The earliest I have seen is in "Untersuchungen =FCber die Theorie des   
Preises" by Rudolf Auspitz and Richard Lieben, 1889, Leipzig: Verlag   
von Duncker und Humblot.  
  
The quasilinear function appears several times, on pp. 471, 474, and   
477; see section 2 of appendix II.  For that part of their exposition,   
Auspitz and Lieben spelled out formally what would ensure a constant   
marginal utility of money.  
  
Their use of that function is a little different from later uses   
because the "linear good" in their function represented end-of-period   
money balances, i.e. the amount of money carried forward into the next   
period.  There is then no need to restrict the amount of the "linear   
good" to be nonnegative.  Also, there is actually a rationale for the   
separate treatment of one of the "goods," and it begins to resemble the   
discounted utility model.  But because the purchasing power in the next   
period of the remaining funds depends on next-period prices, they   
placed anticipated next-period prices into the utility function as well.  
  
In all, their quasilinear function is clearly a more complex entity   
than that which appears in today's textbooks.  But, if one reinterprets   
the linear good as just one more good consumed in the present,   
next-period prices no longer play a role, and the Auspitz-Lieben   
function looks the same as the modern version.  
  
Torsten Schmidt