"The" continuity axiom is an additional Axiom which must be added to those of Euclid's Elements
in order to guarantee that two equal circles of radiusintersect
each other if the separation of their centers is less than (Dunham 1990). The continuity axioms are the three
of Hilbert's axioms which concern geometric equivalence.
Archimedes' Axiom is sometimes also known as
"the continuity axiom."
intersect
each other if the separation of their centers is less than 
(Dunham 1990). The continuity axioms are the three
of Hilbert's axioms which concern geometric equivalence.
