Harriot, Thomas, Mss. 6784

List of thumbnails

< >
151
151 (76) 		152
152 (76v)
153
153 (77) 		154
154 (77v)
155
155 (78) 		156
156 (78v)
157
157 (79) 		158
158 (79v)
159
159 (80) 		160
160 (80v)
< >
page |< < (42) of 862 > >|
    <echo version="1.0RC">
      <text xml:lang="eng" type="free">
        <div type="section" level="1" n="1">
          <pb file="add_6784_f042" o="42" n="83"/>
          <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 in this and the next three folios is to Commandino's edition of
                <emph style="it">Mathematicae collectiones</emph>
                <ref id="pappus_1588"> (Pappus </ref>
              , page 263, Proposition 164. </s>
              <lb/>
              <quote xml:lang="lat">
                <s xml:space="preserve"> Problema XIII. Propositio CLXIII.
                  <lb/>
                Parallelogrammo
                  <math>
                    <mstyle>
                      <mi>A</mi>
                      <mi>D</mi>
                    </mstyle>
                  </math>
                positione dato, a dato puncto
                  <math>
                    <mstyle>
                      <mi>E</mi>
                    </mstyle>
                  </math>
                ducere rectam lineam
                  <math>
                    <mstyle>
                      <mi>E</mi>
                      <mi>F</mi>
                    </mstyle>
                  </math>
                , & facere Triangulum
                  <math>
                    <mstyle>
                      <mi>F</mi>
                      <mi>C</mi>
                      <mi>G</mi>
                    </mstyle>
                  </math>
                parallelogrammo
                  <math>
                    <mstyle>
                      <mi>A</mi>
                      <mi>D</mi>
                    </mstyle>
                  </math>
                æquale. </s>
              </quote>
              <lb/>
              <quote>
                <s xml:space="preserve"> Given the position of a parallelogram
                  <math>
                    <mstyle>
                      <mi>A</mi>
                      <mi>D</mi>
                    </mstyle>
                  </math>
                , from a given point
                  <math>
                    <mstyle>
                      <mi>E</mi>
                    </mstyle>
                  </math>
                , draw a line
                  <math>
                    <mstyle>
                      <mi>E</mi>
                      <mi>F</mi>
                    </mstyle>
                  </math>
                and make a triangle
                  <math>
                    <mstyle>
                      <mi>F</mi>
                      <mi>C</mi>
                      <mi>G</mi>
                    </mstyle>
                  </math>
                equal to the parallelogram
                  <math>
                    <mstyle>
                      <mi>A</mi>
                      <mi>D</mi>
                    </mstyle>
                  </math>
                . </s>
              </quote>
              <s xml:space="preserve">]</s>
            </p>
          </div>
          <head xml:space="preserve"> Ad prop. 164. lib. 7. pappi. pag.
            <lb/>
          [
            <emph style="bf">Translation: </emph>
          On problem 164, Book 7 of Pappus, page ]</head>
          <p xml:lang="lat">
            <s xml:space="preserve"> Synthesis. analysis in alia
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Synthesis. Analysis in another ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Hoc solida habet
              <lb/>
            pro altitudine
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mo>+</mo>
                  <mi>a</mi>
                </mstyle>
              </math>
              <lb/>
            et pro basi
              <math>
                <mstyle>
                  <mi>c</mi>
                  <mi>a</mi>
                  <mo>+</mo>
                  <mi>c</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
            .
              <lb/>
            cuius latera
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mo>+</mo>
                  <mi>b</mi>
                </mstyle>
              </math>
              <lb/>
            Et
              <math>
                <mstyle>
                  <mi>c</mi>
                </mstyle>
              </math>
              <lb/>
            cuius notæ
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            This solid has
              <lb/>
            for altitude
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mo>+</mo>
                  <mi>a</mi>
                </mstyle>
              </math>
              <lb/>
            and for base
              <math>
                <mstyle>
                  <mi>c</mi>
                  <mi>a</mi>
                  <mo>+</mo>
                  <mi>c</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
            .
              <lb/>
            whose sides are
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mo>+</mo>
                  <mi>b</mi>
                </mstyle>
              </math>
              <lb/>
            and
              <math>
                <mstyle>
                  <mi>c</mi>
                </mstyle>
              </math>
              <lb/>
            whose notations ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Hoc solida habet
              <lb/>
            pro altitudine
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mo>+</mo>
                  <mi>b</mi>
                  <mo>+</mo>
                  <mi>d</mi>
                </mstyle>
              </math>
              <lb/>
            et pro basi
              <math>
                <mstyle>
                  <mn>2</mn>
                  <mi>b</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
            .
              <lb/>
            cuius latera
              <math>
                <mstyle>
                  <mn>2</mn>
                  <mi>b</mi>
                </mstyle>
              </math>
              <lb/>
            Et
              <math>
                <mstyle>
                  <mi>c</mi>
                </mstyle>
              </math>
              <lb/>
            cuius notæ
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            This solid has
              <lb/>
            for altitude
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mo>+</mo>
                  <mi>a</mi>
                </mstyle>
              </math>
              <lb/>
            and for base
              <math>
                <mstyle>
                  <mi>c</mi>
                  <mi>a</mi>
                  <mo>+</mo>
                  <mi>c</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
            .
              <lb/>
            whose sides are
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mo>+</mo>
                  <mi>b</mi>
                </mstyle>
              </math>
              <lb/>
            and
              <math>
                <mstyle>
                  <mi>c</mi>
                </mstyle>
              </math>
              <lb/>
            whose notations ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Ergo:
              <math>
                <mstyle>
                  <mi>f</mi>
                  <mi>e</mi>
                  <mo>=</mo>
                  <mn>2</mn>
                  <mi>b</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
            .
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Therefore
              <math>
                <mstyle>
                  <mi>f</mi>
                  <mi>e</mi>
                  <mo>=</mo>
                  <mn>2</mn>
                  <mi>b</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
            , sought. </s>
          </p>
        </div>
      </text>
    </echo>
Impressum