The original question was, "Who was the first to use the term 
"indifference" in economics, where?" 
 
For me, this thread is deja vu all over again because after reading the 
suggested answers, I see the issue is much more complicated than it first 
appears. 
 
I first read the question as "indifference curve" which makes me agree with 
the conventional answer that would credit Edgeworth.  I took a quick look 
at Mathematical Psychics and, sure enough, he means indifference as "equal 
satisfaction" and lays out the equimarginal condition for the contract 
curve.  But he refers to Jevons quite a bit. 
 
In his 1871 Theory of Political Economy, Jevons has an entire section 
titled, "The Law of Indifference."  "Then," you might conclude, "Jevons, 
1871, beats Edgeworth, 1881."  Not so fast.  Here's what Jevons says in 
that section: 
 
"When a commodity is perfectly uniform or homogeneous in quality, any 
portion may be indifferently used in place of an equal portion: hence, in 
the same market, and at the same moment, all portions must be exchanged at 
the same ratio.  There can be no reason why a person should treat exactly 
similar things differently, and the slightest excess in what is demanded 
for one over the other will cause him to take the latter instead of the 
former." 
 
Now, to a modern microeconomist, Jevons is talking about perfect 
substitutes, not indifference curves.  Indifference to Jevons sounds to me 
like another application of Buridan's ass (thanks to Thomas Moser for that 
tidbit of knowledge) and has little to do with the modern concept of 
"trade-off that maintains equal satisfaction." 
 
It seems clear that Edgeworth took a word that had a known meaning and 
adapted it to a more narrow definition.  This happens all the time.  It 
also makes determining the first use pretty difficult.  Given Edgeworth's 
penchant for inventing words, it's too bad he didn't invent one for his 
mathematical concept of variation in X and Y that maintains the same 
utility.  "Isoutility" seems an obvious name.   
 
My answer to the original question would be, "It depends.  Do you mean 
indifference in a general sense or do you mean indifference in the sense of 
a contour line or level curve?" 
 
Humberto Barreto