Harriot, Thomas, Mss. 6785

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page |< < (379) of 882 > >|
    <echo version="1.0RC">
      <text xml:lang="eng" type="free">
        <div type="section" level="1" n="1">
          <pb file="add_6785_f379" o="379" n="757"/>
          <div type="page_commentary" level="0" n="0">
            <p>
              <s xml:space="preserve">[
                <emph style="bf">Commentary:</emph>
              </s>
            </p>
            <p>
              <s xml:space="preserve"> The reference on this page is to the Lemma of Monachos, as found in Proposition 59 of Commandino's edition of Pappus
                <emph style="it">Mathematicae collectiones</emph>
                <ref id="pappus_1588"> (Pappus </ref>
              . </s>
              <lb/>
              <quote xml:lang="lat">
                <s xml:space="preserve"> Theorema LVI. Propositio LIX.
                  <lb/>
                Semicirculo existente AEB, & diametro AB, existentibusque perpendicularibus CE & ducta recta linea EFG, & ad ipsam perpendiculari BG, tria porro contingunt, videlicet rectangulum quidem CBD aequale esse quadrato ex BG; rectangulum vero contentum AC BD quadrato ex FG, & contentum AD CB quadrato ex </s>
              </quote>
              <lb/>
              <quote>
                <s xml:space="preserve"> Given a semicircle AEB with diameter AB, and perpendiculars CE, DF, and having drawn the line EFG, and the perpendicular to it, BG, then three things come about, namely, the rectangle CB.BD is equal to the square of BG; and the rectangle AC.BD to the square of FG, and teh rectangle AD.CB to the square of EG.</s>
              </quote>
              <lb/>
              <s xml:space="preserve"> Harriot's note about the diagram is difficult to read. In the diagram given by
                <math>
                  <mstyle>
                    <mi>C</mi>
                    <mi>E</mi>
                  </mstyle>
                </math>
              and
                <math>
                  <mstyle>
                    <mi>D</mi>
                    <mi>F</mi>
                  </mstyle>
                </math>
              are symmetrically placed about the centre so that
                <math>
                  <mstyle>
                    <mi>E</mi>
                    <mi>G</mi>
                  </mstyle>
                </math>
              is parallel to
                <math>
                  <mstyle>
                    <mi>A</mi>
                    <mi>B</mi>
                  </mstyle>
                </math>
              . Harriot's diagram is therefore more general. </s>
              <s xml:space="preserve">]</s>
            </p>
          </div>
          <head xml:space="preserve" xml:lang="lat"> In Monachos lemma.
            <lb/>
          prop. 59. lib. 7. pappi. pag.
            <lb/>
          [
            <emph style="bf">Translation: </emph>
          On the lemma of Monachos, Proposition 59, Book 7 of Pappus, page ]</head>
          <p xml:lang="lat">
            <s xml:space="preserve"> Data seu posita
              <lb/>
              <math>
                <mstyle>
                  <mi>A</mi>
                  <mi>E</mi>
                  <mi>B</mi>
                </mstyle>
              </math>
            semicirculo
              <lb/>
              <math>
                <mstyle>
                  <mi>A</mi>
                  <mi>B</mi>
                </mstyle>
              </math>
            . Diameter.
              <lb/>
            cui
              <math>
                <mstyle>
                  <mi>C</mi>
                  <mi>E</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>D</mi>
                  <mi>F</mi>
                </mstyle>
              </math>
            , perpendiculares.
              <lb/>
              <math>
                <mstyle>
                  <mi>E</mi>
                  <mi>F</mi>
                  <mi>G</mi>
                </mstyle>
              </math>
            producta
              <lb/>
            cui
              <math>
                <mstyle>
                  <mi>B</mi>
                  <mi>G</mi>
                </mstyle>
              </math>
            perpendic-
              <lb/>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Given or supposed, a semicircle
              <math>
                <mstyle>
                  <mi>A</mi>
                  <mi>E</mi>
                  <mi>B</mi>
                </mstyle>
              </math>
            with diameter
              <math>
                <mstyle>
                  <mi>A</mi>
                  <mi>B</mi>
                </mstyle>
              </math>
            , to which
              <math>
                <mstyle>
                  <mi>C</mi>
                  <mi>E</mi>
                </mstyle>
              </math>
            and
              <math>
                <mstyle>
                  <mi>D</mi>
                  <mi>F</mi>
                </mstyle>
              </math>
            are perpendiculars, and
              <math>
                <mstyle>
                  <mi>E</mi>
                  <mi>F</mi>
                  <mi>G</mi>
                </mstyle>
              </math>
            extended, to which
              <math>
                <mstyle>
                  <mi>B</mi>
                  <mi>G</mi>
                </mstyle>
              </math>
            is a perpendicular. </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Diagrapha [???]
