  In this note we investigate the problem of finding pairs of Pythagorean
triangles $(a, b, c), (A, B, C)$, with given catheti ratios $A/a, B/b$. In
particular, we prove that there are infinitely many essentially different
("non-similar") pairs of Pythagorean triangles $(a, b, c), (A, B, C)$
satisfying given proportions, provided that $Aa\neq Bb$.
