Harriot, Thomas, Mss. 6784

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601
601 (301) 		602
602 (301v)
603
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604 (302v)
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605 (303) 		606
606 (303v)
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608 (304v)
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609 (305) 		610
610 (305v)
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          <pb file="add_6784_f354" o="354" n="707"/>
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              <s xml:space="preserve">[
                <emph style="bf">Commentary:</emph>
              </s>
            </p>
            <p>
              <s xml:space="preserve"> On this page Harriot investigates Propositions 10 and 11 from
                <emph style="it">Supplementum geometriæ</emph>
                <ref id="Viete_1593c" target="http://www.e-rara.ch/zut/content/pageview/2684116"> (Viète 1593c, Props 10, </ref>
              . </s>
              <lb/>
              <quote xml:lang="lat">
                <s xml:space="preserve"> Proposition X.
                  <lb/>
                Si fuerint tres lineæ rectæ proportionales: est ut prima ad tertiam, ita adgregatum quadratorum primæ & secundæ ad adgregatum quadratorum secundæ & </s>
              </quote>
              <lb/>
              <quote>
                <s xml:space="preserve"> If there are three proportional lines, as the first is to the third, so is the sum of squares of the first and second to the sum of squares of the second and third.</s>
              </quote>
              <lb/>
              <quote xml:lang="lat">
                <s xml:space="preserve"> Proposition XI.
                  <lb/>
                Si fuerint tres lineæ rectæ proportionales: est ut prima ad adgregatum primae & tertiæ, ita quadratum secundæ ad adgregatum quadratorum secundæ & </s>
              </quote>
              <lb/>
              <quote>
                <s xml:space="preserve"> If there are three proportional lines, as the first is to the sum of the first and third, so is the square of the second to the sum of squares of the second and third.</s>
              </quote>
              <lb/>
              <s xml:space="preserve"> There are two references to Euclid's
                <emph style="it">Elements</emph>
              , Proposition
                <ref target="http://aleph0.clarku.edu/~djoyce/java/elements/bookVI/propVI20.html"/>
              . </s>
              <lb/>
              <quote>
                <s xml:space="preserve">
                  <ref target="http://aleph0.clarku.edu/~djoyce/java/elements/bookVI/propVI20.html"/>
                Similar polygons my be divided into the same number of similar triangles, each similar pair of which are proportional to the polygons; and the polygons are to each other in the duplicate ratio of their homologous sides. </s>
              </quote>
              <lb/>
              <s xml:space="preserve"> The 'Consectarium' appears verbally in Viete's proposition; Harriot has reinterpreted it </s>
              <s xml:space="preserve">]</s>
            </p>
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          <head xml:space="preserve"> prop. 10.
            <lb/>
          [
            <emph style="bf">Translation: </emph>
          Proposition 10 from the ]</head>
          <p xml:lang="lat">
            <s xml:space="preserve"> Si fuerint tres lineæ rectæ proportionales: Est ut prima ad tertiam, ita adgregatum
              <lb/>
            quadratorum primæ et secundæ ad adgregatum quadratorum secundæ et
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            If there are three proportional lines, as the first is to the third, so is the sum of squares of the first and second to the sum of squares of the second and third.</s>
            <lb/>
            <s xml:space="preserve"> sint tres proportionales
              <lb/>
            continue
              <lb/>
            consequetur
              <lb/>
            vel
              <lb/>
            Et per synæresin
              <lb/>
            Et per 20,6 Euclid
              <lb/>
            Ergo pro
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            let there be three continued proportionals
              <lb/>
            consequently
              <lb/>
            or
              <lb/>
            And by synæresis
              <lb/>
            And by Euclid VI.20
              <lb/>
            Therefore in ]</s>
          </p>
          <head xml:space="preserve"> prop.
            <lb/>
          [
            <emph style="bf">Translation: </emph>
          Proposition ]</head>
          <p xml:lang="lat">
            <s xml:space="preserve"> Si fuerint tres lineæ rectæ proportionales, est ut prima ad adgregatum primae et
              <lb/>
            tertiæ, ita quadratum secundæ ad adgregatum quadratorum secundæ et
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            If there are three proportional lines, as the first is to the sum of the first and third, so is the square of the second to the sum of squares of the second and third.</s>
            <lb/>
            <s xml:space="preserve"> sint tres proportionales
              <lb/>
            per 20,6 El
              <lb/>
            Et per Synæresin
              <lb/>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            let there be three proportionals
              <lb/>
            by Elements VI.20
              <lb/>
            And by synæresin
              <lb/>
            It may be ]</s>
          </p>
          <head xml:space="preserve">
            <lb/>
          [
            <emph style="bf">Translation: </emph>
          ]</head>
          <p xml:lang="lat">
            <s xml:space="preserve"> Itaque si fuerint tres lineæ rectæ proportionales, tria solida ab ijs
              <lb/>
            effecta æqualia sunt. per 10
              <emph style="super">am</emph>
            conculsionem
              <lb/>
            per 11
              <emph style="super">am</emph>
            conclu.
              <lb/>
            […]
              <lb/>
            Dua prima solida sunt æqualia, quia unum factum est ab extremis analogia 10
              <emph style="super">am</emph>
              <lb/>
            et alterum a modijs. Tertium est factum a modijs
              <emph style="st">inferioris</emph>
            analogia 11
              <emph style="super">am</emph>
            ,
              <lb/>
            cuius extremæ sunt eædem
              <emph style="st">superioris</emph>
              <emph style="super">analogia 10am</emph>
            , et illo æquale.
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Therefore if there are three lines in proportion, three solids constructed from them are equal.
              <lb/>
            by the conclusion of the 10th
              <lb/>
            by the conclusion of the 11th
              <lb/>
              <lb/>
            The two first solids are equal, because one is made from the extremes of the ratio of the 10th, and the other by the method
              <lb/>
            The third is made by the method of the ratio of the 11th, whose extremes are the same as in the ratio of the 10th, and is equal to that one.</s>
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