Harriot, Thomas, Mss. 6784

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271 (136) 		272
272 (136v)
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page |< < (146) of 862 > >|
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      <text xml:lang="eng" type="free">
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          <pb file="add_6784_f146" o="146" n="291"/>
          <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 folio is to page 244 of Commandino's edition of
                <emph style="it">Mathematicae collectiones</emph>
                <ref id="pappus_1588"> (Pappus </ref>
              . Page 244 contains Proposition 132. </s>
              <lb/>
              <quote xml:lang="lat">
                <s xml:space="preserve"> Theorema CXXI. Propos. CXXXII.
                  <lb/>
                Rursum si sit descripta figura, &
                  <math>
                    <mstyle>
                      <mi>D</mi>
                      <mi>F</mi>
                    </mstyle>
                  </math>
                ipsi
                  <math>
                    <mstyle>
                      <mi>A</mi>
                      <mi>C</mi>
                    </mstyle>
                  </math>
                fit parallela, erit
                  <math>
                    <mstyle>
                      <mi>A</mi>
                      <mi>B</mi>
                    </mstyle>
                  </math>
                æqualis
                  <math>
                    <mstyle>
                      <mi>B</mi>
                      <mi>C</mi>
                    </mstyle>
                  </math>
                . Sit igitur æqualis. Dico
                  <math>
                    <mstyle>
                      <mi>D</mi>
                      <mi>F</mi>
                    </mstyle>
                  </math>
                ipsi
                  <math>
                    <mstyle>
                      <mi>A</mi>
                      <mi>C</mi>
                    </mstyle>
                  </math>
                parallelum esse. </s>
              </quote>
              <lb/>
              <quote>
                <s xml:space="preserve"> Again let the figure be drawn, with
                  <math>
                    <mstyle>
                      <mi>D</mi>
                      <mi>F</mi>
                    </mstyle>
                  </math>
                parallel to
                  <math>
                    <mstyle>
                      <mi>A</mi>
                      <mi>C</mi>
                    </mstyle>
                  </math>
                , then
                  <math>
                    <mstyle>
                      <mi>A</mi>
                      <mi>B</mi>
                    </mstyle>
                  </math>
                is equal to
                  <math>
                    <mstyle>
                      <mi>B</mi>
                      <mi>C</mi>
                    </mstyle>
                  </math>
                . Let it be equal. I say that
                  <math>
                    <mstyle>
                      <mi>D</mi>
                      <mi>F</mi>
                    </mstyle>
                  </math>
                is parallel to
                  <math>
                    <mstyle>
                      <mi>A</mi>
                      <mi>C</mi>
                    </mstyle>
                  </math>
                . </s>
              </quote>
              <s xml:space="preserve">]</s>
            </p>
          </div>
          <head xml:space="preserve" xml:lang="lat"/>
          <p xml:lang="lat">
            <s xml:space="preserve"> Sit parallelogrammum
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>b</mi>
                  <mi>c</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
              <lb/>
            ducantur.
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>l</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>c</mi>
                  <mi>g</mi>
                </mstyle>
              </math>
            .
              <lb/>
            sese intersecantes in puncto
              <math>
                <mstyle>
                  <mi>e</mi>
                </mstyle>
              </math>
            .
              <lb/>
            Et sit
              <math>
                <mstyle>
                  <mi>f</mi>
                  <mi>h</mi>
                  <mi>k</mi>
                </mstyle>
              </math>
            parallela,
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>a</mi>
                </mstyle>
              </math>
              <lb/>
            Dico quod
              <lb/>
              <math>
                <mstyle>
                  <mi>k</mi>
                  <mi>h</mi>
                  <mo>=</mo>
                  <mi>c</mi>
                  <mi>l</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Let the parallogram
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>b</mi>
                  <mi>c</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            be drawn, with
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>l</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>c</mi>
                  <mi>g</mi>
                </mstyle>
              </math>
            intersecting one another at the point
              <math>
                <mstyle>
                  <mi>e</mi>
                </mstyle>
              </math>
            .
              <lb/>
            And let
              <math>
                <mstyle>
                  <mi>f</mi>
                  <mi>h</mi>
                  <mi>k</mi>
                </mstyle>
              </math>
            be parallel to
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>a</mi>
                </mstyle>
              </math>
              <lb/>
            I say that
              <math>
                <mstyle>
                  <mi>k</mi>
                  <mi>h</mi>
                  <mo>=</mo>
                  <mi>c</mi>
                  <mi>l</mi>
                </mstyle>
              </math>
            . </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> S.W.L.
              <lb/>
            ad resectionem
              <lb/>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Sir william Lower, on the cutting off of an ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Sit
              <math>
                <mstyle>
                  <mo>Δ</mo>
                </mstyle>
              </math>
            .
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>b</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
            .
              <lb/>
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>g</mi>
                </mstyle>
              </math>
            bisecans basim
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
            .
              <lb/>
            et
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>e</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>c</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            ; sese intersecantes
              <lb/>
            in lineam
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>g</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Let there be a triangle
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>b</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
            , with
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>g</mi>
                </mstyle>
              </math>
            bisecting the base
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
            , and
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>e</mi>
                </mstyle>
              </math>
            and
              <math>
                <mstyle>
                  <mi>c</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            intersecting each other on the line
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>g</mi>
                </mstyle>
              </math>
            . </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Vide pappum 244.
              <lb/>
            in porismatis
              <lb/>
            ubi alia huismodi
              <lb/>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            See Pappus, page 244, on porisms, where there are others of this kind, ]</s>
          </p>
        </div>
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