Just how did Democrites arrive at the volume of the pyramid? (Q579226)

According to Archimedes Democritus has found the theorem that any pyramid is one-third of the prism having the same base and height, but only Eudoxus has proved it [\textit{E. J. Dijksterhuis}, Archimedes (Copenhagen 1956) p. 321; English translation Princeton, New Jersey: Princeton University Press (1987; Zbl 0646.01001)]. The author supposes that Euclid XII.7 (any prism which has a triangular base is divided into three pyramids equal to one another which have triangular bases) may indicate the heuristic way by which Democritus may have proceeded.