Harriot, Thomas, Mss. 6785

List of thumbnails

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351
351 (176) 		352
352 (176v)
353
353 (177) 		354
354 (177v)
355
355 (178) 		356
356 (178v)
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357 (179) 		358
358 (179v)
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359 (180) 		360
360 (180v)
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            <p>
              <s xml:space="preserve">[
                <emph style="bf">Commentary:</emph>
              </s>
            </p>
            <p>
              <s xml:space="preserve"> There is a reference on this page to Propositions IX from
                <emph style="it">Effectionum geometricarum canonica recensio</emph>
                <ref id="Viete_1593b" target="http://www.e-rara.ch/zut/content/pageview/2684102"> (Viète 1593b, Prop </ref>
              .
                <lb/>
              There are also references to Salignac, either
                <emph style="it">Tractatus arithmetici</emph>
                <ref id="salignac_1575"> (Salignac </ref>
                <emph style="it">Arithmeticae libri duo</emph>
                <ref id="salignac_1580"> (Salignac </ref>
              and to Stevin, probably to
                <emph style="it">L'arithmétique</emph>
                <ref id="stevin_1585a"> (Stevin </ref>
              . </s>
              <s xml:space="preserve">]</s>
            </p>
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          <p>
            <s xml:space="preserve"> Of 3 magnitudes in continuall proportion: the first being given
              <lb/>
            & the summe of the second & third: to find the </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Per </s>
          </p>
          <p>
            <s xml:space="preserve"> let the first be
              <math>
                <mstyle>
                  <mi>b</mi>
                </mstyle>
              </math>
              <lb/>
            the summe of the second & third
              <math>
                <mstyle>
                  <mi>c</mi>
                </mstyle>
              </math>
              <lb/>
            Then suppose the second
              <math>
                <mstyle>
                  <mi>a</mi>
                </mstyle>
              </math>
            , the third wilbe
              <math>
                <mstyle>
                  <mi>c</mi>
                  <mo>-</mo>
                  <mi>a</mi>
                </mstyle>
              </math>
              <lb/>
            </s>
          </p>
          <p>
            <s xml:space="preserve"> This kind of æquation
              <lb/>
            is not resolved nor
              <lb/>
            compounded by Vieta
              <lb/>
            in Effectionibus Geometricis
              <lb/>
            as I can find.
              <lb/>
            But it is the 9th of his effectiones
              <lb/>
            </s>
          </p>
          <p>
            <s xml:space="preserve"> Multiply the first into the summe of the 2 & third.
              <lb/>
            The half of the first 2
              <lb/>
            his square 4
              <lb/>
            adde the first product 60
              <lb/>
            the summe 64
              <lb/>
            His roote 8
              <lb/>
            subtract the sayd half of the first 2
              <lb/>
            the remayne is 6, the sayd second </s>
          </p>
          <p>
            <s xml:space="preserve"> This solution is
              <lb/>
            according to the
              <lb/>
            ancient manner
              <lb/>
            as in salignacus
              <lb/>
            or Stevin &c.
              <lb/>
            & doth not much differ
              <lb/>
            in practice from my
              <lb/>
            rule before demonstrated
              <lb/>
            by </s>
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