Suppose $f , g , h$ are functions from the set of positive real numbers into itself satisfying $f ( x ) g ( y ) = h \left( \sqrt { x ^ { 2 } + y ^ { 2 } } \right)$ for all $x , y \in ( 0 , \infty )$. Show that the three functions $f ( x ) / g ( x ) , g ( x ) / h ( x )$, and $h ( x ) / f ( x )$ are all constant.