Valerio, Luca - De centro gravitatis solidorvm libri tres

Valerio, Luca, De centro gravitatis solidorvm libri tres

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1

PROPOSIT'IO XXVII.

Solida grauia æquiponderant à longitudini
bus ex contraria parte reſpondentibus.

Sint ſolida grauia A, & B, quorum centra grauitatis
ſint A, B, ſecundum quæ ſuſpenſa intelligantur A, in
puncto C, & B, in puncto D, cuiuslibet rectæ GH, quæ
ſit ita diuiſa in puncto E, vt ſit DE, ad EC, vt eſt A,
ad B. Dico ſolida A, E, æquiponderare à longitudini
bus DE, EC; hoc eſt vtriuſque ſimul centrum grauita
tis eſse E. Nam ſi A, B, ſint æqualia, manifeſtum eſt
propoſitum: ſi au
tem inæqualia, eſto
maius A: maior igi
tur erit DE, quam
EC. abſcindatur
DF, æqualis EC:
erit igitur DE, æ
qualis GF: & CD,
vtrin que producta,
ponatur DH, æ
qualis DF: & CG,
ipſi CF. & circa
axim, & altitudinem
GH, eſto paralle
lepipedum KL, æ
quale duobus ſo

39[Figure 39]
lidis A, B, ſimul & parallelepipedum KL, ſecetur plano
per punctum F, oppoſitis planis parallelo, in duo paral
lelepipeda KN, ML. Quoniam igitur eſt vt GF, ad
FH, ita parallelepipedum KN, ad parallelepipedum

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