Harriot, Thomas, Mss. 6787

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            <p>
              <s xml:space="preserve">[
                <emph style="bf">Commentary:</emph>
              </s>
            </p>
            <p>
              <s xml:space="preserve"> This is the first of a set of 11 pages containing propositions from Book I of
                <emph style="it">Conics</emph>
              of Apollonius. The edition used by Harriot was Commandino's
                <emph style="it">Apollonii Pergaei conicorum libri quattuor</emph>
                <ref id="apollonius_1566"> (Apollonius </ref>
              , but Harriot translated the verbal propositions and proofs into his own symbolic notation.
                <lb/>
              English translations of the propositions are taken from Dana Densmore
                <emph style="it">Apollonius of Perga: Conics Books I–III</emph>
              , Green Lion Press, 1998.
                <lb/>
              </s>
              <lb/>
              <s xml:space="preserve"> Proposition 11 of Book I is Apollonius's definition of a </s>
              <lb/>
              <quote>
                <s xml:space="preserve"> I.11 If a cone is cut by a plane through its axis, and also cut by another plane cutting the base of the cone in a straight line perpendicular to the base of the axial triangle, and if, further, the diameter of the section is parallel to one side of the axial triangle, and if any straight line is drawn from the section of the cone to its diameter such that this straight line is parallel to the common section of the cutting plane and of the cone's base, then this straight line to the diameter will equal in square the rectangle contained by the straight line from the section's vertex to where the straight line to the diameter cuts it off, and another straight line which has the same ratio to the straight line between the angle of the cone and the vertex of the section as the square on the base of the axial triangle has to the rectangle contained by the remaining two sides of the triangle. And let such a section be called a parabola.</s>
              </quote>
              <s xml:space="preserve">]</s>
            </p>
          </div>
          <head xml:space="preserve" xml:lang="lat"> Appol. lib. 1. prop. 11. De
            <lb/>
          [
            <emph style="bf">Translation: </emph>
          Apollonius, Book I, Proposition 11. On ]</head>
          <p xml:lang="lat">
            <s xml:space="preserve"/>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Aliter demonstrationem
              <lb/>
            ordinavimus ut
              <lb/>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Another demonstration, which we have ordered as ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Ratio componitur
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Ratio composed ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve">
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            ]</s>
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