Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
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ARCHIMEDIS
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& </
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<
s
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xml:space
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">quam proportionem habet quadratum 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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<
s
xml:id
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xml:space
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">quare maiorem babet proportionem _k_ r ad i y, quàm di-
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ti.</
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midium k r ad ψ b: </
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">& </
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<
s
xml:id
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">idcirco i y minor eſt, quàm dupla
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ψ b. </
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<
s
xml:id
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">eſt autem ipſius o i dupla. </
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<
s
xml:id
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">ergo o i minor eſt, quàm
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ψ b: </
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<
s
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xml:space
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">& </
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<
s
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">i ω maior, quàm ψ r. </
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<
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xml:space
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">ſed ψ r eſt æqualis ipſi f. </
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<
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">maior
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<
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igitur eſt i ω, quàm f. </
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<
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<
s
xml:id
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xml:space
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">quoniam portio ad humidum in
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/>
grauitate eam ponitur habere proportionem, quam qua-
<
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dratum f q ad quadratum b d: </
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>
<
s
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">quam uero proportionem
<
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/>
habet portio ad humidum in grauitate, eam habet pars ip
<
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/>
ſius demerſa ad totam portionem: </
s
>
<
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xml:space
="
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">& </
s
>
<
s
xml:id
="
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xml:space
="
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">quam pars ipſius de-
<
lb
/>
merſa habet ad totam, eandem habet quadratum p m ad
<
lb
/>
quadratnm o n: </
s
>
<
s
xml:id
="
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xml:space
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">ſequitur quadratum p m ad quadratum
<
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/>
o n eam proportionem habere, quam quadratum f q ad
<
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/>
b d quadratum.
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0058-01
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atque ideo ſ q æ-
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qualis eſt ipſi p m.
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</
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<
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">demõſtrata eſt au
<
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<
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">M</
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>
tem p h maior,
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quàm f. </
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>
<
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xml:space
="
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">cõſtat igi
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/>
tur p m minorem
<
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/>
eſſe, quàm ſeſqui-
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alterã ipſius p h:
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/>
</
s
>
<
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xml:space
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">& </
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<
s
xml:id
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xml:space
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">idcirco p h ma
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iorem, quàm du-
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plam h m. </
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>
<
s
xml:id
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xml:space
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">Sit p z
<
lb
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ipſius z m dupla. </
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>
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<
lb
/>
erit t quidem cẽ-
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trũ grauitatis to-
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tius ſolidi: </
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>
<
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xml:id
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<
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eius partis, quæ intra humidum, punctumz: </
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<
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partis centrum erit in linea z t producta uſque ad g. </
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>
modo demonſtrabitur linea th perpendicularis ad ſuper-
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ficiem humidi. </
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<
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