Harriot, Thomas, Mss. 6787

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            <p>
              <s xml:space="preserve">[
                <emph style="bf">Commentary:</emph>
              </s>
            </p>
            <p>
              <s xml:space="preserve"> At the end of Chapter XIX of
                <emph style="it">Variorum responsorum liber VIII</emph>
              (1593) there is a lengthy section entitled '
                <foreign xml:lang="gre">Eis procheiron scholia</foreign>
              '
                <ref id="Viete_1593d" target="http://www.e-rara.ch/zut/content/pageview/2684285"> (Viete 1593d, Chapter 19, </ref>
              . Section IV is on spherical geometry. The 18th and final proposition contains four statements, which Harriot here translated into symbolic notation
                <ref id="Viete_1593d" target="http://www.e-rara.ch/zut/content/pageview/2684289"> (Viete 1593d, Chapter 19, PROCHEIRON, Section IV, Prop </ref>
              . </s>
              <lb/>
              <quote xml:lang="lat">
                <s xml:space="preserve"> 18 Sit triangulum sphaericum ABD, & in peripheria BD cadat segmentum orthogonii AC.
                  <lb/>
                Primo dico esse transsinuosa anguli BAC ad transsinuosa anguli DAC, sicut prosinum peripheria AB ad prosinum peripheri AD.
                  <lb/>
                Secundo dico esse transsinuosam peripheriæ CB ad transsinuosam peripheriæ CD, sicut transsinuosam peripheriae AB ad transsinuosam peripheriæ AD.
                  <lb/>
                Tertio dico esse sinum CD ad sinum CB, sicut prosinum anguli B ad prosinum anguli D.
                  <lb/>
                Denique & quarto dico esse sinum anguli BAC ad sinum anguli DAC, sicut transsinuosam anguli D ad transsinuosam anguli B.</s>
              </quote>
              <lb/>
              <quote>
                <s xml:space="preserve"> 18. Let there be a spherical triangle ABD, and to the arc BD there falls an orthogonal line AC.
                  <lb/>
                First I say that the secant of angle BAC to the secant of angle DAC is as the tangent of the arc AB to the tangent of the arc AD.
                  <lb/>
                Second I say that the secant of the arc CB to the secant of the arc CD is as the secant of the arc AB to the secant of the arc AD.
                  <lb/>
                Third I say that the sine of CD to the sine of DB is as the tangent of angle B to the tangent of angle D.
                  <lb/>
                Fourth and last I say that the sine of angle BAC to the sine of angle DAC is as the secant of angle D to the secant of angle B.</s>
              </quote>
              <s xml:space="preserve">]</s>
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          <head xml:space="preserve" xml:lang="lat"> Demonstratio eorum quæ desiderant
            <lb/>
          in Vieta. lib. 8. respons. pag. 41.b.
            <lb/>
          sectione
            <lb/>
          [
            <emph style="bf">Translation: </emph>
          Demonstration of what is missing in Viète, Responsorum liber VIII, page 41v, section ]</head>
          <p xml:lang="lat">
            <s xml:space="preserve"> Hinc apparet mendam
              <lb/>
            esse apud Vietam. nam
              <lb/>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Here is is clear that it is wrong in Viète, for ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Istæ quatuor conclusiones
              <lb/>
            sexeis variari possunt ut
              <lb/>
            ex analogijs rectangulorm est
              <lb/>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            These four conclusions have six variations as is clear from the ratios for ]</s>
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Impressum