Harriot, Thomas, Mss. 6787

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page |< < (367) of 1155 > >|
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      <text xml:lang="eng" type="free">
        <div type="section" level="1" n="1">
          <pb file="add_6787_f367" o="367" n="732"/>
          <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"> The inclusion of a page number confirms that Harriot was using Commandino's edition of
                <emph style="it">Apollonii Pergaei conicorum libri quattuor</emph>
                <ref id="apollonius_1566"> (Apollonius </ref>
              .
                <lb/>
              For Proposition 11, the original definition of a parabola, see Add MS
                <ref target="http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/library/MAH52R5E&start=710&viewMode=image&pn=712"> f. </ref>
              . </s>
              <lb/>
              <quote>
                <s xml:space="preserve"> I. 52 Given a straight line in a plane bounded at one point, to find in the plane the section of a cone called parabola, whose diameter is the given straight line, and whose vertex is the end of the straight line, and where whatever straight line is dropped from the section to the diameter at a given angle, will equal in square the rectangle contained by the straight line cut off by it from the vertex of the section and by some other given straight line.</s>
              </quote>
              <s xml:space="preserve">]</s>
            </p>
          </div>
          <head xml:space="preserve" xml:lang="lat"> pag. 37.
            <lb/>
          Appol. pro:
            <lb/>
          [
            <emph style="bf">Translation: </emph>
          page 37, Apollonius, Proposition ]</head>
          <p xml:lang="lat">
            <s xml:space="preserve"> ad latus
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            for the latus </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> per. 11. ergo:
              <math>
                <mstyle>
                  <mi>x</mi>
                  <mi>a</mi>
                  <mi>l</mi>
                </mstyle>
              </math>
            est sectio
              <lb/>
            cuius axis
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
              <lb/>
            et recta
              <math>
                <mstyle>
                  <mi>c</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            by proposition 11, therefore,
              <math>
                <mstyle>
                  <mi>x</mi>
                  <mi>a</mi>
                  <mi>l</mi>
                </mstyle>
              </math>
            is the section whose axis is
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
            with line
              <math>
                <mstyle>
                  <mi>c</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            . </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> sit
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
            diameter
              <lb/>
              <math>
                <mstyle>
                  <mi>c</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            recta
              <lb/>
              <math>
                <mstyle>
                  <mi>h</mi>
                  <mi>a</mi>
                  <mi>e</mi>
                </mstyle>
              </math>
            angulus appl.
              <lb/>
            non
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            let
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
            be the diameter,
              <math>
                <mstyle>
                  <mi>c</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            the line,
              <math>
                <mstyle>
                  <mi>h</mi>
                  <mi>a</mi>
                  <mi>e</mi>
                </mstyle>
              </math>
            the angle of application, not a right angle. </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> unde fit sectio
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>k</mi>
                </mstyle>
              </math>
            ex cono recto
              <lb/>
            ut supra. et transit per
              <lb/>
              <math>
                <mstyle>
                  <mi>e</mi>
                  <mi>a</mi>
                </mstyle>
              </math>
            est contingens, quia
              <math>
                <mstyle>
                  <mi>e</mi>
                  <mi>k</mi>
                  <mo>=</mo>
                  <mi>k</mi>
                  <mi>l</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            whence arises the section
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>k</mi>
                </mstyle>
              </math>
            from the right cone as above, and the crossing line
              <math>
                <mstyle>
                  <mi>e</mi>
                  <mi>a</mi>
                </mstyle>
              </math>
            is a tangent, because
              <math>
                <mstyle>
                  <mi>e</mi>
                  <mi>k</mi>
                  <mo>=</mo>
                  <mi>k</mi>
                  <mi>l</mi>
                </mstyle>
              </math>
            . </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Ergo per 49
              <lb/>
              <math>
                <mstyle>
                  <mi>c</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            est latus
              <lb/>
            rectum. et
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
            diameter &
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Therefore by pproposition 49,
              <math>
                <mstyle>
                  <mi>c</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            is the latus rectum and
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
            the diameter. </s>
          </p>
        </div>
      </text>
    </echo>
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