Harriot, Thomas, Mss. 6782

List of thumbnails

< >
511
511 (256) 		512
512 (256v)
513
513 (257) 		514
514 (257v)
515
515 (258) 		516
516 (258v)
517
517 (259) 		518
518 (259v)
519
519 (260) 		520
520 (260v)
< >
page |< < (276) of 1011 > >|
    <echo version="1.0RC">
      <text xml:lang="eng" type="free">
        <div type="bundle" level="1" n="1">
          <pb file="add_6782_f276" o="276" n="552"/>
          <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"> Powers of
                <math>
                  <mstyle>
                    <mo maxsize="1">(</mo>
                    <mi>b</mi>
                    <mo>+</mo>
                    <mi>c</mi>
                    <mo maxsize="1">)</mo>
                  </mstyle>
                </math>
              up to
                <math>
                  <mstyle>
                    <mo maxsize="1">(</mo>
                    <mi>b</mi>
                    <mo>+</mo>
                    <mi>c</mi>
                    <mrow>
                      <msup>
                        <mo maxsize="1">)</mo>
                        <mn>5</mn>
                      </msup>
                    </mrow>
                  </mstyle>
                </math>
              . Each power is calculated from the previous one by multiplication.
                <lb/>
              Note the use of cossist
                <math>
                  <mstyle>
                    <mi>r</mi>
                  </mstyle>
                </math>
              for a first power,
                <math>
                  <mstyle>
                    <mi>z</mi>
                  </mstyle>
                </math>
              for a square,
                <math>
                  <mstyle>
                    <mi>c</mi>
                  </mstyle>
                </math>
              for a cube,
                <math>
                  <mstyle>
                    <mi>z</mi>
                    <mi>z</mi>
                  </mstyle>
                </math>
              for a square-suare or fourth power,
                <math>
                  <mstyle>
                    <mo>ßß</mo>
                  </mstyle>
                </math>
              for a sursolid or fifth power.
                <lb/>
              Below the main table is a list of the final sums, including the sixth power (
                <math>
                  <mstyle>
                    <mi>z</mi>
                    <mi>c</mi>
                  </mstyle>
                </math>
              ), which has not been calculated on this page but which can be deduced from the pattern for the previous cases.
                <lb/>
              For a similar table see Add MS
                <ref target="http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/library/TRMFCPMB/&start=910&viewMode=image&pn=913"> f. </ref>
              . </s>
              <s xml:space="preserve">]</s>
            </p>
          </div>
          <p xml:lang="lat">
            <s xml:space="preserve"> Forma
              <emph style="st">generationis continue</emph>
              <emph style="super">generandi figurata</emph>
              <lb/>
              <emph style="st">proportionalium ab unitate</emph>
              <emph style="super">in binomia radice</emph>
              <lb/>
            per logisticen speciosam:
              <lb/>
              <emph style="st">ad demonstrandum pro parte alium</emph>
              <lb/>
              <emph style="st">in numeris analysin.</emph>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            A method of generating figurate numbers from binomial roots in ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Nota: pro
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Note: for the ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Species partium
              <lb/>
            unius cuisque potentiæ
              <lb/>
            sunt continue proportionales
              <lb/>
            ut
              <math>
                <mstyle>
                  <mi>c</mi>
                </mstyle>
              </math>
            ad
              <math>
                <mstyle>
                  <mi>b</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            The case of a single part where the powers are in continued proportion as
              <math>
                <mstyle>
                  <mi>c</mi>
                </mstyle>
              </math>
            to
              <math>
                <mstyle>
                  <mi>b</mi>
                </mstyle>
              </math>
            . </s>
            <s xml:space="preserve"> Et in numeris, sunt
              <lb/>
            termini minimi si
              <math>
                <mstyle>
                  <mi>c</mi>
                </mstyle>
              </math>
            et
              <math>
                <mstyle>
                  <mi>b</mi>
                </mstyle>
              </math>
            sunt primi &c.
              <lb/>
            et non in
              <lb/>
            ratione
              <lb/>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            And in numbers, these are the lowest terms, if
              <math>
                <mstyle>
                  <mi>b</mi>
                </mstyle>
              </math>
            and
              <math>
                <mstyle>
                  <mi>c</mi>
                </mstyle>
              </math>
            are the first,
              <lb/>
            and they are not multiplied by some ]</s>
          </p>
        </div>
      </text>
    </echo>
Impressum