Harriot, Thomas, Mss. 6787

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    <echo version="1.0RC">
      <text xml:lang="eng" type="free">
        <div type="section" level="1" n="1">
          <pb file="add_6787_f230" o="230" n="458"/>
          <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"> Further work on Proposition 14 from Chapter XIX of
                <emph style="it">Variorum responsorum liber VIII</emph>
                <ref id="Viete_1593d" target="http://www.e-rara.ch/zut/content/pageview/2684276"> (Viete 1593d, Chapter 19, Prop </ref>
              , continued from Add MS 6787
                <ref target="http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/library/MAH52R5E&start=450&viewMode=image&pn=452"> f. </ref>
              ,
                <ref target="http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/library/MAH52R5E&start=450&viewMode=image&pn=454"> f. </ref>
              , and
                <ref target="http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/library/MAH52R5E&start=450&viewMode=image&pn=456"> f. </ref>
              . </s>
              <s xml:space="preserve">]</s>
            </p>
          </div>
          <head xml:space="preserve"> Vieta. lib. 8. resp. pag. 35. prop. 14.
            <foreign xml:lang="gre">proch?on</foreign>
            <lb/>
          [
            <emph style="bf">Translation: </emph>
          Viète, Responsorum liber VIII, page 35, Proposition ]</head>
          <p xml:lang="lat">
            <s xml:space="preserve"> Synopsis Demonstrationis illius
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Sysnopsis of the demonstration of this ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> sunt in eadem
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            are in the same ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> sit
              <math>
                <mstyle>
                  <mi>O</mi>
                  <mi>H</mi>
                  <mi>M</mi>
                </mstyle>
              </math>
            , angulus rectus
              <lb/>
            Maior est ratio
              <math>
                <mstyle>
                  <mi>H</mi>
                  <mi>α</mi>
                </mstyle>
              </math>
            vel
              <math>
                <mstyle>
                  <mi>H</mi>
                  <mi>O</mi>
                </mstyle>
              </math>
            ad
              <math>
                <mstyle>
                  <mi>T</mi>
                  <mi>V</mi>
                </mstyle>
              </math>
            . nam
              <math>
                <mstyle>
                  <mi>α</mi>
                  <mi>β</mi>
                </mstyle>
              </math>
            ad
              <math>
                <mstyle>
                  <mi>T</mi>
                  <mi>V</mi>
                </mstyle>
              </math>
            est in eadem ratione
              <lb/>
            et
              <math>
                <mstyle>
                  <mi>α</mi>
                  <mi>H</mi>
                </mstyle>
              </math>
            maior est quam
              <math>
                <mstyle>
                  <mi>α</mi>
                  <mi>β</mi>
                </mstyle>
              </math>
            .
              <lb/>
            Maior est etiam ratio
              <math>
                <mstyle>
                  <mi>H</mi>
                  <mi>δ</mi>
                </mstyle>
              </math>
            ad
              <math>
                <mstyle>
                  <mi>X</mi>
                  <mi>Y</mi>
                </mstyle>
              </math>
            . nam
              <math>
                <mstyle>
                  <mi>δ</mi>
                  <mi>ɛ</mi>
                </mstyle>
              </math>
            ad
              <math>
                <mstyle>
                  <mi>X</mi>
                  <mi>Y</mi>
                </mstyle>
              </math>
            est eadem, et
              <math>
                <mstyle>
                  <mi>H</mi>
                  <mi>δ</mi>
                </mstyle>
              </math>
            est maior quam
              <math>
                <mstyle>
                  <mi>δ</mi>
                  <mo>\</mo>
                  <mi>v</mi>
                  <mi>a</mi>
                  <mi>r</mi>
                  <mi>e</mi>
                  <mi>s</mi>
                  <mi>p</mi>
                  <mi>s</mi>
                  <mi>i</mi>
                  <mi>l</mi>
                  <mi>o</mi>
                  <mi>n</mi>
                </mstyle>
              </math>
            .
              <lb/>
            Hæc ita se habent, quia
              <emph style="super">angulus</emph>
              <math>
                <mstyle>
                  <mi>α</mi>
                  <mi>H</mi>
                  <mi>V</mi>
                </mstyle>
              </math>
            est obtusus maior scilicet recto
              <math>
                <mstyle>
                  <mi>O</mi>
                  <mi>H</mi>
                  <mi>M</mi>
                </mstyle>
              </math>
            . et alter
              <math>
                <mstyle>
                  <mi>δ</mi>
                  <mi>H</mi>
                  <mi>X</mi>
                </mstyle>
              </math>
            est
              <lb/>
            minor eadem ratio.
