Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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            <s xml:id="echoid-s1916" xml:space="preserve">Ex quibus perſpicuum eſt lineas omnes ſic ductas ab
              <lb/>
            ipſis ſectionibus in eandem proportionem ſecari. </s>
            <s xml:id="echoid-s1917" xml:space="preserve">eſt enim
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            diuidendo, conuertendoque cm ad mb, & </s>
            <s xml:id="echoid-s1918" xml:space="preserve">cf ad fb, ut
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            ce ad ea.</s>
            <s xml:id="echoid-s1919" xml:space="preserve"/>
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        <div xml:id="echoid-div139" type="section" level="1" n="44">
          <head xml:id="echoid-head49" xml:space="preserve">LEMMA III.</head>
          <p style="it">
            <s xml:id="echoid-s1920" xml:space="preserve">Sed & </s>
            <s xml:id="echoid-s1921" xml:space="preserve">illud constare potest; </s>
            <s xml:id="echoid-s1922" xml:space="preserve">lineas, quæ in portioni-
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            bus eiuſmodi ſimilibus ita ducuntur, ut cú baſibus æqua-
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            les angulos contineant, ab ipſis ſimiles quoque portiones
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            abſcindere: </s>
            <s xml:id="echoid-s1923" xml:space="preserve">hoc eſt, ut in propoſita figura, portiones h b c,
              <lb/>
            m f c, quas lineæ c h, c m abſcindunt, etiam inter ſe
              <lb/>
            ſimiles eſſe.</s>
            <s xml:id="echoid-s1924" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1925" xml:space="preserve">
              <emph style="sc">D_ividantvr_</emph>
            enim ch, cm bifariam in punctis p q: </s>
            <s xml:id="echoid-s1926" xml:space="preserve">& </s>
            <s xml:id="echoid-s1927" xml:space="preserve">per
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            ipſa ducantur lineæ r p s, t q u diametris æquidiſtantes. </s>
            <s xml:id="echoid-s1928" xml:space="preserve">erit portio-
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            nis b s c diameter p s, & </s>
            <s xml:id="echoid-s1929" xml:space="preserve">portionis m u c diameter q u. </s>
            <s xml:id="echoid-s1930" xml:space="preserve">Itaque fiat
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            ut quadratum c r ad quadratum c p, ita linea b n ad aliam lineam,
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            quæ ſit s x: </s>
            <s xml:id="echoid-s1931" xml:space="preserve">& </s>
            <s xml:id="echoid-s1932" xml:space="preserve">ut quadratum c t ad quadratum c q, ita fiat f o ad
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            u y. </s>
            <s xml:id="echoid-s1933" xml:space="preserve">iam exijs
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              <figure xlink:label="fig-0076-01" xlink:href="fig-0076-01a" number="47">
                <image file="0076-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0076-01"/>
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            quæ demóſtra
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            uimus in com-
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            mentarijs in
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            quartam pro-
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            poſitioné. </s>
            <s xml:id="echoid-s1934" xml:space="preserve">Ar-
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            chrmedis de co
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            noidibus, & </s>
            <s xml:id="echoid-s1935" xml:space="preserve">
              <lb/>
            ſphæroidibus,
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            patet quadra-
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            tum c p æqua-
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            le eſſe rectan-
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            gulo p s x:</s>
            <s xml:id="echoid-s1936" xml:space="preserve"/>
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