Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
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DE CENTRO GRAVIT. SOLID.
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relinquetur p e ipſi n χ æqualis. </
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<
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xml:space
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e d, & </
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<
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xml:space
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<
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xml:space
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cet b o unà cum p e ipſius reliqui χ d duplnm erit. </
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<
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b o dupla ζ d. </
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<
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xml:space
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">ergo p e, hoc eſt n χ ipſius χ ρ dupla. </
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<
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xml:id
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xml:space
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">ſed d n
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dupla eſt n ζ. </
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<
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xml:id
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xml:space
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">reliqua igitur d χ dupla reliquæ χ n. </
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<
s
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xml:space
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tem d χ, p n inter ſe æquales: </
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<
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<
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xml:id
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xml:space
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">æquales χ n, p e. </
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<
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xml:space
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re conſtat n p ipſius p e duplam eſſe. </
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<
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xml:space
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">& </
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<
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xml:space
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">idcirco p e ipſi e n
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æqualem. </
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<
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xml:space
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">Rurſus cum ſit μ ν dupla o ν, & </
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<
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xml:space
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">erit
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etiam reliqua ν σ o dupla. </
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<
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xml:space
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">Eadem quoque ratione
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cõcludetur π υ dupla υ m. </
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<
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xml:space
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">ergo ut ν σ ad σ O, ita π υ ad υ m:
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</
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<
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<
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">permutando, ut υ o ad π m, ita o σ ad
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m υ & </
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<
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xml:space
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<
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">quare & </
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<
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xml:id
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xml:space
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<
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xml:space
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terea σ π dupla eſt π τ, & </
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<
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xml:space
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">ν π ipſius π m. </
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<
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xml:space
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">reliqua igitur σ ν re
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liquæ m τ dupla. </
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<
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xml:id
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xml:space
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<
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xml:id
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xml:space
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quales ſunt: </
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<
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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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">ita æquales m υ, n φ. </
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<
s
xml:id
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xml:space
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">at o σ, eſt æqualis
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m υ. </
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<
s
xml:id
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xml:space
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">Sequitur igitur, ut omnes o σ, m τ, m υ, n φ in-
<
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ter ſe ſint æquales. </
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<
s
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xml:space
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">Sed ut ρ π ad π τ, hoc eſt ut 3 ad 2, ita n d
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ad d χ: </
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<
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xml:space
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<
s
xml:id
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xml:space
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">ut ρ π ad n d, ita π τ ad d χ. </
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<
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xml:id
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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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">ſũt æqua
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les ζ π, n d. </
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<
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xml:id
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xml:space
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<
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xml:id
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xml:space
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">π τ æquales. </
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<
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xml:space
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quales n π, π m. </
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<
s
xml:id
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xml:space
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">reliqua igitur π p reliquæ m τ, hoc eſt ipſi
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n φ æqualis erit. </
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<
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xml:id
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xml:space
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">quare dempta p π ex p e, & </
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<
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">φ n dempta ex
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n e, relinquitur p e æqualis e φ. </
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<
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xml:space
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">Itaque π, ρ centra figurarũ
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ſecundo loco deſcriptarum a primis centris p n æquali in-
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teruallo recedunt. </
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<
s
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xml:space
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">quòd ſi rurſus aliæ figuræ deſcribantur,
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eodem modo demonſtrabimus earum centra æqualiter ab
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his recedere, & </
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<
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moueri. </
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<
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xml:space
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">Ex quibus conſtat lineam π φ à centro grauitatis
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portionis diuidi in partes æquales. </
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<
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xml:space
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">Si enim fieri poteſt, non
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ſit centrum in puncto e, quod eſt lineæ π φ medium: </
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<
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xml:space
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ψ: </
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<
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xml:space
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">& </
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<
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xml:space
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">ipſi π ψ æqualis fiat φ ω. </
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<
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xml:id
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xml:space
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">Cum igitur in portione ſolida
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quædam figura inſcribi posſit, ita ut linea, quæ inter cen-
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trum grauitatis portionis, & </
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<
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qualibet linea propoſita ſit minor, quod proxime demon-
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ſtrauimus: </
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<
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