              <lb/>
            Ergo
              <math>
                <mstyle>
                  <mi>T</mi>
                  <mi>V</mi>
                </mstyle>
              </math>
            est minor quam
              <math>
                <mstyle>
                  <mi>D</mi>
                  <mi>P</mi>
                </mstyle>
              </math>
            .
              <lb/>
            Ac etiam
              <math>
                <mstyle>
                  <mi>Y</mi>
                  <mi>X</mi>
                </mstyle>
              </math>
            est minor quam
              <math>
                <mstyle>
                  <mi>D</mi>
                  <mi>P</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Let
              <math>
                <mstyle>
                  <mi>O</mi>
                  <mi>H</mi>
                  <mi>M</mi>
                </mstyle>
              </math>
            be a right angle
              <lb/>
            The ratio
              <math>
                <mstyle>
                  <mi>H</mi>
                  <mi>α</mi>
                </mstyle>
              </math>
            or
              <math>
                <mstyle>
                  <mi>H</mi>
                  <mi>O</mi>
                </mstyle>
              </math>
            to
              <math>
                <mstyle>
                  <mi>T</mi>
                  <mi>V</mi>
                </mstyle>
              </math>
            is greater, for
              <math>
                <mstyle>
                  <mi>α</mi>
                  <mi>β</mi>
                </mstyle>
              </math>
            to
              <math>
                <mstyle>
                  <mi>T</mi>
                  <mi>V</mi>
                </mstyle>
              </math>
            is in the same ratio and
              <math>
                <mstyle>
                  <mi>α</mi>
                  <mi>H</mi>
                </mstyle>
              </math>
            is greater than
              <math>
                <mstyle>
                  <mi>α</mi>
                  <mi>β</mi>
                </mstyle>
              </math>
            .
              <lb/>
            The ratio
              <math>
                <mstyle>
                  <mi>H</mi>
                  <mi>δ</mi>
                </mstyle>
              </math>
            to
              <math>
                <mstyle>
                  <mi>X</mi>
                  <mi>Y</mi>
                </mstyle>
              </math>
            is greater, for
              <math>
                <mstyle>
                  <mi>δ</mi>
                  <mi>ɛ</mi>
                </mstyle>
              </math>
            to
              <math>
                <mstyle>
                  <mi>X</mi>
                  <mi>Y</mi>
                </mstyle>
              </math>
            is the same, and
              <math>
                <mstyle>
                  <mi>H</mi>
                  <mi>δ</mi>
                </mstyle>
              </math>
            is greater than
              <math>
                <mstyle>
                  <mi>δ</mi>
                  <mi>ɛ</mi>
                </mstyle>
              </math>
            .
              <lb/>
            These are had thus, because angle
              <math>
                <mstyle>
                  <mi>α</mi>
                  <mi>H</mi>
                  <mi>V</mi>
                </mstyle>
              </math>
            is obtuse, clearly greater than the right angle
              <math>
                <mstyle>
                  <mi>O</mi>
                  <mi>H</mi>
                  <mi>M</mi>
                </mstyle>
              </math>
            , and the other,
              <math>
                <mstyle>
                  <mi>δ</mi>
                  <mi>H</mi>
                  <mi>X</mi>
                </mstyle>
              </math>
            , is less than the same ratio.
              <lb/>
            Therefore
              <math>
                <mstyle>
                  <mi>T</mi>
                  <mi>V</mi>
                </mstyle>
              </math>
            is less than
              <math>
                <mstyle>
                  <mi>D</mi>
                  <mi>P</mi>
                </mstyle>
              </math>
            .
              <lb/>
            And also
              <math>
                <mstyle>
                  <mi>Y</mi>
                  <mi>X</mi>
                </mstyle>
              </math>
            is less than
              <math>
                <mstyle>
                  <mi>D</mi>
                  <mi>P</mi>
                </mstyle>
              </math>
            . </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Hæc facile applicantur
              <lb/>
            ad diagramma
              <lb/>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            These are easily applied to the preceding ]</s>
          </p>
        </div>
      </text>
    </echo>
Impressum