Axiom:Euclid's Common Notions

This is a set of axiomatic statements that appear at the start of Book I of The Elements by Euclid.

1. Things which are equal to the same thing are also equal to each other.
2. If equals are added to equals, the wholes are equal.
3. If equals are subtracted from equals, the remainders are equal.
4. Things which coincide with one another are equal to one another.
5. The whole is greater than the part.

It has been suggested by Paul Tannery that these may not have been originated by Euclid, but may have been incorporated into The Elements at a later date, perhaps by Apollonius of Perga, who made an attempt to prove them.