Some of Euclid’s axioms are stated as follows.
1. Things which are equal to the same thing are also equal to one another.
2. If equals be added to equals, then the wholes are equal.
3. If equals be subtracted from equals, then the remainders are equal.
4. Things which coincide with one another are equal to one another.
5. The whole is greater than the part.
6. Things which are double of the same things are equal to one another.
7. Things which are halves of the same things are equal to one another.