Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
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quadratum e ψ ad quadr. </
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<
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">itum ψ b.</
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<
s
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">_Sed quam proportionem habet qua-_
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0062-01
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_dratum p i ad quadratum i y, eandem li_
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_nea k r habet ad lineam i y.</
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<
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">]_ Est enim ex
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undecima primi conicorum quadratum p i æqua
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le rectangulo contento linea i o, & </
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<
s
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">ea, iuxta quam poſſunt quæ à
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ſectione ad diametrum ducuntur, uidelicet duplaipſius k r. </
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<
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est i y dupla i o, extrigeſimatertia eiuſdem: </
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<
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">quare ex decimaſext a
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ſexti elementorum, rectangulum, quod fit ex k r, & </
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<
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">i y æ quale eſt
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rectangulo contento linea i o & </
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<
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">ea, iuxta quam poſſunt: </
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<
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">hoc eſt qua
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drato p i. </
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<
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">Sed ut rectangulnm ex k r, & </
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<
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xml:space
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">i y ad quadratum i y, ita
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xml:space
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">lem. 22.
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decimi.</
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linea κ r ad ipſam i y. </
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<
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xml:space
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">ergo linea κ r ad i y eandem proportionem
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habebit, quam rectangulum ex κ r & </
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<
s
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">i y, hoc eſt quadratum p i ad
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quadratum i y.</
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<
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</
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<
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<
s
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">Et quam proportionem habet quadratũ e ψ ad quadra
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tum ψ b, eandem habet dimidium lineæ K r ad lineã ψ b.</
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<
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">Nam cum quadratum e ψ poſitum ſit æquale dimidio rectanguli
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contenti linea κ r, & </
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">ψ b; </
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">hoc est ei, quod dimidia ipſius κ r
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& </
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<
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">linea ψ b continetur: </
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">& </
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<
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">ut rectangulum ex dimidia κ r, & </
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<
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">ψ b
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">lem. 22.
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decimi</
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ad quadratum ψ b, ita ſit dimidia κ r ad line am ψ b: </
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<
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dia κ r ad ψ b proportionem eandem, quam quadratum e ψ ad qua-
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dratum ψ b.</
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<
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">_Etidcirco i y minor eſt, quàm dupla ψ b.</
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">]_ Quam enim pro
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portionem habet dimidium κ r ad ψ b, habeat κ r ad aliam lineam.
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</
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<
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">erit ea maior, quàm i y; </
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">nempe ad quam κ r minorem proportioné
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">10. quinti.</
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habet: </
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">at que erit dupla ψ b. </
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<
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">ergo i y minor eſt, quam dupla ψ b.</
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<
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">_Et i ω maior, quam ψ r.</
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">]_ Cum enim o ω poſita ſit æ qualis b r
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ſi ex b r dematur ψ b, & </
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">ex o ω dematur o i, quæ minor eſt ψ b: </
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reliqua i ω maior reliqua ψ r.</
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<
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">]_ Ex decimaquarta
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quinti elementorum, nam linea o n ipſi b d eſt æ qualis.</
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<
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monstrata est i ω maior, quàm f; </
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<
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