Harriot, Thomas, Mss. 6784

List of thumbnails

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721
721 (361) 		722
722 (361v)
723
723 (362) 		724
724 (362v)
725
725 (363) 		726
726 (363v)
727
727 (364) 		728
728 (364v)
729
729 (365) 		730
730 (365v)
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          <pb file="add_6784_f404v" o="404v" n="808"/>
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            <p>
              <s xml:space="preserve">[
                <emph style="bf">Commentary:</emph>
              </s>
            </p>
            <p>
              <s xml:space="preserve"> For Diophantus see the edition of Xylander,
                <ref id="diophantus_1575"> (Diophantus 1575) </ref>
              </s>
              <s xml:space="preserve">]</s>
            </p>
          </div>
          <p>
            <s xml:space="preserve"> The doctrine of Algebraycall nombers is but
              <lb/>
            the doctrined of such continuall proportionalles of
              <lb/>
            which a unite is the </s>
          </p>
          <p>
            <s xml:space="preserve"> A unite being the first of continuall proportionalles; the second is
              <lb/>
            called a roote: because the third wilbe always a square: & the fourth
              <lb/>
              <emph style="st">third</emph>
            a cube, as Euclide </s>
            <s xml:space="preserve"> The names of the other proportionalles
              <lb/>
            following are all compounded of squares, or cubes or both according
              <lb/>
            to Diophantus & others which follow </s>
            <s xml:space="preserve"> Some or other of the most parte of the later
              <lb/>
            writers gave the name of surdsolidus, of which the first or simple sursolid
              <lb/>
            is the sixt proportionall. &</s>
          </p>
          <p>
            <s xml:space="preserve"> Any nomber may be
              <emph style="super">any</emph>
            terme proportinall in a continuall progression
              <lb/>
            from a </s>
            <s xml:space="preserve"> If the nomber terme be the second, the third is gotten by
              <lb/>
            multiplying the nomber into him </s>
            <s xml:space="preserve">& the fourth by multiplying the
              <lb/>
            third by the second & so </s>
            <s xml:space="preserve"> as also
              <emph style="super">by</emph>
            the doctrine of progression
              <lb/>
            any terme that is found another may be gotten compendiously
              <lb/>
            without continuall </s>
          </p>
          <p>
            <s xml:space="preserve"> If a nomber that is known & designed to be the third, fourth,
              <lb/>
            or fifth or any other proportinall of another denomination: the
              <lb/>
            doctrine to find the second is that which is called the extraction
              <lb/>
            of the roote, which is taught in these </s>
          </p>
          <p>
            <s xml:space="preserve"> The second proportionall is also called the first dignity, & the third the
              <lb/>
            second dignity, & the fourth the third dignity &</s>
          </p>
          <p>
            <s xml:space="preserve"> The third is also called the first power; the 4th the second power &</s>
          </p>
          <p>
            <s xml:space="preserve"> The first proportionall
              <lb/>
            is a </s>
          </p>
          <p>
            <s xml:space="preserve"> The first dignity is
              <lb/>
            the second proportionall,
              <lb/>
            called a </s>
          </p>
          <p>
            <s xml:space="preserve"> The first power is the
              <lb/>
            third proportionall
              <lb/>
              <emph style="st">called a square</emph>
              <lb/>
            or second Dignity
              <lb/>
            called a </s>
          </p>
          <p>
            <s xml:space="preserve"> The first solid is the
              <lb/>
            fourth proprtionall:
              <lb/>
            The third dignity: &
              <lb/>
            The second power,
              <lb/>
            called a </s>
          </p>
          <p>
            <s xml:space="preserve"> The pythagoreans
              <lb/>
            did call 4 the first solid
              <lb/>
            as Boethius </s>
            <lb/>
            <s xml:space="preserve"> The nomber serveth to be, because pyramides are prime solids
              <lb/>
            & 4 amongst nombers is the first </s>
          </p>
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