Commandino, Federico
,
Liber de centro gravitatis solidorum
,
1565
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per f planum baſibus æquidiſtans ducatur, ut ſit ſectio cir
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culus, uel ellipſis circa diametrum fg. </
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<
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">Dico ſectionem ab
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ad ſectionem fg eandem proportionem habere, quam fg
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ad ipſam cd. </
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<
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">Simili enim ratione, qua ſupra, demonſtrabi
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tur quadratum ab ad quadratum fg ita eſſe, ut
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quadratũ
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fg ad cd quadratum. </
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">Sed circuli inter ſe eandem propor
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tionem habent, quam diametrorum quadrata. </
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<
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">ellipſes au
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tem circa ab, fg, cd, quæ ſimiles ſunt, ut oſtendimus in
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abbr
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cõ-mentariis
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mentariis</
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in principium libri Archimedis de conoidibus,
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& ſphæroidibus, eam
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abbr
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habẽt
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proportionem, quam quadra
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ta diametrorum, quæ eiuſdem rationis ſunt, ex corollario
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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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">ergo
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circulus, uel ellipſis ab ad
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circulũ
">circulum</
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,
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uel ellipſim fg eam proportionem
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habet, quam circulus, uel ellipſis
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fg ad circulum uel ellipſim cd. </
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">quod quidem faciendum propo
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ſuimus.</
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2. duode
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cimi</
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">THEOREMA XX. PROPOSITIO XXV.</
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">QVODLIBET 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, & æqualis
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altitudo, eandem
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proportionẽ
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habet, quam utræ
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que baſes, maior, & minor ſimul ſumptæ vnà
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cũ
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ea, quæ inter ipſas ſit proportionalis, ad baſim ma
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iorem.</
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