  A thermodynamic approach to derive the liquid-glass transition line in the
reduced temperature vs reduced density plane for a monatomic Lennard-Jones
fluid is presented. The approach makes use of a recent reformulation of the
classical perturbation theory of liquids [M. Robles and M. L\'opez de Haro,
Phys. Chem. Chem. Phys. {\bf 3}, 5528 (2001)] which is at grips with a rational
function approximation for the Laplace transform of the radial distribution
function of the hard-sphere fluid. The only input required is an equation of
state for the hard-sphere system. Within the Mansoori-Canfield/Rasaiah-Stell
variational perturbation theory, two choices for such an equation of state,
leading to a glass transition for the hard-sphere fluid, are considered. Good
agreement with the liquid-glass transition line derived from recent molecular
dynamic simulations [Di Leonardo et al., Phys. Rev. Lett. {\bf 84}, 6054(2000)]
is obtained.
