Valerio, Luca - De centro gravitatis solidorvm libri tres

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1in axe DN, erit centrum grauitatis. Eadem ratione in
quolibet reliquorum trium axium, pyramidis ABCD, ip
ſius centrum grauitatis eſse oſtenderemus; communis igi
tur ſectio quatuor axium pyramidis ABCD, quod eſt
ipſius centrum E, erit centrum grauitatis pyramidis AB
CD. Quod demonſtrandum erat.

COROLLARIVM.

Hinc manifeſtum eſt centrum grauitatis pyra
midis triangulam baſim habentis eſſe in eopun
cto, in quo axis ſic diuiditur, vt pars quæ ad ver
icem ſit reliquæ tripla.

PROPOSITIO XXXII.

Ominis pyramidis baſim pluſquam trilate
ram habentis centrum grauitatis axim ita diui
dit, vt pars, quæ eſt ad verticem ſit tripla re
liquæ.

Sit pyramis ABCDE, cui vertex E, baſis autem
quadrilatera ABCD, & eſto axis EF, ſegmentum EM,
reliqui MF, triplum. Dico punctum M, eſſe centrum
grauitatis pyramidis ABCDE. Ducta enim AC, ſit
trianguli ABC, centrum grauitatis H, ſicut & K, trian
guli ACD: & iungantur KH, HE, EK: Factaque vt
EM, ad MF, ita EL ad LH, & EN ad NK, iun
gatur LN. Quoniam igitur EF eſt axis pyramidis
ABCDE, erit baſis ABCD centrum grauitatis F.

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