Harriot, Thomas, Mss. 6785

List of thumbnails

< >
171
171 (86) 		172
172 (86v)
173
173 (87) 		174
174 (87v)
175
175 (88) 		176
176 (88v)
177
177 (89) 		178
178 (89v)
179
179 (90) 		180
180 (90v)
< >
page |< < (109) of 882 > >|
    <echo version="1.0RC">
      <text xml:lang="eng" type="free">
        <div type="section" level="1" n="1">
          <pb file="add_6785_f109" o="109" n="217"/>
          <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"> On this page, Harriot works on the second part of Proposition 14 from
                <emph style="it">Effectionum geometricarum canonica recensio</emph>
                <ref id="Viete_1593b" target="http://www.e-rara.ch/zut/content/pageview/2684104"> (Viète 1593b, Prop </ref>
              . </s>
              <lb/>
              <quote xml:lang="lat">
                <s xml:space="preserve"> Propositio XIV.
                  <lb/>
                Idem quadratum a media proportionali inter hypotenusam trianguli rectanguli & perpendiculum ejusdem, proportionale est inter quadratum hpotenusæ & quadratum idem hypotenusæ multatum basis </s>
              </quote>
              <lb/>
              <quote>
                <s xml:space="preserve"> The square of the mean proportional between the hypotenuse of a right-angled triangle and its perpendicular, is the proportional between the square of the hypotenuse and the square of the same hypotenuse minus the square of the </s>
              </quote>
              <lb/>
              <s xml:space="preserve"> Viète demonstrated this proposition geometrically and showed that it can be represented by the quartic
                <math>
                  <mstyle>
                    <mrow>
                      <msup>
                        <mi>A</mi>
                        <mn>4</mn>
                      </msup>
                    </mrow>
                    <mo>-</mo>
                    <mrow>
                      <msup>
                        <mi>B</mi>
                        <mn>2</mn>
                      </msup>
                    </mrow>
                    <mrow>
                      <msup>
                        <mi>A</mi>
                        <mn>2</mn>
                      </msup>
                    </mrow>
                    <mo>=</mo>
                    <mrow>
                      <msup>
                        <mi>D</mi>
                        <mn>4</mn>
                      </msup>
                    </mrow>
                  </mstyle>
                </math>
              (in modern notation), where
                <math>
                  <mstyle>
                    <mi>A</mi>
                  </mstyle>
                </math>
              is the hypotenuse,
                <math>
                  <mstyle>
                    <mi>B</mi>
                  </mstyle>
                </math>
              the base, and
                <math>
                  <mstyle>
                    <mi>D</mi>
                  </mstyle>
                </math>
              the mean. As in the earlier pages in this set, Harriot works the other way round, beginning from the equation
                <math>
                  <mstyle>
                    <mi>a</mi>
                    <mi>a</mi>
                    <mi>a</mi>
                    <mi>a</mi>
                    <mo>-</mo>
                    <mi>b</mi>
                    <mi>b</mi>
                    <mi>a</mi>
                    <mi>a</mi>
                    <mo>=</mo>
                    <mi>d</mi>
                    <mi>d</mi>
                    <mi>d</mi>
                    <mi>d</mi>
                  </mstyle>
                </math>
              and then deriving the corresponding construction. </s>
              <s xml:space="preserve">]</s>
            </p>
          </div>
          <head xml:space="preserve" xml:lang="lat"> h.) Effectiones
            <lb/>
          [
            <emph style="bf">Translation: </emph>
          Geometrical ]</head>
          <p xml:lang="lat">
            <s xml:space="preserve"> 2.)
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>a</mi>
                  <mi>a</mi>
                  <mi>a</mi>
                  <mo>-</mo>
                  <mn>2</mn>
                  <mi>c</mi>
                  <mi>b</mi>
                  <mi>a</mi>
                  <mi>a</mi>
                  <mo>=</mo>
                  <mi>d</mi>
                  <mi>d</mi>
                  <mi>d</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
              <lb/>
            Et intelligatur.
              <math>
                <mstyle>
                  <mn>2</mn>
                  <mi>c</mi>
                  <mo>=</mo>
                  <mi>b</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            2.)
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>a</mi>
                  <mi>a</mi>
                  <mi>a</mi>
                  <mo>-</mo>
                  <mn>2</mn>
                  <mi>c</mi>
                  <mi>b</mi>
                  <mi>a</mi>
                  <mi>a</mi>
                  <mo>=</mo>
                  <mi>d</mi>
                  <mi>d</mi>
                  <mi>d</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            ; and it may be understood that
              <math>
                <mstyle>
                  <mn>2</mn>
                  <mi>c</mi>
                  <mo>=</mo>
                  <mi>b</mi>
                </mstyle>
              </math>
            . </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Notatio pro effectione
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Notation for the geometric ]</s>
          </p>
        </div>
      </text>
    </echo>
Impressum