Page "Hilbert's axioms" Paragraph 25

# If A, B are two points on a straight line a, and if A ′ is a point upon the same or another straight line a ′, then, upon a given side of A ′ on the straight line a ′, we can always find one and only one point B ′ so that the segment AB ( or BA ) is congruent to the segment A ′ B ′.

We indicate this relation by writing AB ≅ A ′ B ′.

Every segment is congruent to itself ; that is, we always have AB ≅ AB. We can state the above axiom briefly by saying that every segment can be laid off upon a given side of a given point of a given straight line in one and only one way.