1GH) erit eiuſdem fruſti ABCDEF, centrum grauitatis
O. Rurſus quoniam vt tres deinceps proportionales BC,
EF, X, ſimul ad BC, ita eſt fruſtum ABCDEF, ad py
ramidem; ſi deſcribatur ABCH: ſed vt triangulum ABC,
ad ſimile triangulum EDF, hoc eſt vt BC, ad X, ita eſt
pyramis ABCH, ad pyramidem GDEF; erit ex æqua
li, vt tres lineæ
BC, EF, X, ſi
mul ad X, ita fru
ſtum ABCDEF,
ad pyramidem
GDEF: & con
uertendo, vt X,
ad compoſitam
ex BC, EF, X,
hoc eſt vt VO,
ad OS, ita pyra
mis GDEF, ad
fruſtum ABC
DEF; & diui
dendo, vt pyra
51[Figure 51]
mis GDEF, ad reliquas tres pyramides fruſti, ita OV,
ad VS; ſed S, eſt centrum grauitatis pyramidis GDEF,
& O, trium reliquarum; fruſti igitur ABCDEF, cen
trum grauitatis erit V. Quod demonſtrandum erat.
O. Rurſus quoniam vt tres deinceps proportionales BC,
EF, X, ſimul ad BC, ita eſt fruſtum ABCDEF, ad py
ramidem; ſi deſcribatur ABCH: ſed vt triangulum ABC,
ad ſimile triangulum EDF, hoc eſt vt BC, ad X, ita eſt
pyramis ABCH, ad pyramidem GDEF; erit ex æqua
li, vt tres lineæ
BC, EF, X, ſi
mul ad X, ita fru
ſtum ABCDEF,
ad pyramidem
GDEF: & con
uertendo, vt X,
ad compoſitam
ex BC, EF, X,
hoc eſt vt VO,
ad OS, ita pyra
mis GDEF, ad
fruſtum ABC
DEF; & diui
dendo, vt pyra
51[Figure 51]mis GDEF, ad reliquas tres pyramides fruſti, ita OV,
ad VS; ſed S, eſt centrum grauitatis pyramidis GDEF,
& O, trium reliquarum; fruſti igitur ABCDEF, cen
trum grauitatis erit V. Quod demonſtrandum erat.
PROPOSITIO XXXVI.
Omnis fruſti pyramidis baſim pluſquam trila
teram habentis centrum grauitatis eſt punctum
illud, in quo axis ſic diuiditur, vt axis fruſti pyra
midis triangulam baſim habentis diuiditur ab
ipſius centro grauitatis.
teram habentis centrum grauitatis eſt punctum
illud, in quo axis ſic diuiditur, vt axis fruſti pyra
midis triangulam baſim habentis diuiditur ab
ipſius centro grauitatis.
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