Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
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Quoniam enim triangula afd, akg, anl ſi-
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milia ſunt; </
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</
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<
s
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">erit ut af ad fd, ita ak ad kg; </
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<
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<
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">4. ſexti.</
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ad fe, ita kg ad kh. </
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<
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">quare ex æquali ut af
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ad fe, ita ak ad kh: </
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">& </
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<
s
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xml:space
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">per conuerſionem ra-
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tionis ut af ad ae, ita ak ad ah. </
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<
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">eodem
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modo oſtendetur, ut af ad a e, ita an ad am.
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</
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<
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">cum igitur an ad am ſit, ut a k ad a h; </
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">erit
<
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<
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">19. quinti</
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reliqua kn ad reliquam h m, hoc eſt ad g q,
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uel o p, ut a n ad a m; </
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<
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</
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<
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xml:space
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">rurſus a k ad a h est, ut a f ad a e. </
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<
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">er-
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go reliqua f k ad e h reliquam, uidelicet
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ad do, ut a f ad a e. </
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>
<
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">Similiter demonſtrabi-
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mus ita eſſe fn ad d p. </
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<
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">quod quidem demonſtra
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re oportebat.</
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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: </
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">& </
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<
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">per r ducatur rtipſi
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e d æquidiſtans; </
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<
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">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. </
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<
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cadere in lineam a c.</
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<
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">Si enim fieri potest, cadat citra: </
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<
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tur rt uſque ad ipſam a c in u. </
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>
<
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">deinde per u
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ducatur u x ipſi f d æquidiſtans. </
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ijs, quæ proxime demonstrauimus a x ad </
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