Harriot, Thomas, Mss. 6785

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page |< < (9) of 882 > >|
    <echo version="1.0RC">
      <text xml:lang="eng" type="free">
        <div type="section" level="1" n="1">
          <pb file="add_6785_f009" o="9" n="17"/>
          <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 instructions on this page refer to the diagram on Add MS
                <ref target="http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/library/KN1CRTZ2/&start=0&viewMode=image&pn=1"> f. </ref>
              . The proof that the point
                <math>
                  <mstyle>
                    <mi>m</mi>
                  </mstyle>
                </math>
              lies on the ellipse is to be found on subsequent pages labelled A.5. </s>
              <s xml:space="preserve">]</s>
            </p>
          </div>
          <head xml:space="preserve"/>
          <p xml:lang="lat">
            <s xml:space="preserve"> Iisdem positis: centro
              <math>
                <mstyle>
                  <mi>a</mi>
                </mstyle>
              </math>
            , et intervallo
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>e</mi>
                </mstyle>
              </math>
            agatur periferia circuli
              <lb/>
            ad partes lineæ
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            , quæ necessario secabit lineam
              <math>
                <mstyle>
                  <mi>o</mi>
                  <mi>n</mi>
                </mstyle>
              </math>
            ,
              <lb/>
            quia ut demonstrandum fuit,
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>e</mi>
                </mstyle>
              </math>
            est maior quam
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>o</mi>
                </mstyle>
              </math>
            . Sit punctum
              <lb/>
            intersectionis
              <math>
                <mstyle>
                  <mi>m</mi>
                </mstyle>
              </math>
            . Deinde continuetur linea
              <math>
                <mstyle>
                  <mi>d</mi>
                  <mi>a</mi>
                </mstyle>
              </math>
            ad
              <emph style="super">partes</emph>
              <math>
                <mstyle>
                  <mi>e</mi>
                </mstyle>
              </math>
              <lb/>
            et fiat
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>e</mi>
                </mstyle>
              </math>
            æqualis
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            . Iam intelligantur rectum
              <math>
                <mstyle>
                  <mi>d</mi>
                </mstyle>
              </math>
            esse maiorem
              <lb/>
            axem seu diametrum elipseos et
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>g</mi>
                </mstyle>
              </math>
            dimidium diametri secunda
              <lb/>
            et sit ipsu elipsis descripta
              <math>
                <mstyle>
                  <mi>d</mi>
                  <mi>g</mi>
                  <mi>e</mi>
                </mstyle>
              </math>
            .
              <lb/>
            Dico quod punctum
              <math>
                <mstyle>
                  <mi>m</mi>
                </mstyle>
              </math>
            est in
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Supposing the same things: with centre
              <math>
                <mstyle>
                  <mi>a</mi>
                </mstyle>
              </math>
            and radius
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>e</mi>
                </mstyle>
              </math>
            , there is constructed the circumference of a circle to the line
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            , which will necessarily cut the line
              <math>
                <mstyle>
                  <mi>o</mi>
                  <mi>n</mi>
                </mstyle>
              </math>
            because, as was demonstrated,
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>e</mi>
                </mstyle>
              </math>
            is smaller than
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>o</mi>
                </mstyle>
              </math>
            . Let the point of intersection be
              <math>
                <mstyle>
                  <mi>m</mi>
                </mstyle>
              </math>
            . Then the line
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            is continued to
              <math>
                <mstyle>
                  <mi>e</mi>
                </mstyle>
              </math>
            , and made
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>e</mi>
                </mstyle>
              </math>
            equal to
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            . Now it is understood that the line
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            is the greater axis or diameter of the ellipse, and
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>g</mi>
                </mstyle>
              </math>
            is half the second diameter, and the described ellipse is
              <math>
                <mstyle>
                  <mi>d</mi>
                  <mi>g</mi>
                  <mi>e</mi>
                </mstyle>
              </math>
            .
              <lb/>
            I say that the point
              <math>
                <mstyle>
                  <mi>m</mi>
                </mstyle>
              </math>
            is on the ellipse. </s>
          </p>
        </div>
      </text>
    </echo>
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