Valerio, Luca, De centro gravitatis solidorvm libri tres

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1
PROPOSITIO XIII.
Cuilibet figuræ ſolidæ parallelepipedum æqua­
le poteſt eſſe.
Sit quælibet figura ſolida A. Dico ſolido A, parallele­
pipedum æquale poſse exiſtere. Exponatur enim paral­
lelepipedum BC, cuius baſis BG. Quoniam igitur eſt vt
ſolidum BC, ad ſolidum A, ita recta linea, ſiue latus BD,
ad aliam rectam lineam; producto latere BD, ſit vt BC,
ad A, ita recta BD, ad rectam DE, & compleatur pa­
rallelepipedum CE. Quoniam itaque eſt vt BD, ad DE,
ita parallelogrammum ſiue baſis BG, ad parallelogram­
20[Figure 20]
mum, ſiue baſim EG; hoc eſt parallelepipedum BC, ad
parallelepipedum CE: ſed vt BD, ad DE, ita eſt paral­
lelepipedum BC, ad ſolidum A; vt igitur parallelepipe­
dum BC, ad ſolidum A, ita erit parallelepipedum BC,
ad parallelepipedum CE; parallelepipedum igitur CE
æquale erit ſolido A. Quod fieri poſse propoſuimus.

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