(geometry) A statement in plane geometry, used implicitly by Euclid, which cannot be derived from Euclid's postulates. It states that, if a line, not passing through any vertex of a triangle, meets one side of the triangle then it meets another side.

(physics) Any of a number of axioms representing an attempt at a mathematically rigorous formulation of quantum field theory.

(mathematics) Any of a set of fundamental axioms describing the natural numbers and their relationships.

Synonym of non-aggression principle

(set theory) The axiom that the power set of any set exists and is a valid set, which appears in the standard axiomatisation of set theory, ZFC.

(set theory) A weaker form of the axiom of choice that states that every countable collection of nonempty sets must have a choice function; equivalently, the statement that the direct product of a countable collection of nonempty sets is nonempty.