Harriot, Thomas, Mss. 6784

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521 (261) 		522
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page |< < (295) of 862 > >|
    <echo version="1.0RC">
      <text xml:lang="eng" type="free">
        <div type="section" level="1" n="1">
          <pb file="add_6784_f295" o="295" n="589"/>
          <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"> There is a reference on this page to Proposition II.4 from
                <emph style="it">Conicorum libri quattuor</emph>
                <ref id="apollonius_1566"> (Apollonius </ref>
              . </s>
              <s xml:space="preserve">]</s>
            </p>
          </div>
          <head xml:space="preserve" xml:lang="lat"> Alhazen. pag. </head>
          <p xml:lang="lat">
            <s xml:space="preserve"> Ducere rectam (
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            ) a puncto (
              <math>
                <mstyle>
                  <mi>a</mi>
                </mstyle>
              </math>
            )
              <lb/>
            ut (
              <math>
                <mstyle>
                  <mi>e</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            ) sit æqualis data (
              <math>
                <mstyle>
                  <mi>h</mi>
                  <mi>z</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Draw a line (
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            ) from the point (
              <math>
                <mstyle>
                  <mi>a</mi>
                </mstyle>
              </math>
            ) so that (
              <math>
                <mstyle>
                  <mi>e</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            ) is equal to a given (
              <math>
                <mstyle>
                  <mi>h</mi>
                  <mi>z</mi>
                </mstyle>
              </math>
            ). </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Ap: 4,2
              <emph style="super">i</emph>
            . fiat per punctum
              <math>
                <mstyle>
                  <mi>t</mi>
                </mstyle>
              </math>
            et
              <math>
                <mstyle>
                  <mi>h</mi>
                  <mi>x</mi>
                  <mi>z</mi>
                </mstyle>
              </math>
              <lb/>
            hyperbola.
              <math>
                <mstyle>
                  <mi>t</mi>
                  <mi>p</mi>
                </mstyle>
              </math>
            . Continuetur
              <math>
                <mstyle>
                  <mi>t</mi>
                  <mi>x</mi>
                </mstyle>
              </math>
            ad
              <math>
                <mstyle>
                  <mi>o</mi>
                </mstyle>
              </math>
              <lb/>
            et fiat
              <math>
                <mstyle>
                  <mi>x</mi>
                  <mi>o</mi>
                  <mo>=</mo>
                  <mi>x</mi>
                  <mi>t</mi>
                </mstyle>
              </math>
            .
              <lb/>
            fiat per punctum
              <math>
                <mstyle>
                  <mi>o</mi>
                </mstyle>
              </math>
            et
              <math>
                <mstyle>
                  <mi>n</mi>
                  <mi>x</mi>
                  <mi>k</mi>
                </mstyle>
              </math>
              <lb/>
            hyperbola contraposita
              <math>
                <mstyle>
                  <mi>o</mi>
                  <mi>u</mi>
                </mstyle>
              </math>
              <lb/>
            Tum a puncto
              <math>
                <mstyle>
                  <mi>t</mi>
                </mstyle>
              </math>
            intelligatur duci
              <math>
                <mstyle>
                  <mi>t</mi>
                  <mi>r</mi>
                </mstyle>
              </math>
              <lb/>
            quæ sit minima omnium quæ duci
              <lb/>
            possunt ad sectionem
              <math>
                <mstyle>
                  <mi>r</mi>
                  <mi>o</mi>
                  <mi>c</mi>
                  <mi>u</mi>
                </mstyle>
              </math>
            .
              <lb/>
            Si
              <math>
                <mstyle>
                  <mi>t</mi>
                  <mi>r</mi>
                </mstyle>
              </math>
              <emph style="super">esset</emph>
            sit æqualis diametro
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>g</mi>
                </mstyle>
              </math>
            et
              <lb/>
              <math>
                <mstyle>
                  <mi>t</mi>
                </mstyle>
              </math>
            fiat centrum et periferia transeat
              <lb/>
            per
              <math>
                <mstyle>
                  <mi>r</mi>
                </mstyle>
              </math>
            , non secabit sectionem sed
              <lb/>
            tanget in puncto
              <math>
                <mstyle>
                  <mi>r</mi>
                </mstyle>
              </math>
            .
              <lb/>
            Seu cum
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>g</mi>
                </mstyle>
              </math>
            sit
              <math>
                <mstyle>
                  <mo>></mo>
                  <mi>t</mi>
                  <mi>r</mi>
                </mstyle>
              </math>
            . centro
              <math>
                <mstyle>
                  <mi>t</mi>
                </mstyle>
              </math>
            intevallo
              <lb/>
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>g</mi>
                </mstyle>
              </math>
            describatur periferia
              <math>
                <mstyle>
                  <mi>c</mi>
                  <mi>γ</mi>
                </mstyle>
              </math>
            quæ secabit
              <lb/>
            oppositum sectionem in
              <emph style="super">duabus</emph>
            punctis
              <math>
                <mstyle>
                  <mi>c</mi>
                </mstyle>
              </math>
            et
              <math>
                <mstyle>
                  <mo>\</mo>
                  <mi>g</mi>
                  <mi>a</mi>
                  <mi>m</mi>
                  <mi>m</mi>
                  <mi>e</mi>
                </mstyle>
              </math>
            .
