Valerio, Luca
,
De centro gravitatis solidorvm libri tres
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baſes ſunt circuli, vel ellipſes, reliqua autem ſu
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perficies tota interius concaua, centrum grauitatis
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eſt in dimidio axis ſegmento, quod baſim, vel ma
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iorem baſim attingit. </
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>Sit figura circa axim in alteram partem deficiens ABC,
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cuius axis BD, baſis, vel maior baſis circulus, vel ellipſis
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circa diametrum AC, reliqua autem ſuperficies tota inte
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rius concaua: ſecto autem axe BD bifariam in puncto G,
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ſit ſolidi ABC centrum grauitatis F nempe in axe BD.
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>Dico punctum F eſſe in ſegmento ED. </
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do ABC, & figu
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ra per axem pla
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no per
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E
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baſi, vel baſibus
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parallelo, fiat ſe
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ctio circulus, vel
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ellipſis ſimilis
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baſi, per diffini
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tionem, & ſectio
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nis diameter K
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N: deinde figu
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ra quædam ex
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duobus cylindris, vel cylindri portionibus KL, AM cir
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ca axes BE, ED, eiuſdem altitudinis circumſcribatur
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ſolido ABC: ſecanturque bifariam BE in puncto G, &
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ED in puncto H. totius autem figuræ circumſcriptæ ſit
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centrum grauitatis O, nempe in axe BD. </
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>Quoniam igi
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tur propter bipartitorum axium ſectiones G, H, eſt ſolidi
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KL centrum grauitatis G: ſolidi autem AM centrum
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grauitatis H, erit in linea GH totius ſolidi AL centrum
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grauitatis O, & vt ſolidum AM ad ſolidum KL, ita GO
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ad OH: ſed maior eſt proportio ſolidi AM ad ſolidum KL </
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