Harriot, Thomas, Mss. 6787

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page |< < (23) of 1155 > >|
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              <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>
              <lb/>
              <quote xml:lang="lat">
                <s xml:space="preserve"> Quæ per factionem sub sinibus peripheriarum & adplicationem ad sinum totum exurgunt, eadem opere additionis vel subductionis præsto sunt.
                  <lb/>
                Cum duæ peripheriæ angulum acutum componunt, est
                  <lb/>
                Vt sinus totus ad sinum duplum primæ, ita sinus secundæ ad sinum complementi differentia, minus sinu complementi composita.</s>
              </quote>
              <lb/>
              <quote>
                <s xml:space="preserve"> What appears from a combination of the sine of the arcs, dividing the sine of the total, is also shown by the operations of addition and subtraction.
                  <lb/>
                When two arcs contain acute angles, then as the whole sine is to twice the sine of the first, so is the sine of the second to the sum of the sine of the complement of the difference minus the sine of the complement of the </s>
              </quote>
              <s xml:space="preserve">]</s>
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          <head xml:space="preserve" xml:lang="lat"> De 3
            <emph style="super">o</emph>
          et 4
            <emph style="super">o</emph>
            <foreign xml:lang="gre">ton syntomon</foreign>
            <lb/>
          [
            <emph style="bf">Translation: </emph>
          On cases 3 and 4 of ]</head>
          <p xml:lang="lat">
            <s xml:space="preserve"> Etsi duo priores casus
              <lb/>
            sufficiunt ad operationes:
              <lb/>
            duo tamen sequentes ad
              <lb/>
            argumentationes sunt ali-
              <lb/>
            quando
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Although the two first cases suffice for working, nevertheless the two following arguments are sometimes necessary.</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve">3
              <emph style="super">us</emph>
            casus est, quando unus
              <lb/>
            datorum arcuum sit maior
              <lb/>
            quadrante; et differentia sit
              <lb/>
            etiam quadrante
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            The 3rd case is when one of the given arcs is greater than a quadrant, and the difference is also greater than a ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve">4
              <emph style="super">us</emph>
            casus est, quando unus datorum
              <lb/>
            arcuum sit maior quadrante;
              <lb/>
            sed differentia sit quadrante
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            The 4th case is when one of the given arcs is greater than a quadrant, but the difference is ]</s>
          </p>
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