Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
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t u, x y ipſi g h æquidiſtare. </
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<
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xml:space
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">Et quoniam triangula, quæ
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fiunt à lineis K y, y u, u s, s h æqualia ſuntinter ſe, & </
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triangulo K m h: </
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K δ y duplam proportionem eius, quæ eſt lineæ k h ad K y.
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<
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κ m h ad triangulum _K_ δ y eãdem proportionem habebit,
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quam ſexdecim ad unũ & </
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u s, s α h habebit eandem, quam fexdecim ad quatuor, hoc
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eſt quam h K ad κ y: </
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bitur trian-
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gulum κ m g
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ad quatuor
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triãgula K δ
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x, x γ t, t β r,
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r z g. </
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quinti.</
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totum trian
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gulum K g h
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ad omnia tri
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angula g z r,
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r β t, t γ x, x δ
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_K_, K δ y, y u,
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u s, s α h ita
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erit, ut h κ a d
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k y, hoc eſt
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ut h m ad m
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q. </
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triangulis a b c, d e f deſcribantur figuræ ſimiles ei, quæ de-
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ſcripta eſt in g h K triangulo: </
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<
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tes plana ducantur: </
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ſolida parallelepipeda y γ, u β, s z, quorum baſes ſunt æ qua
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les & </
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<
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priſmata g z r, r β t, t γ x, x δ K, κ δ y, y u, u s, s α h: </
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item baſes æquales, & </
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do autem in omnibus, totius priſmatis altitudini æ qualis.</
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