Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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        <div xml:id="echoid-div141" type="section" level="1" n="45">
          <p style="it">
            <s xml:id="echoid-s1978" xml:space="preserve">
              <pb file="0078" n="78" rhead="ARCHIMEDIS"/>
            & </s>
            <s xml:id="echoid-s1979" xml:space="preserve">per conuer-
              <lb/>
              <figure xlink:label="fig-0078-01" xlink:href="fig-0078-01a" number="48">
                <image file="0078-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0078-01"/>
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            ſionem rationis
              <lb/>
            ut e b ad e g,
              <lb/>
            ita f d ad f h.
              <lb/>
            </s>
            <s xml:id="echoid-s1980" xml:space="preserve">eſt autem ut a e
              <lb/>
            ad e b, ita c f
              <lb/>
            ad f d. </s>
            <s xml:id="echoid-s1981" xml:space="preserve">ex æqua
              <lb/>
            li igitur ut a e
              <lb/>
            ad e g, ita c f
              <lb/>
            ad f h.</s>
            <s xml:id="echoid-s1982" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1983" xml:space="preserve">
              <emph style="sc">A_liter_</emph>
            . </s>
            <s xml:id="echoid-s1984" xml:space="preserve">Aptentur lineæ a b, c d inter ſe ſe, ita ut ad partes
              <lb/>
            a c angulum faciant; </s>
            <s xml:id="echoid-s1985" xml:space="preserve">& </s>
            <s xml:id="echoid-s1986" xml:space="preserve">ſint a c in uno atque eodem puncto: </s>
            <s xml:id="echoid-s1987" xml:space="preserve">deinde
              <lb/>
            iungantur d b, h g, fe. </s>
            <s xml:id="echoid-s1988" xml:space="preserve">cum igitur ſit ut a e ad e b, ita c f, hoc eſt
              <lb/>
            a f ad f d; </s>
            <s xml:id="echoid-s1989" xml:space="preserve">æquidiſtabit fe ipſi d b: </s>
            <s xml:id="echoid-s1990" xml:space="preserve">& </s>
            <s xml:id="echoid-s1991" xml:space="preserve">ſimiliter h g eidem d b
              <lb/>
              <note position="left" xlink:label="note-0078-01" xlink:href="note-0078-01a" xml:space="preserve">2. ſexti:</note>
            æquidiſtabit: </s>
            <s xml:id="echoid-s1992" xml:space="preserve">quoniam a h ad h d eſt, ut a g ad g b. </s>
            <s xml:id="echoid-s1993" xml:space="preserve">ergo f c, h g
              <lb/>
              <note position="left" xlink:label="note-0078-02" xlink:href="note-0078-02a" xml:space="preserve">30. primi</note>
            inter ſe ſe æquidiſtant: </s>
            <s xml:id="echoid-s1994" xml:space="preserve">& </s>
            <s xml:id="echoid-s1995" xml:space="preserve">idcirco ut a e ad e g, ita a f; </s>
            <s xml:id="echoid-s1996" xml:space="preserve">hoc eſt c f ad
              <lb/>
            fh. </s>
            <s xml:id="echoid-s1997" xml:space="preserve">quod demonſtrare oportebat.</s>
            <s xml:id="echoid-s1998" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div144" type="section" level="1" n="46">
          <head xml:id="echoid-head51" xml:space="preserve">LEMMA V.</head>
          <p style="it">
            <s xml:id="echoid-s1999" xml:space="preserve">Sint rurſus duæ portiones ſimiles, contentæ rectis li-
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            neis, & </s>
            <s xml:id="echoid-s2000" xml:space="preserve">rectangulorum conorum ſectionibus, ut in ſupe-
              <lb/>
            riori figura a b c, cuius diameter b d: </s>
            <s xml:id="echoid-s2001" xml:space="preserve">& </s>
            <s xml:id="echoid-s2002" xml:space="preserve">e f c, cuius
              <lb/>
            diameter f g: </s>
            <s xml:id="echoid-s2003" xml:space="preserve">ducaturque à puncto e linea e h, diame-
              <lb/>
            tris b d, f g æquidiſtans, quæ ſectionem a b c in _k_ ſe-
              <lb/>
            cet: </s>
            <s xml:id="echoid-s2004" xml:space="preserve">& </s>
            <s xml:id="echoid-s2005" xml:space="preserve">à puncto c ducatur c h contingens ſectionem
              <lb/>
            a b c in c conueniensque cumlinea e h in h, quæ ſectio
              <lb/>
            nem quoque e f c in eodem c puncto continget, ut demon
              <lb/>
            strabitur. </s>
            <s xml:id="echoid-s2006" xml:space="preserve">Dico lineam ductam ab ipſa c h uſque ad ſe-
              <lb/>
            ctionem e f c, ita ut lineæ e h æquidistet, in eandem pro
              <lb/>
            portionem diuidi à ſectione a b c; </s>
            <s xml:id="echoid-s2007" xml:space="preserve">in quam linea c a </s>
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