Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
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DE CENTRO GRA VIT. SOLID.
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Itaque ſolidi parallelepipedi y γ centrum grauitatis eſt in
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linea δ: </
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<
s
xml:id
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xml:space
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">ſolidi u β centrum eſt in linea ε η: </
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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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">ſolidi s z in li
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nea η m, quæ quidem lineæ axes ſunt, cum planorum oppo
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ſitorum centra coniungant. </
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<
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xml:space
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">ergo magnitudinis ex his ſoli
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dis compoſitæ centrum grauitatis eſt in linea δ m, quod ſit
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θ; </
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<
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xml:space
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">& </
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<
s
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xml:space
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">iuncta θ o producatur: </
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<
s
xml:id
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xml:space
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">à puncto autem h ducatur h μ
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ipſi m κ æquidiſtans, quæ cum θ o in μ conueniat. </
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<
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lum igitur g h κ ad omnia triangula g z r, r β t, t γ x, x δ k,
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κ δ y, y u, u s, s α h eandem habet proportionem, quam h m
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ad m q; </
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<
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<
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">nam ſi h m, μ θ produci in
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telligantur, quouſque coeant; </
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<
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xml:space
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">erit ob linearum q y, m k æ-
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quidiſtantiam, ut h q ad q m, ita μ λ ad ad λ θ: </
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<
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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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do, ut h m ad m q, ita μ θ ad θ λ. </
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<
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xml:space
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quàm θ λ: </
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">habebit igitur μ θ ad θ λ maiorem proportio-
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xml:space
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">8. quinti.</
note
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nem, quàm ad θ o. </
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<
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xml:space
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">quare triangulum etiam g h k ad omnia
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iam dicta triangula maiorem proportionẽ habebit, quàm
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μ θ ad θ o. </
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<
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">ſed ut triangulũ g h k ad omnia triangula, ita to-
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tũ priſma a f ad omnia priſmata g z r, r β t, t γ x, x δ k, k δ y,
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y u, u s, s α h: </
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<
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xml:space
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">quoniam enim ſolida parallelepipeda æque al
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ta, eandem inter ſe proportionem habent, quam baſes; </
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ex trigeſimaſecunda undecimi elementorum conſtat. </
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cimi</
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autem ſolida parallelepipeda priſmatum triangulares ba-
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ſes habentium dupla: </
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matainter ſe ſint, ſicut eorum baſes. </
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<
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">ergo totum priſma ad
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omnia priſmata maiorem proportionem habet, quam μ θ
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ad θ o: </
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<
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<
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xml:space
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">diuidendo ſolida parallelepipeda y γ, u β, s z ad o-
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xml:space
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">19. quinti
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apud Cã
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panum.</
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mnia prifmata proportionem habent maiorem, quàm μ o
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ad o θ. </
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<
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omnia priſmata. </
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<
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">Itaque cum à priſmate a f, cuius cẽtrum
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grauitatis eſt o, auferatur magnitudo ex ſolidis parallelepi
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pedis y γ, u β, s z conſtans: </
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<
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ſit θ: </
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conſtat, grauitatis centrum erit in linea θ o producta: </
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in puncto ν, ex o ctaua propoſitione eiuſdem libri </
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