The basic facts which are taken for granted without proof are called axioms.

Some Euclid's axioms are:

1. The things which are equal to the same thing are equal to one another.

2. If equals be added to the equals, the wholes are equal.

3. If equals be subtracted from equals, the remainders are equals.

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 thing are equal to one another.

7. Things which are halves of the same thing are equal to one another