  We prove two theorems which relate the Lie point symmetries and the Noether
symmetries of a dynamical system moving in a Riemannian space with the special
projective group and the homothetic group of the space respectively. The
theorems are applied to classify the two dimensional Newtonian dynamical
systems, which admit a Lie point/Noether symmetry. Two cases are considered,
the non-conservative and the conservative forces. The use of the results is
demonstrated for the Kepler - Ermakov system, which in general is
non-conservative and for potentials similar to the H\`enon Heiles potential.
Finally it is shown that in a FRW background with no matter present, the only
scalar cosmological model which is integrable is the one for which 3-space is
flat and the potential function of the scalar field is exponential. It is
important to note that in all applications the generators of the symmetry
vectors are found by reading the appropriate entry in the relevant tables.
