Let M and N be respectively a moment of {alpha} and a moment of {beta}.

In M there is the direction of {beta} and in N there is the direction of {alpha}.

But M and N, being moments of different time-systems, intersect in a level.

Call this level {lambda}.

Then {lambda} is an instantaneous plane in the instantaneous space of M and also in the instantaneous space of N.It is the locus of all the event-particles which lie both in M and in N.
In the instantaneous space of M the level {lambda} is perpendicular to the direction of {beta} in M, and in the instantaneous space of N the level {lambda} is perpendicular to the direction of {alpha} in N.This is the fundamental property which forms the definition of perpendicularity.