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 |< < (360) of 862 > >|
    <echo version="1.0RC">
      <text xml:lang="eng" type="free">
        <div type="section" level="1" n="1">
          <pb file="add_6784_f360" o="360" n="719"/>
          <head xml:space="preserve"> b) </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 velocitas motus
              <math>
                <mstyle>
                  <mi>a</mi>
                </mstyle>
              </math>
            , ad velocitatem 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/>
            [
              <emph style="bf">Translation: </emph>
            Let the speed of motion of
              <math>
                <mstyle>
                  <mi>a</mi>
                </mstyle>
              </math>
            to the speed of 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>
            . </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Sit distantia inter (
              <math>
                <mstyle>
                  <mi>a</mi>
                </mstyle>
              </math>
            ) et (
              <math>
                <mstyle>
                  <mi>t</mi>
                </mstyle>
              </math>
            ).
              <math>
                <mstyle>
                  <mi>d</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            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>
            . </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Et sit motus utriusque in eadem linea et ad easdem partes, nempe ab (
              <math>
                <mstyle>
                  <mi>a</mi>
                </mstyle>
              </math>
            ), et (
              <math>
                <mstyle>
                  <mi>t</mi>
                </mstyle>
              </math>
            )
              <lb/>
            versus
              <math>
                <mstyle>
                  <mi>w</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            And let the mtion of both be in the same line and 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"> Ponatur illud punctum esse
              <math>
                <mstyle>
                  <mi>w</mi>
                </mstyle>
              </math>
            . et sit
              <math>
                <mstyle>
                  <mi>t</mi>
                  <mi>w</mi>
                </mstyle>
              </math>
            .
              <math>
                <mstyle>
                  <mi>e</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Suppose this point is
              <math>
                <mstyle>
                  <mi>w</mi>
                </mstyle>
              </math>
            , and let the distance
              <math>
                <mstyle>
                  <mi>t</mi>
                  <mi>w</mi>
                </mstyle>
              </math>
            be
              <math>
                <mstyle>
                  <mi>e</mi>
                </mstyle>
              </math>
            . </s>
            <lb/>
            <s xml:space="preserve"> Datur igitur
              <math>
                <mstyle>
                  <mi>e</mi>
                </mstyle>
              </math>
            . Et inde
              <math>
                <mstyle>
                  <mi>w</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Therefore
              <math>
                <mstyle>
                  <mi>e</mi>
                </mstyle>
              </math>
            is found; and hence
              <math>
                <mstyle>
                  <mi>w</mi>
                </mstyle>
              </math>
            . </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> In numeris sit
              <math>
                <mstyle>
                  <mi>b</mi>
                </mstyle>
              </math>
            . 10.
              <lb/>
              <math>
                <mstyle>
                  <mi>c</mi>
                </mstyle>
              </math>
            . 2.
              <lb/>
              <math>
                <mstyle>
                  <mi>d</mi>
                </mstyle>
              </math>
            . 2.
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            In numbers let
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mo>=</mo>
                  <mn>1</mn>
                  <mn>0</mn>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>c</mi>
                  <mo>=</mo>
                  <mn>2</mn>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>d</mi>
                  <mo>=</mo>
                  <mn>2</mn>
                </mstyle>
              </math>
            miles </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve">
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Another ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Aliter 2
              <emph style="super">o</emph>
            .
              <lb/>
            Quæritur
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>w</mi>
                </mstyle>
              </math>
            et sit
              <math>
                <mstyle>
                  <mi>y</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            A second way.
              <lb/>
            There is sought
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>w</mi>
                </mstyle>
              </math>
            , and suppose it is
              <math>
                <mstyle>
                  <mi>y</mi>
                </mstyle>
              </math>
            . </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Exemplum de duabus [¿]numeribus[?]
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            An example from two ]</s>
          </p>
        </div>
      </text>
    </echo>
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