Valerio, Luca
,
De centro gravitatis solidorvm libri tres
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PROPOSITIO XXXI.
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<
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>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. </
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>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. </
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>Dico BG ad GD eſſe vt quinque ad tria.
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>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. </
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<
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>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. </
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>Quod demonſtrandum erat. </
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