Question about one of the axioms of connection from Hilbert's The Foundations of Geometry

34 Views Asked by At

The axiom is on page 3 and is as follows: If two planes α, β have a point A in common, then they have at least a second point B in common

Then on the same page a theorem is deduced and is as follows: Theorem 1. Two straight lines of a plane have either one point or no point in common; two planes have no point in common or a straight line in common; a plane and a straight line not lying in it have no point or one point in common.

How can these statements be both true?