Harriot, Thomas, Mss. 6784

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page |< < (411) of 862 > >|
    <echo version="1.0RC">
      <text xml:lang="eng" type="free">
        <div type="section" level="1" n="1">
          <pb file="add_6784_f411" o="411" n="821"/>
          <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"> Here and on folio Add MS
                <ref target="http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/library/XT0KZ8QC/&start=820&viewMode=image&pn=823"> f. </ref>
              , Harriot shows that the product of two or three unequal parts is always less than the product of the same number of equal parts. </s>
              <s xml:space="preserve">]</s>
            </p>
          </div>
          <head xml:space="preserve" xml:lang="lat">1
            <emph style="super">o</emph>
          . de
            <lb/>
          [
            <emph style="bf">Translation: </emph>
          1. on ]</head>
          <p xml:lang="lat">
            <s xml:space="preserve"> Sit: tota linea.
              <math>
                <mstyle>
                  <mn>2</mn>
                  <mi>b</mi>
                </mstyle>
              </math>
            .
              <lb/>
            vel duæ æquales partes.
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mo>+</mo>
                  <mi>b</mi>
                </mstyle>
              </math>
            .
              <lb/>
            magnitudo facta ab illis
              <lb/>
            erit quadratum
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Let the total line be
              <math>
                <mstyle>
                  <mn>2</mn>
                  <mi>b</mi>
                </mstyle>
              </math>
              <lb/>
            or two equal parts
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mo>+</mo>
                  <mi>b</mi>
                </mstyle>
              </math>
            ,
              <lb/>
            the size of their product will be the square
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
            . </s>
            <lb/>
            <s xml:space="preserve"> Sint inæquales partes.
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mo>+</mo>
                  <mi>c</mi>
                </mstyle>
              </math>
              <lb/>
            et:
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mo>-</mo>
                  <mi>c</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Let there be unequal parts
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mo>+</mo>
                  <mi>c</mi>
                </mstyle>
              </math>
            and
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mo>-</mo>
                  <mi>c</mi>
                </mstyle>
              </math>
            . </s>
            <lb/>
            <s xml:space="preserve"> magnitudo facta:
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>b</mi>
                  <mo>-</mo>
                  <mi>c</mi>
                  <mi>c</mi>
                  <mo>&</mo>
                  <mi>l</mi>
                  <mi>t</mi>
                  <mo>;</mo>
                  <mi>b</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            the size of the product is
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>b</mi>
                  <mo>-</mo>
                  <mi>c</mi>
                  <mi>c</mi>
                  <mo>&</mo>
                  <mi>l</mi>
                  <mi>t</mi>
                  <mo>;</mo>
                  <mi>b</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
            . </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Si linea dividatur utcunque in tot
              <lb/>
            partes inæquales, quot æquales:
              <lb/>
            Magnitudo facta ab inæquali-
              <lb/>
            bus, minor est illa quæ facta
              <lb/>
            ab
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            If a line is divided in any way into as many unequal parts as equal parts, the size of the product of the unequal parts is less than the product of the equal parts.</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve">
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            ]</s>
            <lb/>
            <s xml:space="preserve"> Si aggregatum linearum inæqualium æqueretur
              <lb/>
            aggregato tot æqualium: Magnitudo facta &
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            If the sum of the unnequal lines is equal to the sum of as many equals, the size of the product ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve">
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            ]</s>
            <lb/>
            <s xml:space="preserve"> plana facta ab inæqualibus
              <lb/>
            minora sunt quaduratis
              <lb/>
            facta ab
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            planes made from unequals are less than squares made from ]</s>
          </p>
          <head xml:space="preserve" xml:lang="lat">2
            <emph style="it">o</emph>
          . De sectione in tres
            <lb/>
          [
            <emph style="bf">Translation: </emph>
          2. On sectioning into three ]</head>
          <p xml:lang="lat">
            <s xml:space="preserve"> Casus
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            First ]</s>
            <lb/>
            <s xml:space="preserve"> Sint tres inæquales
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Let there be three ]</s>
            <lb/>
            <s xml:space="preserve"> magnitudo facta:
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>b</mi>
                  <mi>b</mi>
                  <mo>-</mo>
                  <mi>b</mi>
                  <mi>c</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            the size of the product is
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>b</mi>
                  <mi>b</mi>
                  <mo>-</mo>
                  <mi>b</mi>
                  <mi>c</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
            . </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Tres æquales
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Three equal ]</s>
            <lb/>
            <s xml:space="preserve"> magnitudo facta
              <lb/>
            quæ cubus.
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>b</mi>
                  <mi>b</mi>
                  <mo>></mo>
                  <mi>b</mi>
                  <mi>b</mi>
                  <mi>b</mi>
                  <mo>-</mo>
                  <mi>b</mi>
                  <mi>c</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            the size of the product which is a cube is
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>b</mi>
                  <mi>b</mi>
                  <mo>></mo>
                  <mi>b</mi>
                  <mi>b</mi>
                  <mi>b</mi>
                  <mo>-</mo>
                  <mi>b</mi>
                  <mi>c</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
            . </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Casus 2
              <emph style="super">a</emph>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Case ]</s>
            <lb/>
            <s xml:space="preserve"> Sint tres inæquales
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Let there be three unequal ]</s>
            <lb/>
            <s xml:space="preserve"> magnitudo facta.
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>b</mi>
                  <mi>b</mi>
                  <mo>+</mo>
                  <mn>3</mn>
                  <mo>,</mo>
                  <mi>b</mi>
                  <mi>b</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            the size of the product is
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>b</mi>
                  <mi>b</mi>
                  <mo>+</mo>
                  <mn>3</mn>
                  <mi>b</mi>
                  <mi>b</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
            . </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Tres æquales
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Three equal ]</s>
            <lb/>
            <s xml:space="preserve"> magnitudo facta
              <lb/>
            quæ cubus.
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>b</mi>
                  <mi>b</mi>
                  <mo>+</mo>
                  <mn>3</mn>
                  <mo>,</mo>
                  <mi>b</mi>
                  <mi>b</mi>
                  <mi>c</mi>
                  <mo>+</mo>
                  <mn>3</mn>
                  <mo>,</mo>
                  <mi>b</mi>
                  <mi>c</mi>
                  <mi>c</mi>
                  <mo>+</mo>
                  <mi>c</mi>
                  <mi>c</mi>
                  <mi>c</mi>
                  <mo>></mo>
                  <mi>b</mi>
                  <mi>b</mi>
                  <mi>b</mi>
                  <mo>+</mo>
                  <mn>3</mn>
                  <mo>,</mo>
                  <mi>b</mi>
                  <mi>b</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            the size of the product which is a cube is
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>b</mi>
                  <mi>b</mi>
                  <mo>+</mo>
                  <mn>3</mn>
                  <mi>b</mi>
                  <mi>b</mi>
                  <mi>c</mi>
                  <mo>+</mo>
                  <mn>3</mn>
                  <mi>b</mi>
                  <mi>c</mi>
                  <mi>c</mi>
                  <mo>+</mo>
                  <mi>c</mi>
                  <mi>c</mi>
                  <mi>c</mi>
                  <mo>></mo>
                  <mi>b</mi>
                  <mi>b</mi>
                  <mi>b</mi>
                  <mo>+</mo>
                  <mn>3</mn>
                  <mi>b</mi>
                  <mi>b</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
            . </s>
          </p>
        </div>
      </text>
    </echo>
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