A statement, also known as an axiom, which is taken to be true without proof. Postulates are the basic structure from which lemmas and theorems are derived. The whole of Euclidean geometry, for example, is based on five postulates known as Euclid's postulates.

Archimedes' axiom | axiom | Bertrand's postulate | conjecture | equidistance postulate | Euclid's postulates | lemma | parallel postulate | porism | proof | theorem | triangle postulate