Lotschnittaxiom

The Lotschnittaxiom (German for "axiom of the intersecting perpendiculars") is an axiom in the foundations of geometry, introduced and studied by Friedrich Bachmann. It states: Perpendiculars raised on each side of a right angle intersect. Bachmann showed that, in the absence of the Archimedean axiom, it is strictly weaker than the rectangle axiom, which states that there is a rectangle, which in turn is strictly weaker than the Parallel Postulate, as shown by Max Dehn. In the presence of the Archimedean axiom, the Lotschnittaxiom is equivalent with the Parallel Postulate. (Wikipedia).