Harriot, Thomas, Mss. 6784

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      <text xml:lang="eng" type="free">
        <div type="section" level="1" n="1">
          <pb file="add_6784_f123" o="123" n="245"/>
          <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 references on this page are to Commandino's edition of
                <emph style="it">Mathematicae collectiones</emph>
                <ref id="pappus_1588"> (Pappus </ref>
              , Book 7, Proposition 122, page 235, and to Giambattista Benedetti,
                <emph style="it">Diversarum speculationum mathematicarum et physicarum liber</emph>
                <ref id="benedetti_1585" target="http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/mpiwg/online/permanent/library/163127KK&tocMode=concordance&viewMode=images&pn=374&start=361"> (Benedetti 1585, </ref>
              . Proposition 122 from Pappus is as follows. </s>
              <lb/>
              <quote xml:lang="lat">
                <s xml:space="preserve"> Theorema CXI. Propositio CXXII.
                  <lb/>
                Sit triangulum
                  <math>
                    <mstyle>
                      <mi>A</mi>
                      <mi>B</mi>
                      <mi>C</mi>
                    </mstyle>
                  </math>
                , & ducatur quædam recta linea
                  <math>
                    <mstyle>
                      <mi>A</mi>
                      <mi>D</mi>
                    </mstyle>
                  </math>
                , quem ipsam
                  <math>
                    <mstyle>
                      <mi>B</mi>
                      <mi>C</mi>
                    </mstyle>
                  </math>
                bisariam secet. Dico quadrata ex
                  <math>
                    <mstyle>
                      <mi>B</mi>
                      <mi>A</mi>
                    </mstyle>
                  </math>
                  <math>
                    <mstyle>
                      <mi>A</mi>
                      <mi>C</mi>
                    </mstyle>
                  </math>
                quadratorum ex
                  <math>
                    <mstyle>
                      <mi>A</mi>
                      <mi>D</mi>
                    </mstyle>
                  </math>
                  <math>
                    <mstyle>
                      <mi>D</mi>
                      <mi>C</mi>
                    </mstyle>
                  </math>
                dupla esse. </s>
              </quote>
              <lb/>
              <quote>
                <s xml:space="preserve"> Let there be a triangle
                  <math>
                    <mstyle>
                      <mi>A</mi>
                      <mi>B</mi>
                      <mi>C</mi>
                    </mstyle>
                  </math>
                and there is drawn a straight line
                  <math>
                    <mstyle>
                      <mi>A</mi>
                      <mi>D</mi>
                    </mstyle>
                  </math>
                , which bisects
                  <math>
                    <mstyle>
                      <mi>B</mi>
                      <mi>C</mi>
                    </mstyle>
                  </math>
                . I say that the squares of
                  <math>
                    <mstyle>
                      <mi>B</mi>
                      <mi>A</mi>
                    </mstyle>
                  </math>
                and
                  <math>
                    <mstyle>
                      <mi>A</mi>
                      <mi>C</mi>
                    </mstyle>
                  </math>
                are twice the squares of
                  <math>
                    <mstyle>
                      <mi>A</mi>
                      <mi>D</mi>
                    </mstyle>
                  </math>
                and
                  <math>
                    <mstyle>
                      <mi>A</mi>
                      <mi>C</mi>
                    </mstyle>
                  </math>
                . </s>
              </quote>
              <s xml:space="preserve"> Harriot's triangles are lettered
                <math>
                  <mstyle>
                    <mi>a</mi>
                    <mi>b</mi>
                    <mi>d</mi>
                  </mstyle>
                </math>
              with the point
                <math>
                  <mstyle>
                    <mi>b</mi>
                  </mstyle>
                </math>
              bisecting
                <math>
                  <mstyle>
                    <mi>c</mi>
                    <mi>d</mi>
                  </mstyle>
                </math>
              . </s>
              <lb/>
              <s xml:space="preserve"> The working is continued on the reverse of the folio, Add MS
                <ref target="http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/library/XT0KZ8QC/&start=240&viewMode=image&pn=246"> f. </ref>
              . </s>
              <s xml:space="preserve">]</s>
            </p>
          </div>
          <p xml:lang="lat">
            <s xml:space="preserve"> sit triangulum
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>c</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            let there be a triangle
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>c</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            </s>
            <lb/>
            <s xml:space="preserve"> dico
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            I say ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> sit
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>e</mi>
                </mstyle>
              </math>
            perpendicularis ad,
              <math>
                <mstyle>
                  <mi>c</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            let
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>e</mi>
                </mstyle>
              </math>
            be perpendicular to
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Unde
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            whence it ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Vide, Pappum. lib. 7. prop: 122. pag. 235.
              <lb/>
            et: Jo: Baptistum Benedictum pag.
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            See Pappus, Book 7, Proposition 122, page 235; and Johan Baptista Benedictus, page ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve">
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            turn ]
              <lb/>
            [
              <emph style="bf">Commentary: </emph>
            The working is continued on the reverse of the folio, Add MS
              <ref target="http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/library/XT0KZ8QC/&start=240&viewMode=image&pn=246"> f. </ref>
            . </s>
          </p>
        </div>
      </text>
    </echo>
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