Harriot, Thomas, Mss. 6785

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page |< < (138) of 882 > >|
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      <text xml:lang="eng" type="free">
        <div type="section" level="1" n="1">
          <pb file="add_6785_f138" o="138" n="275"/>
          <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"> For the edition of Apollonius used by Harriot see
                <ref id="apollonius_1566"> (Apollonius </ref>
              . </s>
              <s xml:space="preserve">]</s>
            </p>
          </div>
          <head xml:space="preserve"> Mesographa
            <lb/>
          Heronis.
            <lb/>
          Philonis Bizantij.
            <lb/>
          </head>
          <p xml:lang="lat">
            <s xml:space="preserve"> Cum Annotatione nostra de
              <lb/>
            faciliori
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            With my annotations for easier ]</s>
          </p>
          <p>
            <s xml:space="preserve"> where
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
            is
              <lb/>
            double to
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
              <lb/>
            as </s>
          </p>
          <p>
            <s xml:space="preserve"> Note:
              <lb/>
            whether these
              <lb/>
            lines be </s>
          </p>
          <p>
            <s xml:space="preserve"> then
              <math>
                <mstyle>
                  <mi>d</mi>
                  <mi>h</mi>
                </mstyle>
              </math>
            would be parallel to
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
              <lb/>
            & the problem performed nearly
              <lb/>
            and also other wayes &</s>
          </p>
          <p>
            <s xml:space="preserve"> Although Eutocius prefereth philo Bizantius his pratice of finding two
              <lb/>
            mean proportionalls Before that of </s>
            <s xml:space="preserve"> Because the number being devided
              <lb/>
            into small æquall parts, it may
              <emph style="super">now</emph>
            easily be seene when
              <math>
                <mstyle>
                  <mi>h</mi>
                  <mi>g</mi>
                </mstyle>
              </math>
            &
              <math>
                <mstyle>
                  <mi>f</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
            be æquall,
              <lb/>
            then by often applying of the compasses to find
              <math>
                <mstyle>
                  <mi>e</mi>
                  <mi>f</mi>
                </mstyle>
              </math>
            &
              <math>
                <mstyle>
                  <mi>e</mi>
                  <mi>g</mi>
                </mstyle>
              </math>
            </s>
            <s xml:space="preserve"> Yet in
              <lb/>
            my improvement the pratice would be better & more easy </s>
            <s xml:space="preserve"> Let the figures
              <lb/>
            nombring the æquall parts beginne at
              <math>
                <mstyle>
                  <mi>k</mi>
                </mstyle>
              </math>
            . & let their numeration runne towards
              <math>
                <mstyle>
                  <mi>f</mi>
                </mstyle>
              </math>
            ;
              <lb/>
            & the like from
              <math>
                <mstyle>
                  <mi>k</mi>
                </mstyle>
              </math>
            towards
              <math>
                <mstyle>
                  <mi>g</mi>
                </mstyle>
              </math>
            </s>
            <s xml:space="preserve"> Then will the shape of a rectangle or gnomon
              <lb/>
            keepe
              <math>
                <mstyle>
                  <mi>k</mi>
                  <mi>e</mi>
                </mstyle>
              </math>
            always at rectangles with the ruler
              <math>
                <mstyle>
                  <mi>f</mi>
                  <mi>g</mi>
                </mstyle>
              </math>
            .
              <emph style="st">and then</emph>
            and moving
              <lb/>
            the ruler with the gnomon keeping the poynt
              <math>
                <mstyle>
                  <mi>c</mi>
                </mstyle>
              </math>
            also in the line till you find
              <lb/>
              <math>
                <mstyle>
                  <mi>k</mi>
                  <mi>f</mi>
                </mstyle>
              </math>
            and
              <math>
                <mstyle>
                  <mi>k</mi>
                  <mi>g</mi>
                </mstyle>
              </math>
            æquall; then is that performed
              <emph style="st">whi</emph>
            also which they now have
              <lb/>
            &
              <emph style="st">[???]</emph>
              <emph style="super">thus</emph>
            easier in practice because that æquallity is sooner found
              <lb/>
              <emph style="st">because</emph>
            the figures go
              <emph style="super">in</emph>
            both wayes a like, which in philoes practice cannot
              <lb/>
            be observed but with
              <emph style="st">with</emph>
            as much difficulty almost, if not so much as
              <lb/>
            that of
              <emph style="st">her</emph>
            </s>
          </p>
        </div>
      </text>
    </echo>
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