Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
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FED. COMMANDINI
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fruſtum a d. </
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">Sed pyramis q æqualis eſt fruſto à pyramide
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abſciſſo, ut dem onſtrauimus. </
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<
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">ergo & </
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<
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">conus, uel coni por-
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tio q, cuius baſis ex tribus circulis, uel ellipſibus a b, e f, c d
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conſtat, & </
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<
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xml:space
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">altitudo eadem, quæ fruſti: </
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<
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xml:space
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">ipſi fruſto a d eſt æ-
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qualis. </
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<
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">atque illud eſt, quod demonſtrare oportebat.</
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<
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<
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fruſti à pyramide, uel cono,
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uel coni portione abſcisſi, centrum grauitatis eſt
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in axe, ita ut eo primum in duas portiones diui-
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ſo, portio ſuperior, quæ minorem baſim attingit
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ad portionem reliquam eam habeat proportio-
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nem, quam duplum lateris, uel diametri maioris
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baſis, vnà cum latere, uel diametro minoris, ipſi
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reſpondente, habet ad duplum lateris, uel diame-
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tri minoris baſis vnà cũ latere, uel diametro ma-
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ioris: </
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<
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xml:space
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">deinde à puncto diuiſionis quarta parte ſu
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perioris portionis in ipſa ſumpta: </
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<
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xml:space
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">& </
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<
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">rurſus ab in-
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ferioris portionis termino, qui eſt ad baſim maio
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rem, ſumpta quarta parte totius axis: </
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<
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">centrum ſit
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in linea, quæ his finibus continetur, atque in eo li
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neæ puncto, quo ſic diuiditur, ut tota linea ad par
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tem propinquiorem minori baſi, eãdem propor-
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tionem habeat, quam fruſtum ad pyramidẽ, uel
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conum, uel coni portionem, cuius baſis ſit ea-
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dem, quæ baſis maior, & </
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<
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æqualis.</
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