Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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            <s xml:id="echoid-s2028" xml:space="preserve">
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            cto continget. </s>
            <s xml:id="echoid-s2029" xml:space="preserve">Itaque iuncta cm producatur ad ſectionem a b c in p:
              <lb/>
            </s>
            <s xml:id="echoid-s2030" xml:space="preserve">& </s>
            <s xml:id="echoid-s2031" xml:space="preserve">à p ad a c ducatur p q, quæ ipſi b d æquidiſtet. </s>
            <s xml:id="echoid-s2032" xml:space="preserve">quoniam igi-
              <lb/>
            tur linea c h contingit ſectionem e f c in c puncto; </s>
            <s xml:id="echoid-s2033" xml:space="preserve">habebit l m
              <lb/>
            ad m d proportionem eandem, quam c d ad d e, ex quinta propoſi-
              <lb/>
            tione Archimedis in libro de quadratura parabolæ. </s>
            <s xml:id="echoid-s2034" xml:space="preserve">& </s>
            <s xml:id="echoid-s2035" xml:space="preserve">propter triá
              <lb/>
            gulorum c m d, c p q
              <lb/>
              <figure xlink:label="fig-0080-01" xlink:href="fig-0080-01a" number="50">
                <image file="0080-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0080-01"/>
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            ſimilitudinem, ut c m
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            ad c d, ita erit c p ad
              <lb/>
            c q: </s>
            <s xml:id="echoid-s2036" xml:space="preserve">permutandôq;
              <lb/>
            </s>
            <s xml:id="echoid-s2037" xml:space="preserve">ut c m ad c p, ita c d
              <lb/>
            ad c q. </s>
            <s xml:id="echoid-s2038" xml:space="preserve">ut autem c m
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            ad c p, ſic c e ad c a: </s>
            <s xml:id="echoid-s2039" xml:space="preserve">
              <lb/>
            quod proxime demó-
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            ſtrauimus. </s>
            <s xml:id="echoid-s2040" xml:space="preserve">quare ut
              <lb/>
            c e ad c a, ſit c d ad
              <lb/>
            c q: </s>
            <s xml:id="echoid-s2041" xml:space="preserve">hoc eſt ut totum
              <lb/>
            ad totum, ſic pars ad
              <lb/>
            partem, reliquum igi
              <lb/>
            tur d e ad reliquum
              <lb/>
            q a eſt ut c e ad c a; </s>
            <s xml:id="echoid-s2042" xml:space="preserve">
              <lb/>
            uidelicet ut c d ad
              <lb/>
            c q: </s>
            <s xml:id="echoid-s2043" xml:space="preserve">& </s>
            <s xml:id="echoid-s2044" xml:space="preserve">permutando
              <lb/>
            c d ad d e, ut c q ad
              <lb/>
            q a. </s>
            <s xml:id="echoid-s2045" xml:space="preserve">êſtq; </s>
            <s xml:id="echoid-s2046" xml:space="preserve">l m ad m
              <lb/>
            d, ut c d ad d e. </s>
            <s xml:id="echoid-s2047" xml:space="preserve">ergo
              <lb/>
            l m ad m d, ut c q ad
              <lb/>
            q a. </s>
            <s xml:id="echoid-s2048" xml:space="preserve">ſed l b ad b d
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            ex quinta Archime-
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            dis, quam diximus; </s>
            <s xml:id="echoid-s2049" xml:space="preserve">
              <lb/>
            eſt ut c d ad d a. </s>
            <s xml:id="echoid-s2050" xml:space="preserve">con
              <lb/>
            ſtat igitur ex antece-
              <lb/>
            denti lemmate c d ad d q ita eſſe, ut l b ad b m. </s>
            <s xml:id="echoid-s2051" xml:space="preserve">ut autem c d ad d q,
              <lb/>
              <note position="left" xlink:label="note-0080-01" xlink:href="note-0080-01a" xml:space="preserve">2. ſexti.</note>
            ita c m ad m p. </s>
            <s xml:id="echoid-s2052" xml:space="preserve">ergo l b ad b m, ut c m ad m p. </s>
            <s xml:id="echoid-s2053" xml:space="preserve">Quòd cum demon
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            ſtratum fuerit, c m ad m p, ut c e ad e a: </s>
            <s xml:id="echoid-s2054" xml:space="preserve">habebit l b ad b m </s>
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