Valerio, Luca
,
De centro gravitatis solidorvm libri tres
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cylindri, vel portionis cylindricæ AE reliquum dempto
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hemiſphærio, vel hemiſphæroide ABC æquale eſt cono,
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vel portioni conicæ ABC: & cylindrus, vel portio cylin
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drica AE tripla eſt co
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ni, vel portionis conicæ
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ABC; triplus itidem
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erit cylindrus, vel cylin
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drica portio AE dicti
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reſidui dempto hemi
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ſphærio, vel hemiſphæ
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roide ABC; ac propte
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rea hemiſphærij, vel he
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miſphæroidis ABC
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ſeſquialter, hoc eſt hemiſphærium, vel hemiſphæroides
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ABC cylindri, vel portionis cylindricæ AE ſubſeſquial
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terum. </
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<
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>Quod erat demonſtrandum. </
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PROPOSITIO XVI.
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<
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>Omnis minor portio ſphæræ, vel ſphæroidis ad
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cylindrum, vel cylindri portionem, cuius baſis
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æqualis eſt circulo maximo, vel æqualis, & ſimi
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lis ellipſi per centrum baſi portionis parallelæ,
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& eadem altitudo portioni; eam habet proportio
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nem, quam rectangulum contentum ſphæræ, vel
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ſphæroidis dimidij axis axi portionis congruen
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tis ijs, quæ à centro baſis portionis fiunt
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,
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vnà cum duobus tertiis quadrati axis portionis; ad
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ſphæræ, vel ſphæroidis dimidij axis quadratum. </
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<
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>Sit minor portio ABC, ſphæræ, vel ſphæroidis, cuius
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centrum D, axis autem axi portionis congruens BEDR: </
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