Let $f$ be a definable $C^1$ function defined in a neighborhood of the origin in $R^n$. Using Lagrange specialization and the deformation to the normal cone we describe geometrically the space of limits at the origin of secant lines and gradient directions of $f$, understood as a subset of $P^{n-1} \times P^{n-1}$.

We apply this description to study the gradient flow of $f$.