Everyone here has already made up his mind.

Seriously, Counting came before Arithmetic. Arithmetic is a set of formal rules and procedures that systematize and extend Counting. For example, even the most primitive tribal culture needs to count things, even add and subtract. More advanced Arithmetic, like multiplication, division and fractions, comes later. 5+7 = 7+5 = 12.
From there on you progress to:

Algebra: the application of arithmetic to abstract, general numbers (as opposed to actual numbers). a+b = b+a = c. In Algebra you don't deal with numbers, you deal with symbols which can be ANY number.

Real Analysis: (Which includes calculus and differential equations) which studies the behavior and changes of algebraic statements.

Complex analysis: Which introduces the tool of imaginary numbers to help make sense of real analysis.

And of course, there are things like Geometry, the study of space itself and of relationships within it, which doesn't seem to easily fit in with the earlier progression. Logic plays a big role in Geometry, so my guess is it came first, but I don't really know for sure.

Its only fair to warn you, I didn't learn or read this anywhere, its only my opinion. I have a book called "An Introduction to the History of Mathematics" on my bookshelf, but I must confess I've never read it.