Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
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DE CENTRO GRAVIT. SOLID.
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uel coni portionis axis à centro grauitatis ita diui
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ditur, ut pars, quæ terminatur ad uerticem reli-
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quæ partis, quæ ad baſim, ſit tripla.</
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<
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">Sit pyramis, cuius baſis triangulum a b c; </
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<
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uitatis centrum _K_. </
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<
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">Dico lineam d k ipſius _K_ e triplam eſſe.
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<
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">trianguli enim b d c centrum grauitatis ſit punctum f; </
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guli a d c centrũ g; </
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<
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">trianguli a d b ſit h: </
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<
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<
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">iungantur a f,
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b g, c h. </
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<
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">Quoniam igitur centrũ grauitatis pyramidis in axe
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cõſiſtit: </
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">d e, a f, b g, c h eiuſdẽ pyramidis axes: </
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nient omnes in idẽ punctũ _k_, quod eſt grauitatis centrum.
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">Itaque animo concipiamus hanc pyramidem diuiſam in
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quatuor pyramides, quarum baſes ſint ipſa pyramidis
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triangula; </
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0167-01
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ctum k quæ quidem py-
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ramides inter ſe æquales
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ſunt, ut demõſtrabitur.
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d c, d e planum ſecãs, ut
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ſit ipſius, & </
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munis ſectio recta linea
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c e l: </
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guli a d b ſitlinea d h l. </
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erit linea a l æqualis ipſi
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l b: </
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<
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">nam centrum graui-
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tatis trianguli conſiſtit
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in linea, quæ ab angulo
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ad dimidiam baſim per-
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ducitur, ex tertia deci-
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ma Archimedis. </
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triangulum a c l æquale
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eſt triangulo b c l: </
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<
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">propterea pyramis, cuius baſis trian-
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gulum a c l, uertex d, eſt æqualis pyramidi, cuius baſis b c l
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triangulum, & </
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<
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<
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cimi.</
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