3. When equals are taken from equals the remainders are equal.
4. When equals are added to unequals the wholes are unequal.
5. When equals are taken from unequals the remainders are unequal.
6. Things which are double of the same thing, or equal things, are equal to each other.
7. Things which are halves of the same thing, or of equal things, are equal to each other.
8. The whole is greater than any of its parts.
9. Every whole is equal to all its parts taken together.
10. Things which coincide, or fill the same space, are identical, or mutually equal in all their parts.
11. All right angles are equal to one another.
12. A straight line is the shortest distance between two points.