob.
            <lb/>
          [
            <emph style="bf">Translation: </emph>
          Apollonius Gallus, Problem ]</head>
          <p xml:lang="lat">
            <s xml:space="preserve"> Desirit Duo casus (et alij)
              <lb/>
            in Vieta:
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            There are two cases missing in Viète, ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Datis duobus puncti
              <math>
                <mstyle>
                  <mi>d</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>b</mi>
                </mstyle>
              </math>
            .
              <lb/>
            Et circulo,
              <math>
                <mstyle>
                  <mi>g</mi>
                  <mi>e</mi>
                  <mi>f</mi>
                </mstyle>
              </math>
            :
              <lb/>
            per datum, circulum contingentem
              <lb/>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Given the two points
              <math>
                <mstyle>
                  <mi>d</mi>
                </mstyle>
              </math>
            and
              <math>
                <mstyle>
                  <mi>b</mi>
                </mstyle>
              </math>
            , and the circle
              <math>
                <mstyle>
                  <mi>g</mi>
                  <mi>e</mi>
                  <mi>f</mi>
                </mstyle>
              </math>
            , describe a circle through the given points, touching the circle. </s>
            <lb/>
            <s xml:space="preserve"> Sit iam factum:
              <lb/>
            Et sit contactus in
              <math>
                <mstyle>
                  <mi>g</mi>
                </mstyle>
              </math>
              <lb/>
            agantur rectæ
              <math>
                <mstyle>
                  <mi>d</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>g</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>d</mi>
                  <mi>g</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>e</mi>
                  <mi>f</mi>
                </mstyle>
              </math>
              <lb/>
            arcus
              <math>
                <mstyle>
                  <mi>g</mi>
                  <mi>f</mi>
                </mstyle>
              </math>
            , et
              <math>
                <mstyle>
                  <mi>g</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
            sunt similes
              <lb/>
            ita
              <math>
                <mstyle>
                  <mi>g</mi>
                  <mi>e</mi>
                </mstyle>
              </math>
            , et
              <math>
                <mstyle>
                  <mi>g</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            .
              <math>
                <mstyle>
                  <mi>o</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
            contingentium.
              <lb/>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            And let it be done thus:
              <lb/>
            And let it meet in
              <math>
                <mstyle>
                  <mi>g</mi>
                </mstyle>
              </math>
            .
              <lb/>
            Connect the lines
              <math>
                <mstyle>
                  <mi>d</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>g</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>d</mi>
                  <mi>g</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>e</mi>
                  <mi>f</mi>
                </mstyle>
              </math>
            .
              <lb/>
            The arcs
              <math>
                <mstyle>
                  <mi>g</mi>
                  <mi>e</mi>
                </mstyle>
              </math>
            and
              <math>
                <mstyle>
                  <mi>g</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
            are simlar, thus
              <math>
                <mstyle>
                  <mi>g</mi>
                  <mi>e</mi>
                </mstyle>
              </math>
            and
              <math>
                <mstyle>
                  <mi>g</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            , touching
              <math>
                <mstyle>
                  <mi>o</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
            . </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Datur latera triangulorum
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>f</mi>
                  <mi>h</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>b</mi>
                  <mi>h</mi>
                </mstyle>
              </math>
              <lb/>
              <math>
                <mstyle>
                  <mi>f</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
            est distantia
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Given the sides of triangles
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>f</mi>
                  <mi>h</mi>
                </mstyle>
              </math>
            and
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>b</mi>
                  <mi>h</mi>
                </mstyle>
              </math>
            , The distance to the vertex is
              <math>
                <mstyle>
                  <mi>f</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
            . </s>
            <lb/>
            <s xml:space="preserve"> In alia charta
              <lb/>
            modus
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            The method of investigation is in another ]</s>
            <lb/>
            <s xml:space="preserve"> Si linea a
              <math>
                <mstyle>
                  <mi>d</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>b</mi>
                </mstyle>
              </math>
              <emph style="super">per se vel producta</emph>
            non secat circulum
              <lb/>
            datum: fierunt duo circuli
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            If the lines from
              <math>
                <mstyle>
                  <mi>d</mi>
                </mstyle>
              </math>
            and
              <math>
                <mstyle>
                  <mi>b</mi>
                </mstyle>
              </math>
            , either in themselves or produced, do not cut the given circle, then there will arise two touching circles. </s>
            <lb/>
            <s xml:space="preserve"> Si unum punctum sit intra alterum extra
              <lb/>
            circulum datum: casus
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            If one point is inside, the other outside, the given circle, the case is ]</s>
            <lb/>
            <s xml:space="preserve"> Si ab uno datorum punctum
              <lb/>
            sint duæ tangentes
              <lb/>
            circulum: et altera fit:
              <lb/>
            extra
              <lb/>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            If from one of the given points there are two tangents to the circle, and the other is constructed
              <lb/>
            outside
              <lb/>
            ]</s>
          </p>
        </div>
      </text>
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