ABSTRACT
In a special dissertation, Bernard Bolzano tries Drei Dimensionen (DD) to prove that physical space is tridimensional. The proof is difficult to analyse or to follow or to accept at times, but one merit stands out clearly. Although force is defined in metaphysical terms (ZK, §17), Bolzano touches incidentally on theorems of dynamics and statics. Using his principle of similarity, that similar determinants entail similar determinands, he undertakes to prove the inertial rectilinearity of free movement: for the path of such a movement must have certain properties, the straight line has them, and no other line has them. After long explorations, during which a function only known to be continuous is unfortunately assumed differentiable (ZK, §52), Bolzano satisfies himself, not only of the obvious fact that f(x1,x2,x3,…xn)=x1+x2+x3+…+xn is a solution, but also that no other solution exists.
