Valerio, Luca - De centro gravitatis solidorvm libri tres

Valerio, Luca, De centro gravitatis solidorvm libri tres

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1

Si parallelepipedum AB, cuius axis CD, ſectum in
duo parallelepipeda AE, EN, quare & axis CD, in
axes CL, LD, parallelepipedorum AE, EN. Et ſint
centra grauitatis; F, parallelepipedi EN, & G, paral
lelepipedi AE, & H, parallelepipedi AB, in medio cu
iuſque axis ex antecedenti. Dico eſse FH, ad HG,
vt parallelepipedum AE, ad EN, parallelepipedum.
Iungantur enim diametri baſium oppoſitarum, quæ per
puncta axium D, L, G, tranſibunt, ADM, KLE,
NCB; iamque parallelogramma
erunt AB, AE, EN, DB, DE,
EC, propter eas, quæ parallelas
iungunt, & æquales: quorum bi
na latera oppoſita ſecta erunt bi
fariam in punctis C, L, D, per
definitionem axis: punctum igitur
F, in medio rectæ CL, oppoſi
torum laterum bipartitorum ſectio
nes coniungentis, erit parallelo
grammi EN, centrum grauitatis.
Eadem ratione & parallelogram

38[Figure 38]
mi AE, centrum grauitatis erit G, & H, parallelogram
mi AB. Vt igitur parallelogrammum AE, ad paralle
logrammum EN, hoc eſt, vt baſis ME, ad baſim EB;
hoc eſt, vt parallelogrammum MO, ad parallelogram
mum OB: hoc eſt, vt parallelepipedum AE, ad paral
lelepipedum EN: ita erit FH, ad HG. Quod de
monſtrandum erat.

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