Valerio, Luca - De centro gravitatis solidorvm libri tres

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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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