(related to Subsection: Common Notions (all Books))
And the whole [is] greater than the part.
The cardinality of a set is greater than the cardinality of its subset.
Today we know that this modern formulation is not true! It holds only for finite sets. In the time of Euclid, mathematicians and philosophers had only a vivid concept of "the whole" and "its part" which is totally different from contemporary set-theoretical concepts. ↩