I do not get what Landau wants to do in the final remarks of his Theorem 182. He says something about a third case and divides the problem in subcases, but this tell me nothing. Because I can not post pictures, the statement and the proof from the book are in this link and this.
Here is used this definition of addition. Note that the case for two positives is not included because this definition is an extension for the addition of positive cuts.
