Euclid's axioms:
i) Things which are equal to the same thing are equal to one another.
ii) If equals are added to equals, the wholes are equals.
iii) If equals are subtracted from equals, the remainders are equal.
iv) Things which coincide with one another are equal to one another.
v) The whole is greater than a part.
vi) Things which are double of the same thing are equal to one another.
vii) Things which are halves of the same thing are equal to one another.