              <lb/>
            in Græco [???]
              <lb/>
            et apud
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Diagram [???]
              <lb/>
            in the Greek [???]
              <lb/>
            and in ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Tria
              <lb/>
            Consequentia
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Three consequences to be ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Constructiones seu linearum ductiones
              <lb/>
            […]
              <lb/>
            Consequentia ex ductis et constructis.
              <lb/>
            […]
              <lb/>
            quia puncta
              <math>
                <mstyle>
                  <mi>D</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>B</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>G</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>F</mi>
                </mstyle>
              </math>
            , sunt in circulo.
              <lb/>
            quia super eadem peripheriam.
              <lb/>
            quia
              <math>
                <mstyle>
                  <mi>C</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>E</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>G</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>B</mi>
                </mstyle>
              </math>
            , sunt in circulo.
              <math>
                <mstyle>
                  <mi>E</mi>
                  <mi>B</mi>
                </mstyle>
              </math>
            [???]
              <lb/>
            diameter.
              <lb/>
            […]
              <lb/>
            Tum: Traing.
              <math>
                <mstyle>
                  <mi>D</mi>
                  <mi>G</mi>
                  <mi>B</mi>
                </mstyle>
              </math>
            et
              <math>
                <mstyle>
                  <mi>C</mi>
                  <mi>G</mi>
                  <mi>B</mi>
                </mstyle>
              </math>
            sunt æquiangula. quia
              <math>
                <mstyle>
                  <mi>C</mi>
                  <mi>B</mi>
                  <mi>G</mi>
                </mstyle>
              </math>
            communis utrisque.
              <lb/>
            […]
              <lb/>
            Prima
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Construction ordrawing of the lines
              <lb/>
              <lb/>
            Consequence from the drawing and ex ductis construction.
              <lb/>
              <lb/>
            becasue the opoints
              <math>
                <mstyle>
                  <mi>D</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>B</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>G</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>F</mi>
                </mstyle>
              </math>
            are on a circle.
              <lb/>
            because on the same circumference.
              <lb/>
            because
              <math>
                <mstyle>
                  <mi>C</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>E</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>G</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>B</mi>
                </mstyle>
              </math>
            are on a circle.
              <math>
                <mstyle>
                  <mi>E</mi>
                  <mi>B</mi>
                </mstyle>
              </math>
            [???] diameter.
              <lb/>
              <lb/>
            Then triangles
              <math>
                <mstyle>
                  <mi>D</mi>
                  <mi>G</mi>
                  <mi>B</mi>
                </mstyle>
              </math>
            et
              <math>
                <mstyle>
                  <mi>C</mi>
                  <mi>G</mi>
                  <mi>B</mi>
                </mstyle>
              </math>
            are equiangular because
              <math>
                <mstyle>
                  <mi>C</mi>
                  <mi>B</mi>
                  <mi>G</mi>
                </mstyle>
              </math>
            is common to both.
              <lb/>
              <lb/>
            First ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> per primam consequens.
              <lb/>
            2
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            by the first consequence
              <lb/>
            Consequence ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> per primam consequens.
              <lb/>
            3.
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            by the first consequence
              <lb/>
            Consequence ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve">
              <math>
                <mstyle>
                  <mi>A</mi>
                  <mi>G</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>E</mi>
                  <mi>D</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>A</mi>
                  <mi>D</mi>
                </mstyle>
              </math>
            , non necessario
              <lb/>
            et
              <math>
                <mstyle>
                  <mi>A</mi>
                  <mi>E</mi>
                </mstyle>
              </math>
            omissa. apud
              <lb/>
            Commandinum.
              <lb/>
              <math>
                <mstyle>
                  <mi>A</mi>
                  <mi>D</mi>
                </mstyle>
              </math>
            etiam superflua.
              <lb/>
            Malo etiam in
              <lb/>
            [
              <emph style="bf">Translation: </emph>
              <math>
                <mstyle>
                  <mi>A</mi>
                  <mi>G</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>E</mi>
                  <mi>D</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>A</mi>
                  <mi>D</mi>
                </mstyle>
              </math>
            are not necessary and
              <math>
                <mstyle>
                  <mi>A</mi>
                  <mi>E</mi>
                </mstyle>
              </math>
            is omitted by Commandino.
              <lb/>
              <math>
                <mstyle>
                  <mi>A</mi>
                  <mi>D</mi>
                </mstyle>
              </math>
            is also superfluous.
              <lb/>
            Also badly done in the ]</s>
          </p>
        </div>
      </text>
    </echo>
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