Harriot, Thomas, Mss. 6785

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              <s xml:space="preserve">[
                <emph style="bf">Commentary:</emph>
              </s>
            </p>
            <p>
              <s xml:space="preserve"> On this page Harriot examines Proposition V from
                <emph style="it">Supplementum geometriæ</emph>
                <ref id="Viete_1593c" target="http://www.e-rara.ch/zut/content/pageview/2684112"> (Viète 1593c, Prop </ref>
              . See also Add MS 6785, 134. </s>
              <lb/>
              <quote xml:lang="lat">
                <s xml:space="preserve"> Propositio V.
                  <lb/>
                Datis duabus lineis rectis, invenire inter easdem duas medias continue, </s>
              </quote>
              <lb/>
              <quote>
                <s xml:space="preserve"> Given two straight lines, to find two mean proportionals between </s>
              </quote>
              <s xml:space="preserve">]</s>
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          <head xml:space="preserve" xml:lang="lat"> In 5
            <emph style="super">am</emph>
          Supplementi. De medias proportionales inter
            <lb/>
          [
            <emph style="bf">Translation: </emph>
          From the 5th proposition of the Supplement. On two mean proportionals between given ]</head>
          <p xml:lang="lat">
            <s xml:space="preserve"> per constructione
              <lb/>
            […]
              <lb/>
            lineæ extreiores
              <lb/>
            lineæ interiores
              <lb/>
            Ergo per 4
              <emph style="super">am</emph>
            prop
              <math>
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                  <mi>I</mi>
                  <mi>K</mi>
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            .
              <math>
                <mstyle>
                  <mi>H</mi>
                  <mi>B</mi>
                </mstyle>
              </math>
            .
              <math>
                <mstyle>
                  <mi>H</mi>
                  <mi>I</mi>
                </mstyle>
              </math>
            .
              <math>
                <mstyle>
                  <mi>B</mi>
                  <mi>C</mi>
                </mstyle>
              </math>
            . continuæ
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            by construction
              <lb/>
              <lb/>
            external lines
              <lb/>
            internal lines
              <lb/>
            Therefore by the 4th proposition,
              <math>
                <mstyle>
                  <mi>I</mi>
                  <mi>K</mi>
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            ,
              <math>
                <mstyle>
                  <mi>H</mi>
                  <mi>B</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>H</mi>
                  <mi>I</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>B</mi>
                  <mi>C</mi>
                </mstyle>
              </math>
            are continued proportionals. </s>
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