Valerio, Luca - De centro gravitatis solidorvm libri tres

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PROPOSITIO XXXIII.

Omnis priſmatis triangulam baſim habentis
centrum grauitatis eſt in medio axis.

Sit priſma ABCDEF, cuius baſes oppoſitæ trian
gula ABC, DEF, axis autem GH, ſectus ſit bifariam
in puncto K. Dico punctum K, eſse priſinatis ABCD
EF, centrum grauitatis. Ducantur enim rectæ FGO,
CHP, PO. Quoniam igitur GH, eſt axis priſmatis
ABCDEF, erit punctum G, centrum grauitatis trian
guli DEF: ſicut & H, trian
guli ABC; vtraque igitur
dupla eſt AG, ipſius GO,
& CH, ipſius PH, ſectæ
que erunt AB, DE, bifa
riam in punctis P, O: pa
rallela igitur, & æqualis eſt
OP, ipſi DA, iamque ipſi
FC. quæ igitur illas con
iungunt CP, FO, æqua
les ſunt, & parallelæ, & pa
rallelogrammum FP.
Nunc ſecta OP, bifariam in
puncto N, iungantur GN,
NF, AF, FH, FB, & fa
cta FL, tripla ipſius LH,

48[Figure 48]
à puncto L, per punctum K, ducatur recta LKMR.
Quoniam igitur eſt vt FG, ad GO, ita CH, ad HP,
& parallelogrammum eſt FCPO; parallelogramma
etiam erunt CG, GP, angulus igitur FGH, æqualis
erit angulo NGO, quos circa æquales angulos latera

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