Harriot, Thomas, Mss. 6782

List of thumbnails

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page |< < (269) of 1011 > >|
    <echo version="1.0RC">
      <text xml:lang="eng" type="free">
        <div type="bundle" level="1" n="1">
          <pb file="add_6782_f269" o="269" n="537"/>
          <head xml:space="preserve" xml:lang="lat"> De compositio rationum.
            <lb/>
          [
            <emph style="bf">Translation: </emph>
          On the composition of ratios. A ]</head>
          <p xml:lang="lat">
            <s xml:space="preserve"> Composita ratio fit ex simplicibus duabus vel pluribus quotcunque.
              <lb/>
            Simplex ratio est ut
              <math>
                <mstyle>
                  <mi>b</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>c</mi>
                </mstyle>
              </math>
            . Hoc est ut numerus ad numerum
              <lb/>
            vel: ut linea ad
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Let a ratio be composed from two simple ones or from more, however many.
              <lb/>
            The simple ratio is as
              <math>
                <mstyle>
                  <mi>b</mi>
                </mstyle>
              </math>
            to
              <math>
                <mstyle>
                  <mi>c</mi>
                </mstyle>
              </math>
            . That is, as a number to a number, or as a line to a line. </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Composita ratio
              <lb/>
            ex duabus est
              <lb/>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            The ratio composed from two is ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> hoc est, si quantitates sunt numeri
              <lb/>
            ut
              <math>
                <mstyle>
                  <mi>b</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>d</mi>
                </mstyle>
              </math>
            multiplicata ad
              <math>
                <mstyle>
                  <mi>c</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>f</mi>
                </mstyle>
              </math>
              <lb/>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            That is, if the quantities are numbers, as
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            to
              <math>
                <mstyle>
                  <mi>c</mi>
                  <mi>f</mi>
                </mstyle>
              </math>
            . </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Si autem lineæ. Ut parallegrammum
              <lb/>
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            : ad parallelogrammum
              <math>
                <mstyle>
                  <mi>c</mi>
                  <mi>f</mi>
                </mstyle>
              </math>
            . Sed
              <lb/>
            parallelogramma sunt intelligenda
              <lb/>
            æqualium
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            And if lines, as the parallelogram
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            to the parallelogram
              <math>
                <mstyle>
                  <mi>c</mi>
                  <mi>f</mi>
                </mstyle>
              </math>
            . But the parallelograms are understood to have equal angles. </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Et ita enunciatur:
              <lb/>
            ratio
              <math>
                <mstyle>
                  <mi>x</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>y</mi>
                </mstyle>
              </math>
            : componitur
              <lb/>
            ex ratione,
              <math>
                <mstyle>
                  <mi>b</mi>
                </mstyle>
              </math>
            ad
              <math>
                <mstyle>
                  <mi>c</mi>
                </mstyle>
              </math>
            ,
              <lb/>
            et ex ratione
              <math>
                <mstyle>
                  <mi>d</mi>
                </mstyle>
              </math>
            ad
              <math>
                <mstyle>
                  <mi>f</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            And it is conveyed thus:
              <lb/>
            the ratio
              <math>
                <mstyle>
                  <mi>x</mi>
                </mstyle>
              </math>
            to
              <math>
                <mstyle>
                  <mi>y</mi>
                </mstyle>
              </math>
            is composed from the ratios
              <math>
                <mstyle>
                  <mi>b</mi>
                </mstyle>
              </math>
            to
              <math>
                <mstyle>
                  <mi>c</mi>
                </mstyle>
              </math>
            and from the ratio
              <math>
                <mstyle>
                  <mi>d</mi>
                </mstyle>
              </math>
            to
              <math>
                <mstyle>
                  <mi>f</mi>
                </mstyle>
              </math>
            . </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Composita ratio ex tribus
              <lb/>
            est ut:
              <math>
                <mstyle>
                  <mi>b</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>c</mi>
                </mstyle>
              </math>
            .
              <lb/>
              <math>
                <mstyle>
                  <mi>d</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>f</mi>
                </mstyle>
              </math>
            .
              <lb/>
              <math>
                <mstyle>
                  <mi>g</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>h</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            A ratio composed from three is ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> hoc est: si numeri:
              <lb/>
            ut
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>d</mi>
                  <mi>g</mi>
                </mstyle>
              </math>
            multiplicati: ad
              <math>
                <mstyle>
                  <mi>c</mi>
                  <mi>f</mi>
                  <mi>h</mi>
                </mstyle>
              </math>
            multip.
