Abstract
We are dealing with the mathematical and historical background of Hilbert's Third Problem. Max Dehn solved it immediately in the year 1900, when it was formulated.
Roots of this problem can be found in Elements of Euclid XII,5, where we can find proof of the two same height tetrahedra relation using the method of exhaustion. The question of the exhaustion method necessity led to the Hilbert's Third Problem formulation: to specify two tetrahedra of equal bases and equal altitudes which can in no way be split up into congruent tetrahedra.