Valerio, Luca, De centro gravitatis solidorum, 1604

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1
PROPOSITIO XXXIV.
Omnis priſmatis baſim pluſquam trilateram
habentis centrum grauitatis eſt in medio axis.
Sit priſma ABCDEFGH, baſim habens quadrila­
teram ABCD: axis autem KL, bifariam ſectus in pun­
cto M. Dico punctum M, eſse centrum grauitatis priſ­
matis ABCDEFGH. Iungantur enim rectæ BD, FH,
vt parallelogrammum ſit BH, ſectumque totum priſma
in duo priſmata, quorum ba­
ſes ſunt triangula, in quæ ſecta
ſunt quadrilatera AC, EG,
ſint autem axes duorum priſ­
matum triangulas baſes ha­
bentium NO, Pque Erunt
igitur centra grauitatis O, tri­
anguli ABD, & L, quadri­
lateri AC, & Q, trianguli
BCD, itemque N, trianguli
EFH, & K, quadrilateri EG,
& P, trianguli FGH: iun­
ctæ igitur OQ, NP, per pun
49[Figure 49]
cta L, K, tranſibunt: cumque tres prædicti axes ſint
lateribus priſmatis, atque ideo inter ſe quoque paralleli;
parallelogramma erunt OP, NL, LP. ducta igitur per
punctum M, ipſi OQ, vel NP, parallela RS, erit vt
NK, ad KP, ita RM, ad MS: & vt KM, ad ML, ita
NR, ad RO, & PS, ad SQ: ſed KM, eſt æqualis ML;
igitur & KR, ipſi RO, & PS, ipſi SQ, æqualis erit: ſunt
autem hæ ſegmenta axium NO, Pque punctum igitur
R, eſt centrum grauitatis priſmatis ABDEFH: & per

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