Harriot, Thomas, Mss. 6785

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              <s xml:space="preserve">[
                <emph style="bf">Commentary:</emph>
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              <s xml:space="preserve"> The first row contains numbers of the form
                <math>
                  <mstyle>
                    <mrow>
                      <msup>
                        <mn>2</mn>
                        <mi>n</mi>
                      </msup>
                    </mrow>
                  </mstyle>
                </math>
              . The second row contains numbers of the form
                <math>
                  <mstyle>
                    <mrow>
                      <msup>
                        <mn>2</mn>
                        <mi>n</mi>
                      </msup>
                    </mrow>
                    <mo>-</mo>
                    <mn>1</mn>
                  </mstyle>
                </math>
              . Those that are prime, for example, 3, 7, and 31, give rise to perfect numbers of the form
                <math>
                  <mstyle>
                    <mrow>
                      <msup>
                        <mn>2</mn>
                        <mrow>
                          <mi>n</mi>
                          <mo>-</mo>
                          <mn>1</mn>
                        </mrow>
                      </msup>
                    </mrow>
                    <mo maxsize="1">(</mo>
                    <mrow>
                      <msup>
                        <mn>2</mn>
                        <mi>n</mi>
                      </msup>
                    </mrow>
                    <mo>-</mo>
                    <mn>1</mn>
                    <mo maxsize="1">)</mo>
                  </mstyle>
                </math>
              , as stated in Euclid, Proposition
                <ref target="http://aleph0.clarku.edu/~djoyce/java/elements/bookIX/propIX36.html"/>
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                If as many numbers as we please beginning from a unit are set out continuously in double proportion until the sum of all becomes prime, and if the sum multiplied into the last makes some number, then the product is perfect. </s>
              </quote>
              <lb/>
              <s xml:space="preserve"> See also Add MS
                <ref target="http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/library/TRMFCPMB/&start=460&viewMode=image&pn=460"> f. </ref>
              . </s>
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