What are Hilbert's axioms? - ProProfs Discuss

# What are Hilbert's axioms?

Asked by K. Tanaka, Last updated: Feb 24, 2020

#### John F. connor

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John F. connor, Content Marketing executive, MA, Minsk,Poland

David Hilbert published a book in 1899 about geometry. It is called The Foundations of Geometry. There are over twenty assumptions made by Hilbert. The three terms used in Hilbert’s axioms are the point, the line and the plane. There are also three primitive relations. These are called betweenness, congruence and lies on. There are five parts to Hilbert’s axioms. They are called the Incident, Order, Congruence, Parallels and Continuity.

Incidence is a set of rules about two points and the lines between them. Order refers to the rules or steps about point B being in between A and C. Congruence is the steps about two points, A and B, being on a line. Parallels refers to Euclid’s Axiom which is about a line and a point that is not on the line. Continuity is about the Axiom of Archimedes.

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