# An introduction to Euclid - Axioms and Postulates

Index --- introduction --- definitions --- axioms and postulates --- propositions --- other

Euclid describes Axioms and Postulates, given below. The Postulates talk about straight lines, circles, right angles and parallel lines (these have been defined already, but here is more information about them). The Axioms are about relationships; what does equal mean, how do you add or subtract things, and so on. Remember that we are talking about lines and angles, not numbers, so adding and subtracting need to be thought about.

In modern mathematics, the first principles of any formal deductive system are 'axioms', so perhaps the Postulates, Axioms and Definitions should all be considered axioms.

Euclid's Axioms (or Common Notions)
Axiom 1 - Things which equal the same thing also equal one another.
Axiom 2 - If equals are added to equals, then the wholes are equal.
Axiom 3 - If equals are subtracted from equals, then the remainders are equal.
Axiom 4 - Things which coincide with one another equal one another.
Axiom 5 - The whole is greater than the part.