Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
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FED. COMMANDINI
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per f planum baſibus æquidiſtans ducatur, ut ſit ſectio cir
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culus, uel ellipſis circa diametrum f g. </
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ad ſectionem f g eandem proportionem habere, quam f g
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ad ipſam c d. </
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<
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">Simili enim ratione, qua ſupra, demonſtrabi-
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tur quadratum a b ad quadratum f g ita eſſe, ut quadratũ
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f g ad c d quadratum. </
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cimi</
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tionem habent, quam diametrorum quadrata. </
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<
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tem circa a b, f g, c d, quæ ſimiles ſunt, ut oſten dimus in cõ-
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mentariis in principium libri Archimedis de conoidibus,
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& </
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<
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">ſphæroidibus, eam habẽt proportionem, quam quadrar
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ta diametrorum, quæ eiuſdem rationis ſunt, ex corollaio-
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ſeptimæ propoſitionis eiuſdem li-
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bri. </
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">ellipſes enim nunc appello ip-
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ſa ſpacia ellipſibus contenta. </
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<
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circulus, uel ellipſis a b ad circulũ,
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uel ellipſim f g eam proportionem
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habet, quam circulus, uel ellipſis
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f g ad circulum uel ellipſim c d.
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ſuimus.</
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<
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fruſtum pyramidis, uel coni,
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uel coni portionis ad pyramidem, uel conum, uel
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coni portionem, cuius baſis eadem eſt, & </
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<
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altitudo, eandem proportionẽ habet, quam utræ
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que baſes, maior, & </
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ea, quæ inter ipſas ſit proportionalis, ad baſim ma
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iorem.</
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