Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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ARCHIMEDIS
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            Quoniam enim triangula afd, akg, anl ſi-
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            milia ſunt; </s>
            <s xml:space="preserve">itémq; </s>
            <s xml:space="preserve">ſimilia efd, h k g, mnl:
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            </s>
            <s xml:space="preserve">erit ut af ad fd, ita ak ad kg; </s>
            <s xml:space="preserve">ut autem fd
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              <anchor type="note" xlink:label="note-0048-01a" xlink:href="note-0048-01"/>
            ad fe, ita kg ad kh. </s>
            <s xml:space="preserve">quare ex æquali ut af
              <lb/>
            ad fe, ita ak ad kh: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">per conuerſionem ra-
              <lb/>
            tionis ut af ad ae, ita ak ad ah. </s>
            <s xml:space="preserve">eodem
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            modo oſtendetur, ut af ad a e, ita an ad am.
              <lb/>
            </s>
            <s xml:space="preserve">cum igitur an ad am ſit, ut a k ad a h; </s>
            <s xml:space="preserve">erit
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              <anchor type="note" xlink:label="note-0048-02a" xlink:href="note-0048-02"/>
            reliqua kn ad reliquam h m, hoc eſt ad g q,
              <lb/>
            uel o p, ut a n ad a m; </s>
            <s xml:space="preserve">hoc estut a f ad a e.
              <lb/>
            </s>
            <s xml:space="preserve">rurſus a k ad a h est, ut a f ad a e. </s>
            <s xml:space="preserve">er-
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            go reliqua f k ad e h reliquam, uidelicet
              <lb/>
            ad do, ut a f ad a e. </s>
            <s xml:space="preserve">Similiter demonſtrabi-
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            mus ita eſſe fn ad d p. </s>
            <s xml:space="preserve">quod quidem demonſtra
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            re oportebat.</s>
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            <note position="left" xlink:label="note-0048-01" xlink:href="note-0048-01a" xml:space="preserve">4. ſexti.</note>
            <note position="left" xlink:label="note-0048-02" xlink:href="note-0048-02a" xml:space="preserve">19. quinti</note>
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          <head xml:space="preserve">LEMMA II.</head>
          <p style="it">
            <s xml:space="preserve">Sint in eadem linea a b puncta
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            duo r s ita diſpoſita, ut a s ad a r
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            eandem proportionem habeat, quam
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            a f ad ae: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">per r ducatur rtipſi
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            e d æquidiſtans; </s>
            <s xml:space="preserve">per s uero ducatur
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            s t æquidiſtans fd, ita ut cum r t in
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            t puncto conueniat. </s>
            <s xml:space="preserve">Dico punctum t
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            cadere in lineam a c.</s>
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            <s xml:space="preserve">Si enim fieri potest, cadat citra: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">produca
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            tur rt uſque ad ipſam a c in u. </s>
            <s xml:space="preserve">deinde per u
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            ducatur u x ipſi f d æquidiſtans. </s>
            <s xml:space="preserve">Itaque ex
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            ijs, quæ proxime demonstrauimus a x ad ar</s>
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