Harriot, Thomas, Mss. 6787

List of thumbnails

< >
561
561 (281v) 		562
562 (282)
563
563 (282v) 		564
564 (283)
565
565 (283v) 		566
566 (284)
567
567 (284v) 		568
568 (285)
569
569 (285v) 		570
570 (286)
< >
page |< < (339) of 1155 > >|
    <echo version="1.0RC">
      <text xml:lang="eng" type="free">
        <div type="section" level="1" n="1">
          <pb file="add_6787_f339" o="339" n="676"/>
          <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"> Calculations based on a general series with constant second difference
                <math>
                  <mstyle>
                    <mi>a</mi>
                  </mstyle>
                </math>
              .
                <lb/>
              The second and first rows begin with
                <math>
                  <mstyle>
                    <mi>e</mi>
                  </mstyle>
                </math>
              and
                <math>
                  <mstyle>
                    <mi>o</mi>
                  </mstyle>
                </math>
              respectively.
                <lb/>
              The series 5, 8, 13, 20, ... is used as an example, thus
                <math>
                  <mstyle>
                    <mi>o</mi>
                    <mo>=</mo>
                    <mn>5</mn>
                  </mstyle>
                </math>
              ,
                <math>
                  <mstyle>
                    <mi>e</mi>
                    <mo>=</mo>
                    <mn>3</mn>
                  </mstyle>
                </math>
              ,
                <math>
                  <mstyle>
                    <mi>a</mi>
                    <mo>=</mo>
                    <mn>2</mn>
                  </mstyle>
                </math>
              . (A second version takes
                <math>
                  <mstyle>
                    <mi>o</mi>
                    <mo>=</mo>
                    <mn>5</mn>
                  </mstyle>
                </math>
              ,
                <math>
                  <mstyle>
                    <mi>e</mi>
                    <mo>=</mo>
                    <mn>1</mn>
                  </mstyle>
                </math>
              ,
                <math>
                  <mstyle>
                    <mi>a</mi>
                    <mo>=</mo>
                    <mn>2</mn>
                  </mstyle>
                </math>
              .)
                <math>
                  <mstyle>
                    <mi>b</mi>
                  </mstyle>
                </math>
              ,
                <math>
                  <mstyle>
                    <mi>c</mi>
                  </mstyle>
                </math>
              ,
                <math>
                  <mstyle>
                    <mi>d</mi>
                  </mstyle>
                </math>
              denote successive sums of terms, taken two at a time. </s>
              <s xml:space="preserve">]</s>
            </p>
          </div>
          <head xml:space="preserve" xml:lang="lat"> 5. Differentiæ differentiarum
            <lb/>
          [
            <emph style="bf">Translation: </emph>
          Differences of differences of ]</head>
          <p xml:lang="lat">
            <s xml:space="preserve">
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve">
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Another ]</s>
          </p>
        </div>
      </text>
    </echo>
Impressum