Ladies' Diary/Dutchmen's Three Wives/Proof 2

Proof
It is immediate from the last condition that each man paid $63$ shillings more than his wife.

It is also immediate from the first condition that the amount paid for the hogs by each person is a square number.

So we are looking for pairs of square numbers which differ by $63$.

This leads us to the pairs:
 * $\tuple {1^2, 8^2}$, that is $\tuple {1, 64}$
 * $\tuple {9^2, 12^2}$, that is $\tuple {81, 144}$
 * $\tuple {31^2, 32^2}$, that is $\tuple {961, 1024}$

The relations between Hendrick and Catrin, and Claas and Geertrick, provide us with the information we need to match husband and wife for all three.