  We perform a detailed analysis on the scaling properties of the total
$\gamma^*\mathrm{p}$ cross section, $\sigma_{\gamma^*\mathrm{p}}$. We write the
cross section as a product of two functions $W$ and $V$ representing,
respectively, the dynamical degrees of freedom and the contribution from the
valence partons. Analyzing data from HERA and fixed target experiments we find
that $V$ is nearly independent of $Q^2$ and concentrated at large $x$, while
$W$ carries all the information on the $Q^2$ evolution of $\gamma^*\mathrm{p}$.
We define the reduced cross section $\tilde{\sigma}_{\gamma^*\mathrm{p}} \equiv
W=\sigma_{\gamma^*\mathrm{p}}/V$, and show that it is very close to a
generalized homogeneous function. This property gives rise to geometric scaling
not only for small $x$, but for all the current measured kinematic plane. As a
consequence of our {\em Ansatz} we also obtain a compact parameterization of
$\sigma_{\gamma^*\mathrm{p}}$ describing all data above $Q^2=1$ GeV$^2$.
