  We consider the homothetic motion group. We construct a homothetic covariant
Newtonian gravitation theory which unifies inertial homothetic forces and
gravitational fields. This is achieved through an equivalence principle based
on a local homothetic frame of motion. As a consequence, we can obtain a
coherent Newtonian cosmology which admits a cosmological principle and leads to
the Friedman equations for a dust universe. Finally we prove that this gravity
theory can be obtained as the non-relativistic limit of a class of metrics in
General Relativity. The Friedmann-Lema\^\i tre-Robertson-Walker (FLRW) metric
and its limit are also studied.
