Harriot, Thomas, Mss. 6785

List of thumbnails

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791
791 (396) 		792
792 (396v)
793
793 (397) 		794
794 (397v)
795
795 (398) 		796
796 (398v)
797
797 (399) 		798
798 (399v)
799
799 (400) 		800
800 (400v)
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          <pb file="add_6785_f361" o="361" n="721"/>
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            <p>
              <s xml:space="preserve">[
                <emph style="bf">Commentary:</emph>
              </s>
            </p>
            <p>
              <s xml:space="preserve"> The reference at the top of the page is to a lemma given by Federico Commandino to
                <ref target="http://aleph0.clarku.edu/~djoyce/java/elements/bookX/propX43.html"/>
              of Euclid's
                <emph style="it">Elements</emph>
              , in his
                <emph style="it">Euclidis Elementorum XV</emph>
                <ref id="euclid_1572" target="http://www.e-rara.ch/zut/content/pageview/3682490"> (Euclid 1572, </ref>
              . The original proposition is: </s>
              <lb/>
              <quote>
                <s xml:space="preserve">
                  <ref target="http://aleph0.clarku.edu/~djoyce/java/elements/bookX/propX43.html"/>
                A first bimedial straightline is divided at one point only. </s>
              </quote>
              <lb/>
              <s xml:space="preserve"> There are also references to
                <ref target="http://aleph0.clarku.edu/~djoyce/java/elements/bookII/propII5.html"/>
                <ref target="http://aleph0.clarku.edu/~djoyce/java/elements/bookII/propII9.html"/>
              (marked as 5,2. and 9,2.): </s>
              <lb/>
              <quote>
                <s xml:space="preserve">
                  <ref target="http://aleph0.clarku.edu/~djoyce/java/elements/bookII/propII5.html"/>
                If a straight line is cut into equal and unequal segments, then the rectangle contained by the unequal segments of the whole together with the square on the straight line between the points of section equals the square on the half. </s>
              </quote>
              <lb/>
              <quote>
                <s xml:space="preserve">
                  <ref target="http://aleph0.clarku.edu/~djoyce/java/elements/bookII/propII9.html"/>
                If a straight line is cut into equal and unequal segments, then the sum of the squares on the unequal segments of the whole is double the sum of the square on the half and the square on the straight line between the points of section. </s>
              </quote>
              <s xml:space="preserve">]</s>
            </p>
          </div>
          <head xml:space="preserve" xml:lang="lat"> Comandinus
            <lb/>
          Lemma ad 43 p. 10. lib.
            <lb/>
          [
            <emph style="bf">Translation: </emph>
          Commandino, Lemma to Proposition 43, Book X of the ]</head>
          <p xml:lang="lat">
            <s xml:space="preserve"> est
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            is less ]</s>
            <lb/>
            <s xml:space="preserve">
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            ]</s>
            <lb/>
            <s xml:space="preserve">
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve">
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Another ]</s>
            <lb/>
            <s xml:space="preserve">
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            ]</s>
            <lb/>
            <s xml:space="preserve"> prima
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            first ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> sed
              <lb/>
            maius est […] per prima demonstratio
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            but is greater than by the first demonstration </s>
            <lb/>
            <s xml:space="preserve"> ergo
              <lb/>
            minus est […] secunda conclusio
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            therefore is less than second conclusion </s>
          </p>
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