Harriot, Thomas, Mss. 6784

List of thumbnails

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611
611 (306) 		612
612 (306v)
613
613 (307) 		614
614 (307v)
615
615 (308) 		616
616 (308v)
617
617 (309) 		618
618 (309v)
619
619 (310) 		620
620 (310v)
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            <p>
              <s xml:space="preserve">[
                <emph style="bf">Commentary:</emph>
              </s>
            </p>
            <p>
              <s xml:space="preserve"> On this page Harriot investigates Propositions 12, 13, and 14 from
                <emph style="it">Supplementum geometriæ</emph>
                <ref id="Viete_1593c" target="http://www.e-rara.ch/zut/content/pageview/2684117"> (Viète 1593c, Props 12, 13, </ref>
              . </s>
              <lb/>
              <quote xml:lang="lat">
                <s xml:space="preserve"> Proposition XII.
                  <lb/>
                Si fuerint tres lineæ rectæ proportionales: cubus compositæ e duabus extremis, minus solido quod fit sub eadem composita & adgregato quadratorum a tribus, æqualis est solido sub eadem composita & quadrato </s>
              </quote>
              <lb/>
              <quote>
                <s xml:space="preserve"> If there are three proportional lines, the cube of the sum of the two extremes, minus the product of that sum and the sum of squares of all three, is equal to the product of the sum and the square of the </s>
              </quote>
              <lb/>
              <quote xml:lang="lat">
                <s xml:space="preserve"> Proposition XIII.
                  <lb/>
                Si fuerint tres lineæ rectæ proportionales: solidum sub prima & adgregato quadratorum a tribus, minus cubo e prima, æquale est solido sub eadem prima & adgregato quadratorum secundæ & </s>
              </quote>
              <lb/>
              <quote>
                <s xml:space="preserve"> If there are three proportional lines, the product of the first and the sum of squares of all three, minus the cube of the first, is equal to the product of the first and the sum of squares of the second and third.</s>
              </quote>
              <lb/>
              <quote xml:lang="lat">
                <s xml:space="preserve"> Proposition XIV.
                  <lb/>
                Si fuerint tres lineæ rectæ proportionales: solidum sub prima & adgregatum quadratorum a tribus, minus cubo e tertia, æquale est solido sub eadem tertia & adgregato quadratorum primæ & </s>
              </quote>
              <lb/>
              <quote>
                <s xml:space="preserve"> If there are three proportional lines, the product of the first and the sum of squares of all three, minus the cube of the third, is equal to the product of the third and the sum of the first and second.</s>
              </quote>
              <lb/>
              <s xml:space="preserve"> The 'Consectarium' appears verbally in Viete's proposition; Harriot has re-written it in symbolic </s>
              <s xml:space="preserve">]</s>
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          </div>
          <head xml:space="preserve"> prop. 12.
            <lb/>
          [
            <emph style="bf">Translation: </emph>
          Proposition 12 from the ]</head>
          <p xml:lang="lat">
            <s xml:space="preserve"> Si fuerint tres lineæ rectæ proportionales: cubus compositæ e duabus extremis,
              <lb/>
            minus solido quod fit sub eadem composita et adgregato quadratorum a tribus:
              <lb/>
            æqualis est solido sub eadem composita et quadrato
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            If there are three proportional lines, the cube of the sum of the two extremes, minus the product of that sum and the sum of squares of all three, is equal to the product of the sum and the square of the ]</s>
            <lb/>
            <s xml:space="preserve"> Sint 3 continue proportionales
              <lb/>
            utrinque addatur
              <lb/>
            […]
              <lb/>
            Fiant solida ab extremis et etiam a medijs, et inde:
              <lb/>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            let there be three continued proportionals
              <lb/>
            add to each side
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              <lb/>
            There may be made solids from the extremes and also form the means, and hence the ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Prop. 13. Si fuerint tres lineæ rectæ proportionales: solidum sub prima et adgregato
              <lb/>
            quadratorum tribus, minus cubo e prima: æquale est solido sub eadem
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            prima et adgregato quadratorum secundæ et
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Proposition 13. If there are three proportional lines, the product of the first and the sum of squares of all three, minus the cube of the first, is equal to the product of the first and the sum of squares of the second and third.</s>
            <lb/>
            <s xml:space="preserve"> Sint tres continue proportionales
              <lb/>
            […]
              <lb/>
            Resoluatur Analogia et erit:
              <lb/>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Let there be three continued proportionals
              <lb/>
              <lb/>
            The ratio is resolved, and hence the ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Prop. 14. Si fuerint tres lineæ rectæ proportionales: solidum sub prima et adgregatum quadratorum
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            a tribus minus cubo e tertia: æquale est solido sub eadem tertia et adgregato
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            quadratorum primæ et
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Proposition 14. If there are three proportional lines, the product of the first and the sum of squares of all three, minus the cube of the third, is equal to the product of the third and the sum of the first and second.</s>
            <lb/>
            <s xml:space="preserve"> Sint tres continue proportionales
              <lb/>
            […]
              <lb/>
            Resoluatur Analogia et erit:
              <lb/>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Let there be three continued proportionals
              <lb/>
              <lb/>
            The ratio is resolved, and hence the ]</s>
          </p>
          <head xml:space="preserve">
            <lb/>
          [
            <emph style="bf">Translation: </emph>
          ]</head>
          <p xml:lang="lat">
            <s xml:space="preserve"> Quia æquantur æqualibus
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            ex antecedente
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            [
              <emph style="bf">Translation: </emph>
            Because equals are equated to equals, by the preceding ]</s>
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