Valerio, Luca - De centro gravitatis solidorvm libri tres

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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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