Why do we use $\varepsilon$ and $\delta$? My understanding (from a talk by Rob Bradley) is that Cauchy is responsible for
the now-standard $\varepsilon{-}\delta$ formulation of calculus, introduced in his
1821 Cours d’analyse.  Although perhaps instead it was introduced by Bolzano a few years
earlier.  My question is not about who was first with this notation, but
rather:

Why were the symbols $\varepsilon$ and $\delta$ used?

Why not, say, $\alpha$ and $\beta$?
(Imagine how different our mathematical discourse would be...)
Are there appropriate (French) words beginning with 'e' and/or 'd' that determined the choice?
Or perhaps Cauchy used up $\alpha,\beta,\gamma$ for other purposes prior to introducing $\delta,\varepsilon$?  Does anyone know?
 A: Thanks to H. M. Šiljak for finding the 1983 Amer. Math. Monthly
paper by Judith Grabiner, which I feel settles the question (at least for $\epsilon$).
Here is a longer quote encompassing that which H.M. excerpted:

Mathematicians are used to taking the rigorous foundations of the calculus as a 
  completed whole. What I have tried to do as a historian is to reveal what went into 
  making up that great achievement. This needs to be done, because completed wholes by 
  their nature do not reveal the separate strands that go into weaving them—especially 
  when the strands have been considerably transformed. In Cauchy's work, though, one 
  trace indeed was left of the origin of rigorous calculus in approximations—the letter 
  epsilon. The $\epsilon$ corresponds to the initial letter in the word "erreur" (or "error"), and 
  Cauchy in fact used $\epsilon$ for "error" in some of his work on probability [31]. It is both 
  amusing and historically appropriate that the "$\epsilon$," once used to designate the "error" in 
  approximations, has become transformed into the characteristic symbol of precision 
  and rigor in the calculus. As Cauchy transformed the algebra of inequalities from a tool 
  of approximation to a tool of rigor, so he transformed the calculus from a powerful 
  method of generating results to the rigorous subject we know today.
[31] Cauchy, Sur la plus grande erreur à craindre dans un résultat moyen, et sur le 
  système de facteurs qui rend cette plus grande erreur un minimum, Comptes rendus 
  37, 1853; in Oeuvres, series 1, vol. 12, pp. 114–124. 


A further finding by H. M. Šiljak (linked in a comment above), 
verifying that Cauchy did indeed use both $\epsilon$ and $\delta$:

         

      
