Harriot, Thomas, Mss. 6784

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161 (81) 		162
162 (81v)
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164 (82v)
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166 (83v)
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            <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>
              , pages 171 and 172 (Propositions 17 to 21). Proposition 17, for example, is as follows. </s>
              <lb/>
              <quote xml:lang="lat">
                <s xml:space="preserve"> Sint duæ rectæ lineæ
                  <math>
                    <mstyle>
                      <mi>A</mi>
                      <mi>B</mi>
                    </mstyle>
                  </math>
                  <math>
                    <mstyle>
                      <mi>B</mi>
                      <mi>C</mi>
                    </mstyle>
                  </math>
                , & inter
                  <math>
                    <mstyle>
                      <mi>A</mi>
                      <mi>B</mi>
                    </mstyle>
                  </math>
                  <math>
                    <mstyle>
                      <mi>B</mi>
                      <mi>C</mi>
                    </mstyle>
                  </math>
                media proportionalis fit
                  <math>
                    <mstyle>
                      <mi>B</mi>
                      <mi>D</mi>
                    </mstyle>
                  </math>
                , ipsique
                  <math>
                    <mstyle>
                      <mi>A</mi>
                      <mi>D</mi>
                    </mstyle>
                  </math>
                æqualis ponatur
                  <math>
                    <mstyle>
                      <mi>D</mi>
                      <mi>E</mi>
                    </mstyle>
                  </math>
                . Dico rectam lineam
                  <math>
                    <mstyle>
                      <mi>C</mi>
                      <mi>E</mi>
                    </mstyle>
                  </math>
                excessum, quo utreque
                  <math>
                    <mstyle>
                      <mi>A</mi>
                      <mi>B</mi>
                    </mstyle>
                  </math>
                  <math>
                    <mstyle>
                      <mi>B</mi>
                      <mi>C</mi>
                    </mstyle>
                  </math>
                excedunt eam, quem potest id, quod quater
                  <math>
                    <mstyle>
                      <mi>A</mi>
                      <mi>B</mi>
                    </mstyle>
                  </math>
                  <math>
                    <mstyle>
                      <mi>B</mi>
                      <mi>C</mi>
                    </mstyle>
                  </math>
                continetur. </s>
              </quote>
              <lb/>
              <quote>
                <s xml:space="preserve"> Let there be two straight lines
                  <math>
                    <mstyle>
                      <mi>A</mi>
                      <mi>B</mi>
                    </mstyle>
                  </math>
                and
                  <math>
                    <mstyle>
                      <mi>B</mi>
                      <mi>C</mi>
                    </mstyle>
                  </math>
                , and the mean proportional between
                  <math>
                    <mstyle>
                      <mi>A</mi>
                      <mi>B</mi>
                    </mstyle>
                  </math>
                and
                  <math>
                    <mstyle>
                      <mi>B</mi>
                      <mi>C</mi>
                    </mstyle>
                  </math>
                is
                  <math>
                    <mstyle>
                      <mi>B</mi>
                      <mi>D</mi>
                    </mstyle>
                  </math>
                , and
                  <math>
                    <mstyle>
                      <mi>D</mi>
                      <mi>E</mi>
                    </mstyle>
                  </math>
                is made equal to
                  <math>
                    <mstyle>
                      <mi>A</mi>
                      <mi>D</mi>
                    </mstyle>
                  </math>
                . I say that the line
                  <math>
                    <mstyle>
                      <mi>C</mi>
                      <mi>E</mi>
                    </mstyle>
                  </math>
                is the excess by which
                  <math>
                    <mstyle>
                      <mi>A</mi>
                      <mi>B</mi>
                    </mstyle>
                  </math>
                and
                  <math>
                    <mstyle>
                      <mi>B</mi>
                      <mi>C</mi>
                    </mstyle>
                  </math>
                together exceed the line euqal in square to four times the product of
                  <math>
                    <mstyle>
                      <mi>A</mi>
                      <mi>B</mi>
                    </mstyle>
                  </math>
                and
                  <math>
                    <mstyle>
                      <mi>B</mi>
                      <mi>C</mi>
                    </mstyle>
                  </math>
                . </s>
              </quote>
              <s xml:space="preserve">]</s>
            </p>
          </div>
          <head xml:space="preserve" xml:lang="lat"> Pappus 171. ad resectione </head>
          <p xml:lang="lat">
            <s xml:space="preserve"> Pappus. </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Utile ad
              <lb/>
            epilogum 13,
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Useful for the position of epilogue ]</s>
          </p>
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Impressum