Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
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DE CENTRO GRAVIT. SOLID.
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DE CENTRO GRAVIT. SOLID.
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">SIT fruſtũ pyramidis, uel coni, uel coni portionis a d,
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cuius maior baſis a b, minor c d. </
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<
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baſi æquidiſtante, ita utſectio e f ſit proportionalis inter
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baſes a b, c d. </
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">conſtituatur autẽ pyramis, uel conus, uel co-
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ni portio a g b, cuius baſis ſit eadem, quæ baſis maior fru-
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ſti, & </
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co fruſtum a d ad pyrami-
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dem, uel conum, uel coni
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portionem a g b eandem
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proportionẽ habere, quã
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utræque baſes, a b, c d unà
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cum e f ad baſim a b. </
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enim fruſtum a d æquale
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pyramidi, uel cono, uel co-
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ni portioni, cuius baſis ex
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tribus baſibus a b, e f, c d
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conſtat; </
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<
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">altitudo ipſius
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altitudini eſt æqualis: </
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">quod mox oſtendemus. </
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">Sed pyrami
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des, coni, uel coni portiões,
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quæ ſunt æquali altitudine,
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eãdem inter ſe, quam baſes,
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proportionem habent, ſicu-
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ti demonſtratum eſt, partim
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ab Euclide in duodecimo li-
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bro elementorum, partim à
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nobis in cõmentariis in un-
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decimam propoſitionẽ Ar-
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chimedis de conoidibus, & </
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ſphæroidibus. </
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<
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">quare pyra-
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mis, uel conus, uel coni por-
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tio, cuius baſis eſt tribus illis
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baſibus æqualis ad a g b eam
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habet proportionem, quam
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baſes a b, e f, c d ad ab bafim. </
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<
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">Fruſtum igitur a d ad a g b</
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