Harriot, Thomas, Mss. 6784

List of thumbnails

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611
611 (306) 		612
612 (306v)
613
613 (307) 		614
614 (307v)
615
615 (308) 		616
616 (308v)
617
617 (309) 		618
618 (309v)
619
619 (310) 		620
620 (310v)
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page |< < (359) of 862 > >|
    <echo version="1.0RC">
      <text xml:lang="eng" type="free">
        <div type="section" level="1" n="1">
          <pb file="add_6784_f359" o="359" n="717"/>
          <head xml:space="preserve"> a) </head>
          <p xml:lang="lat">
            <s xml:space="preserve"> Sit
              <math>
                <mstyle>
                  <mi>a</mi>
                </mstyle>
              </math>
            , Achilles.
              <lb/>
              <math>
                <mstyle>
                  <mi>t</mi>
                </mstyle>
              </math>
            ,
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Let
              <math>
                <mstyle>
                  <mi>a</mi>
                </mstyle>
              </math>
            be Achilles,
              <math>
                <mstyle>
                  <mi>t</mi>
                </mstyle>
              </math>
            the tortoise. </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Sit ratio motus
              <math>
                <mstyle>
                  <mi>a</mi>
                </mstyle>
              </math>
            , ad motus
              <math>
                <mstyle>
                  <mi>t</mi>
                </mstyle>
              </math>
            ,
              <lb/>
            ut:
              <math>
                <mstyle>
                  <mi>b</mi>
                </mstyle>
              </math>
            , ad
              <math>
                <mstyle>
                  <mi>c</mi>
                </mstyle>
              </math>
            .
              <lb/>
            nempe: 10 ad
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Let the ratio of the motion of
              <math>
                <mstyle>
                  <mi>a</mi>
                </mstyle>
              </math>
            to the motion of
              <math>
                <mstyle>
                  <mi>t</mi>
                </mstyle>
              </math>
            be as
              <math>
                <mstyle>
                  <mi>b</mi>
                </mstyle>
              </math>
            to
              <math>
                <mstyle>
                  <mi>c</mi>
                </mstyle>
              </math>
            , namely, 1 to 10. </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Et sit distantia
              <math>
                <mstyle>
                  <mi>a</mi>
                </mstyle>
              </math>
            , et
              <math>
                <mstyle>
                  <mi>t</mi>
                </mstyle>
              </math>
            .
              <math>
                <mstyle>
                  <mi>d</mi>
                </mstyle>
              </math>
            . nempe 1
              <foreign xml:lang="fr">mille</foreign>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            And let the distance between
              <math>
                <mstyle>
                  <mi>a</mi>
                </mstyle>
              </math>
            and
              <math>
                <mstyle>
                  <mi>t</mi>
                </mstyle>
              </math>
            be
              <math>
                <mstyle>
                  <mi>d</mi>
                </mstyle>
              </math>
            , namely, one thousand pases. </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Et sit motus utriusque in eadem linea et ad easdem partes, nempe
              <lb/>
            ab
              <math>
                <mstyle>
                  <mi>a</mi>
                </mstyle>
              </math>
            , et
              <math>
                <mstyle>
                  <mi>t</mi>
                </mstyle>
              </math>
            versus
              <math>
                <mstyle>
                  <mi>w</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            And suppose the motion of both is in the same line and in the same direction, namely, from
              <math>
                <mstyle>
                  <mi>a</mi>
                </mstyle>
              </math>
            and
              <math>
                <mstyle>
                  <mi>t</mi>
                </mstyle>
              </math>
            towards
              <math>
                <mstyle>
                  <mi>w</mi>
                </mstyle>
              </math>
            . </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Quæritur ex datis punctum ubi Achilles comprehendet
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            From what is given there is sought the point where Achilles catches up with the ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Quæestio solvitur exhibendo summam infinitæ progressionis decrescentis
              <lb/>
            ut sequitur: (species summa infinitæ progressionis decrescentis
              <lb/>
            ut in doctrinam de
              <reg norm="progressionis" type="abbr">prog</reg>
              <reg norm="geometricæ" type="abbr">geom</reg>
            :
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            The problem is solved by producing the sum of an infinite decreasing progression as follows: (the case of the sum of an infinite decreasing progression as in the teaching of geometric porgressions is:)</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Alia
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Other ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> (ut Archimedes de
              <lb/>
            quad: parab: pr:
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            (as Archimedes in the quadrature of the parabola, proposition ]</s>
          </p>
        </div>
      </text>
    </echo>
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