If a rational and a medial area be added together, four irrational straight lines arise, namely either a binomial, a first bimedial, a major, or a side of a rational plus a medial area.
Proof
The square of any of the four classes (X.36, X.37, X.39, X.40) is
the sum of a rational and a medial; conversely, every such sum
arises in exactly one of these forms.