Historical reason for calling $\nabla\cdot F$ divergence? Consider the continuously differentiable vector field in ${\mathbb R}^3$:
$$
F:{\mathbb R}^3\to{\mathbb R}^3,\qquad F(x,y,z)=(U,V,W)
$$
where 
$$
U,V,W:{\mathbb R}^3\to{\mathbb R}.
$$
According to the wikipedia article for divergence, the divergence of the vector field $F$ at the point $p\in {\mathbb R}^3$ is defined as
$$
\text{div} F(p):=\lim_{V\to\{p\}}\iint\limits_{S(V)}\frac{F\cdot n}{|V|}dS.
$$
This formula is of much clearer meaning in physics. Here is my question:

Is it because the divergence theorem that people call $\nabla \cdot F$ divergence? Or is there any direct calculation in physics that leads to the quantity $\nabla\cdot F$?


Look up "Divergence" at http://jeff560.tripod.com/d.html
