Valerio, Luca
,
De centro gravitatis solidorvm libri tres
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PROPOSIT'IO XXVII.
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<
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>Solida grauia æquiponderant à longitudini
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bus ex contraria parte reſpondentibus. </
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>Sint ſolida grauia A, & B, quorum centra grauitatis
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ſint A, B, ſecundum quæ ſuſpenſa intelligantur A, in
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puncto C, & B, in puncto D, cuiuslibet rectæ GH, quæ
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ſit ita diuiſa in puncto E, vt ſit DE, ad EC, vt eſt A,
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ad B. </
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>Dico ſolida A, E, æquiponderare à longitudini
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bus DE, EC; hoc eſt vtriuſque ſimul centrum grauita
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tis eſse E. </
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>Nam ſi A, B, ſint æqualia, manifeſtum eſt
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propoſitum: ſi au
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tem inæqualia, eſto
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maius A: maior igi
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tur erit DE, quam
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EC. abſcindatur
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DF, æqualis EC:
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erit igitur DE, æ
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qualis GF: & CD,
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vtrin que producta,
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ponatur DH, æ
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qualis DF: & CG,
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ipſi CF. & circa
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axim, &
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GH, eſto paralle
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lepipedum KL, æ
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quale duobus ſo
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lidis A, B, ſimul & parallelepipedum KL, ſecetur plano
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per punctum F, oppoſitis planis parallelo, in duo paral
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lelepipeda KN, ML. </
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<
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>Quoniam igitur eſt vt GF, ad
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FH, ita parallelepipedum KN, ad parallelepipedum </
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