Harriot, Thomas, Mss. 6785

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          <pb file="add_6785_f441" o="441" n="881"/>
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            <p>
              <s xml:space="preserve">[
                <emph style="bf">Commentary:</emph>
              </s>
            </p>
            <p>
              <s xml:space="preserve"> This page and the next explore sides of polygons inscribed in circles. Harriot refers to Euclid, Propositions
                <ref target="http://aleph0.clarku.edu/~djoyce/java/elements/bookXIII/propXIII12.html"/>
                <ref target="http://aleph0.clarku.edu/~djoyce/java/elements/bookXIII/propXIII9.html"/>
              . </s>
              <lb/>
              <quote>
                <s xml:space="preserve">
                  <ref target="http://aleph0.clarku.edu/~djoyce/java/elements/bookXIII/propXIII12.html"/>
                If an equilateral triangle is inscribed in a circle, then the square on the side of the triangle is triple the square on the radius of the circle. </s>
              </quote>
              <lb/>
              <quote>
                <s xml:space="preserve">
                  <ref target="http://aleph0.clarku.edu/~djoyce/java/elements/bookXIII/propXIII9.html"/>
                If the side of the hexagon and that of the decagon inscribed in the same circle be added together, the whole straight line has been cut in extreme and mean ratio, and its greater segment is the side of the hexagon. </s>
              </quote>
              <lb/>
              <s xml:space="preserve"> There is also a reference to Euclid,
                <ref target="http://aleph0.clarku.edu/~djoyce/java/elements/bookX/propX13.html"/>
              . </s>
              <lb/>
              <quote>
                <s xml:space="preserve">
                  <ref target="http://aleph0.clarku.edu/~djoyce/java/elements/bookX/propX13.html"/>
                If two magnitudes be commensurable, and one of them be incommensurable with some magnitude, the remaning one will also be incommensuarble with the same. </s>
              </quote>
              <s xml:space="preserve">]</s>
            </p>
          </div>
          <head xml:space="preserve" xml:lang="lat"> De lateribus polygonon in
            <lb/>
          [
            <emph style="bf">Translation: </emph>
          On the sides of polygons in ]</head>
          <p>
            <s xml:space="preserve"> Euclid.lib.13.pr.12 Euclid Book XIII, Proposition 12.</s>
            <lb/>
            <s xml:space="preserve">[…]</s>
            <lb/>
            <s xml:space="preserve"> latus
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            The side of a ]</s>
          </p>
          <p>
            <s xml:space="preserve">
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Book XIII, Proposition ]</s>
            <lb/>
            <s xml:space="preserve"> Apot. 5
              <emph style="super">a</emph>
            .
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            A fifth apotome, for ]</s>
            <lb/>
            <s xml:space="preserve"> cuius quadratum […] Apot 1
              <emph style="super">a</emph>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            whose square is a first ]</s>
            <lb/>
            <s xml:space="preserve"> ergo etiam […] decagoni latus
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            therefore also the side of a decagon </s>
          </p>
          <p>
            <s xml:space="preserve"> lateri
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            sides of ]</s>
          </p>
          <p>
            <s xml:space="preserve"> sint
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
            , et
              <math>
                <mstyle>
                  <mi>c</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            , lateri pentagoni
              <lb/>
            ergo:
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            latus
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            let
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
            and
              <math>
                <mstyle>
                  <mi>c</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            be sides of a pentagon, therefore
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            is the side of a pentagon </s>
            <lb/>
            <s xml:space="preserve"> ut supra latus
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            as above for the side of a ]</s>
            <lb/>
            <s xml:space="preserve">[…]</s>
            <lb/>
            <s xml:space="preserve"> Minor. Latus
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Lesser. Side of a ]</s>
          </p>
          <p>
            <s xml:space="preserve"> per
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            by Proposition X.13 of ]</s>
            <lb/>
            <s xml:space="preserve"> lateris
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            side of a ]</s>
            <lb/>
            <s xml:space="preserve"> Lateri pentagoni.
              <lb/>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Side of a pentagon; ]</s>
          </p>
          <p>
            <s xml:space="preserve"> verte paginam pro
              <lb/>
            ambitiosa
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            turn the page for the complicated ]</s>
          </p>
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