  Rotation curves of spiral galaxies are known with reasonable precision for a
large number of galaxies with similar morphologies. The data implies that
non-Keplerian fall--off is seen. This implies that (i) large amounts of dark
matter must exist at galactic scales or (ii) that Newtonian gravity must
somehow be corrected. We present a method for inverting the integral relation
between an elemental law of gravity (such as Newton's) and the gravitational
field generated by a thin disk distribution with exponential density. This
allows us to identify, directly from observations, {\it extensions} of
Newtonian gravity with the property of fitting a large class of rotation
curves. The modification is inferred from the observed rotation curve and is
finally written in terms of Newton's constant or the effective potential of a
test mass moving in the field generated by a point-like particle.