              <lb/>
            si lineæ: ut solidum
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>d</mi>
                  <mi>g</mi>
                </mstyle>
              </math>
            ad solidum
              <lb/>
            ex
              <math>
                <mstyle>
                  <mi>c</mi>
                  <mi>f</mi>
                  <mi>h</mi>
                </mstyle>
              </math>
            : sed intelligenda sunt
              <lb/>
            æqualium
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            That is, if numbers, as
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>d</mi>
                  <mi>g</mi>
                </mstyle>
              </math>
            to
              <math>
                <mstyle>
                  <mi>c</mi>
                  <mi>f</mi>
                  <mi>h</mi>
                </mstyle>
              </math>
            . If lines, as the solid
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>d</mi>
                  <mi>g</mi>
                </mstyle>
              </math>
            to the solid from
              <math>
                <mstyle>
                  <mi>c</mi>
                  <mi>f</mi>
                  <mi>h</mi>
                </mstyle>
              </math>
            , but they must be understood as equiangular. </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Et ita enunciatur:
              <lb/>
            ratio;
              <math>
                <mstyle>
                  <mi>x</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>y</mi>
                </mstyle>
              </math>
            : componitur
              <lb/>
            ex ratione,
              <lb/>
              <math>
                <mstyle>
                  <mi>b</mi>
                </mstyle>
              </math>
            ad
              <math>
                <mstyle>
                  <mi>c</mi>
                </mstyle>
              </math>
              <lb/>
              <math>
                <mstyle>
                  <mi>d</mi>
                </mstyle>
              </math>
            ad
              <math>
                <mstyle>
                  <mi>f</mi>
                </mstyle>
              </math>
              <lb/>
              <math>
                <mstyle>
                  <mi>g</mi>
                </mstyle>
              </math>
            ad
              <math>
                <mstyle>
                  <mi>h</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            And it is conveyed thus: the ratio
              <math>
                <mstyle>
                  <mi>x</mi>
                </mstyle>
              </math>
            to
              <math>
                <mstyle>
                  <mi>y</mi>
                </mstyle>
              </math>
            is composed from the ratios
              <math>
                <mstyle>
                  <mi>b</mi>
                </mstyle>
              </math>
            to
              <math>
                <mstyle>
                  <mi>c</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>d</mi>
                </mstyle>
              </math>
            to
              <math>
                <mstyle>
                  <mi>f</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>g</mi>
                </mstyle>
              </math>
            to
              <math>
                <mstyle>
                  <mi>h</mi>
                </mstyle>
              </math>
            . </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Instar plurium: fit ratio composita ex quinque, ut
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            It stands thus for more: let a ratio be composed from five, as follows.</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Hoc est, ratio:
              <math>
                <mstyle>
                  <mi>y</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>z</mi>
                </mstyle>
              </math>
            : æqualis est
              <lb/>
            compositæ
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            That is, the ratio
              <math>
                <mstyle>
                  <mi>y</mi>
                </mstyle>
              </math>
            to
              <math>
                <mstyle>
                  <mi>z</mi>
                </mstyle>
              </math>
            is equal to that composed from: </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> hoc est:
              <math>
                <mstyle>
                  <mi>y</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>z</mi>
                </mstyle>
              </math>
            :
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>d</mi>
                  <mi>g</mi>
                  <mi>m</mi>
                  <mi>o</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>c</mi>
                  <mi>f</mi>
                  <mi>h</mi>
                  <mi>n</mi>
                  <mi>p</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            That is,
              <math>
                <mstyle>
                  <mi>y</mi>
                  <mo>:</mo>
                  <mi>z</mi>
                  <mo>=</mo>
                  <mi>b</mi>
                  <mi>d</mi>
                  <mi>g</mi>
                  <mi>m</mi>
                  <mi>o</mi>
                  <mo>:</mo>
                  <mi>c</mi>
                  <mi>f</mi>
                  <mi>h</mi>
                  <mi>n</mi>
                  <mi>p</mi>
                </mstyle>
              </math>
            . </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve">
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Turn ]</s>
          </p>
        </div>
      </text>
    </echo>
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