PROPOSITIO XXIV.

Si duarum pyramidum triangul as bases haben
tium æqualium, & similium inter se, tria latera
tribus lateribus homologis fuerint in directum
constituta, in vertice communi erit vtriusque si
mul centrum grauitatis.

Sint duæ pyramides similes, & æquales, quarum ver
tex communis G, bases autem triangula ABC, DEF.
Et sint latera homologa pyramidum in directum inter se
constituta: vt AG, GF: & BG, GD, & CG, GE.
Dico compositi ex duabus pyramidibus ABCG, GDEF,
ita constitut is centrum gra
uitatis esse in puncto G.
Esto enim H, centrum gra
uitatis pyramidis ABCG,
& ducta HGK, ponatur
GK, æqualis GH, & iun
gantur EK, KD, BH,
CH. Quoniam igitur est
vt HG, ad GK, ita CG,
ad GE, & proportio est
æqualitatis: & angulus
HGC, æqualis angulo EG
K, erit triangulum CGH,

simile, & æquale triangulo EGK. Similiter triangulum
BGH, trian gulo DGK; & triangulum BGC, triangu
lo DGE: quare & triangulum BCH, triangulo DEK.
pyramis igitur BCGH, similis, & æqualis est pyramidi
EDGK. Congruentibus igitur inter se duobus triangu