Harriot, Thomas, Mss. 6787

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page |< < (25) of 1155 > >|
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      <text xml:lang="eng" type="free">
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          <pb file="add_6787_f025" o="25" n="49"/>
          <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"> This page contains further work on Viète's statement of 'Syntomon' in Chapter XIX, Proposition 21,
                <emph style="it">Variorum responsorum liber VIII</emph>
                <ref id="Viete_1593d" target="http://www.e-rara.ch/zut/content/pageview/2684281"> (Viete 1593d, Chapter 19, Prop </ref>
              . </s>
              <s xml:space="preserve">]</s>
            </p>
          </div>
          <head xml:space="preserve" xml:lang="lat"/>
          <p xml:lang="lat">
            <s xml:space="preserve"> Aliter.
              <lb/>
            In diagrammatis (
              <emph style="super">In</emph>
            utriusque casibus, 1
              <emph style="super">o</emph>
            et 2
              <emph style="super">o</emph>
            )
              <lb/>
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            , secat,
              <math>
                <mstyle>
                  <mi>e</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
            , in puncto
              <math>
                <mstyle>
                  <mi>x</mi>
                </mstyle>
              </math>
            .
              <lb/>
            fiat
              <math>
                <mstyle>
                  <mi>x</mi>
                  <mi>z</mi>
                </mstyle>
              </math>
            parallela
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>n</mi>
                </mstyle>
              </math>
            .
              <lb/>
              <math>
                <mstyle>
                  <mi>x</mi>
                  <mi>z</mi>
                </mstyle>
              </math>
            secabit
              <math>
                <mstyle>
                  <mi>d</mi>
                  <mi>g</mi>
                </mstyle>
              </math>
            in puncto
              <math>
                <mstyle>
                  <mi>y</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Another way,
              <lb/>
            In the diagram for syntomon, (in either case 1 or 2)
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            cuts
              <math>
                <mstyle>
                  <mi>e</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
            at the point
              <math>
                <mstyle>
                  <mi>x</mi>
                </mstyle>
              </math>
            . Make
              <math>
                <mstyle>
                  <mi>x</mi>
                  <mi>z</mi>
                </mstyle>
              </math>
            parallel to
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>n</mi>
                </mstyle>
              </math>
            , and
              <math>
                <mstyle>
                  <mi>x</mi>
                  <mi>z</mi>
                </mstyle>
              </math>
            will cut
              <math>
                <mstyle>
                  <mi>d</mi>
                  <mi>g</mi>
                </mstyle>
              </math>
            at the point
              <math>
                <mstyle>
                  <mi>y</mi>
                </mstyle>
              </math>
            . </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve">1
              <emph style="super">m</emph>
            Dico quod: […] hoc est sinuui
              <lb/>
            complementi
              <reg norm="differentiaæ" type="abbr">dræ</reg>
              <lb/>
            arcuum
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            1st, I say that this is the sine of the complement of the difference of the given ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Quod fiat
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Which was to be demonstrated. </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Sequitur etiam per 1
              <emph style="super">m</emph>
            : quod:
              <lb/>
            in utroque
              <lb/>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            There follows from the first, because in either ]</s>
          </p>
        </div>
      </text>
    </echo>
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