Valerio, Luca - De centro gravitatis solidorum

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PROPOSITIO XLI.

Omnis cylindri centrum grauitatis axim bifa
riam diuidit.

Sit cylindrus ABCD, cuius axis EF, & ſit ſectus bi
fariam in puncto G. Dico punctum G, eſse centrum
grauitatis cylindri ABCD. Nam ſi cylindro AD, in
ſcriptum intelligatur priſma,
cuius baſes oppoſitæ æquilate
ræ ſint, & æquiangulæ; erunt,
qua ratione ſupra diximus, ea
rum centra figuræ, & grauitatis
E, F; axis igitur inſcripti priſ
matis erit EF: & centrum gra
uitatis G. poteſt autem tale
priſma ſic inſcribi cylindro
ABCD, vt ab illo deficiat
minori ſpacio quantacumque
magnitudine propoſita; cylin
dri igitur ABCD, centrum
grauitatis erit G. Quod demonſtrandum erat.

57[Figure 57]

PROPOSITIO XLII.

Sphæræ, & ſphæroidis idem eſt centrum gra
uitatis, & figuræ.

Sit ſphæra, vel ſphæroides ABCD, cuius centrum E,

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