  Given a non-oscillating gradient trajectory G of a real analytic function f,
we show that the limit v of the secants at the limit point O of G along the
trajectory G is an eigen-vector of the limit of the direction of the Hessian
matrix Hess (f) at O along G. The same holds true at infinity if the function
is globally subanalytic. We also deduce some interesting estimates along the
trajectory.
