Axiom:Euclid's Common Notions

This is a set of axiomatic statements that appear at the start of Book I of 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 at a later date, perhaps by Apollonius of Perga, who made an attempt to prove them.