Valerio, Luca, De centro gravitatis solidorvm libri tres
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              PROPOSITIO XXXI.
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              <s>Hemiſphærij, vel hemiſphæroidis centrum
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              grauitatis eſt punctum illud, in quo axis ſit diui­
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              ditur, vt pars ad verticem ſit ad reliquam vt quin
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              que ad tria. </s>
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              <s>Eſto hemiſphærium, vel hemiſphæroides ABC, cuius
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              axis BD, baſis circulus, vel ellipſis, cuius diameter AD
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              C: ſitque ſolidi ABC centrum grauitatis G, nempe
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              in axe BD. </s>
              <s>Dico BG ad GD eſſe vt quinque ad tria.
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              <s>Nam circa axim BD ſuper baſim circulum, vel ellipſim cir
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              ca AC, ſtet circumſcri
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              ptus ſolido ABC cy­
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              lindrus, vel portio cy­
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              lindrica AE, & ſecta
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              BD bifariam in F, rur
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              ſus FB bifariam ſece­
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              tur in puncto H. </s>
              <s>Quo­
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              niam igitur ſolidum A
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              BC eſt ſolidi AE, ſub­
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              ſeſquialterum, erit di­
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              uidendo ſolidum ABC reliqui ex ſolido AE duplum
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              cum igitur ſint centra grauitatis, G ſolidi ABC, & H
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              prædicti reliqui, & F totius AE; quo fit vt ex con­
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              traria parte ſit vt ſolidum ABC ad prædictum reſiduum,
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              ita HF ad FG, erit HF dupla ipſius FG; quadrupla
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              igitur BF ipſius FG: ſed talium quatuor partium eſt BF,
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              qualium BD eſt octo, cum ſit BF dimidia ipſius BD;
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              qualium igitur octo eſt BD, talium erit BG quinque, &
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              GD trium. </s>
              <s>Quod demonſtrandum erat. </s>
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