              <lb/>
            Agantur
              <math>
                <mstyle>
                  <mi>t</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>t</mi>
                  <mi>γ</mi>
                </mstyle>
              </math>
            : utræque æqualis
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>g</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Apollonius II.4. Through the point
              <math>
                <mstyle>
                  <mi>t</mi>
                </mstyle>
              </math>
            and
              <math>
                <mstyle>
                  <mi>h</mi>
                  <mi>x</mi>
                  <mi>z</mi>
                </mstyle>
              </math>
            make a hyperbola
              <math>
                <mstyle>
                  <mi>t</mi>
                  <mi>p</mi>
                </mstyle>
              </math>
            .
              <lb/>
            Continue
              <math>
                <mstyle>
                  <mi>t</mi>
                  <mi>x</mi>
                </mstyle>
              </math>
            to
              <math>
                <mstyle>
                  <mi>o</mi>
                </mstyle>
              </math>
            and make
              <math>
                <mstyle>
                  <mi>x</mi>
                  <mn>0</mn>
                  <mo>=</mo>
                  <mi>x</mi>
                  <mi>t</mi>
                </mstyle>
              </math>
            .
              <lb/>
            Through the point
              <math>
                <mstyle>
                  <mi>o</mi>
                </mstyle>
              </math>
            and
              <math>
                <mstyle>
                  <mi>n</mi>
                  <mi>x</mi>
                  <mi>k</mi>
                </mstyle>
              </math>
            make the opposite hyperbola.
              <lb/>
            Then from the point
              <math>
                <mstyle>
                  <mi>t</mi>
                </mstyle>
              </math>
            there is understood to be ocnstructed
              <math>
                <mstyle>
                  <mi>t</mi>
                  <mi>r</mi>
                </mstyle>
              </math>
            , which is the minimum of all that can be constructed to the segment
              <math>
                <mstyle>
                  <mi>r</mi>
                  <mi>o</mi>
                  <mi>c</mi>
                  <mi>u</mi>
                </mstyle>
              </math>
            .
              <lb/>
            If
              <math>
                <mstyle>
                  <mi>t</mi>
                  <mi>r</mi>
                </mstyle>
              </math>
            is equal to the diameter
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>g</mi>
                </mstyle>
              </math>
            and
              <math>
                <mstyle>
                  <mi>t</mi>
                </mstyle>
              </math>
            is the centre, and the circumference passes through
              <math>
                <mstyle>
                  <mi>r</mi>
                </mstyle>
              </math>
            , it will not cut the segment but touch at the point
              <math>
                <mstyle>
                  <mi>r</mi>
                </mstyle>
              </math>
            .
              <lb/>
            Or when
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>g</mi>
                  <mo>></mo>
                  <mi>t</mi>
                  <mi>r</mi>
                </mstyle>
              </math>
            , with centre
              <math>
                <mstyle>
                  <mi>t</mi>
                </mstyle>
              </math>
            and distance
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>g</mi>
                </mstyle>
              </math>
            , draw a circumference
              <math>
                <mstyle>
                  <mi>c</mi>
                  <mi>γ</mi>
                </mstyle>
              </math>
            which will cut the opposite segment at the points
              <math>
                <mstyle>
                  <mi>c</mi>
                </mstyle>
              </math>
            adn
              <math>
                <mstyle>
                  <mi>γ</mi>
                </mstyle>
              </math>
            .
              <lb/>
            Construct
              <math>
                <mstyle>
                  <mi>t</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
            and
              <math>
                <mstyle>
                  <mi>t</mi>
                  <mi>γ</mi>
                </mstyle>
              </math>
            : both are equal to
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>g</mi>
                </mstyle>
              </math>
            . </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve">
              <math>
                <mstyle>
                  <mi>t</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
            , secabit
              <math>
                <mstyle>
                  <mi>z</mi>
                  <mi>n</mi>
                </mstyle>
              </math>
            in
              <math>
                <mstyle>
                  <mi>q</mi>
                </mstyle>
              </math>
            . et
              <math>
                <mstyle>
                  <mi>h</mi>
                  <mi>l</mi>
                </mstyle>
              </math>
            in
              <math>
                <mstyle>
                  <mi>f</mi>
                </mstyle>
              </math>
            .
              <lb/>
            […]
              <lb/>
            Dico quod:
              <math>
                <mstyle>
                  <mi>e</mi>
                  <mi>d</mi>
                  <mo>=</mo>
                  <mi>h</mi>
                  <mi>z</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
              <math>
                <mstyle>
                  <mi>t</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
            will cut
              <math>
                <mstyle>
                  <mi>z</mi>
                  <mi>n</mi>
                </mstyle>
              </math>
            at
              <math>
                <mstyle>
                  <mi>q</mi>
                </mstyle>
              </math>
            and
              <math>
                <mstyle>
                  <mi>h</mi>
                  <mi>l</mi>
                </mstyle>
              </math>
            at
              <math>
                <mstyle>
                  <mi>f</mi>
                </mstyle>
              </math>
            .
              <lb/>
              <lb/>
            I say that
              <math>
                <mstyle>
                  <mi>e</mi>
                  <mi>d</mi>
                  <mo>=</mo>
                  <mi>h</mi>
                  <mi>z</mi>
                </mstyle>
              </math>
            </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> (per construct.
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            (by the construction </s>
          </p>
        </div>
      </text>
    </echo>
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