  Maxwell's electrodynamics postulates the finite propagation speed of
electromagnetic (EM) action and the notion of EM fields, but it only satisfies
the requirement of the covariance in Minkowski metric (Lorentz invariance).
Darwin's force law of moving charges, which originates from Maxwell's field
theory complies the Lorentz invariance as well. Poincar\'e's principle stating
that physical laws can be formulated with identical meaning on different
geometries suggest, that the retarded EM interaction of moving charges might be
covariant even in Euclidean geometry (Galilean invariance). Keeping the
propagation speed finite, but breaking with Maxwell's field theory in this
study an attempt is made to find a Galilean invariant force law. Through the
altering of the Li\'enard-Wiechert potential (LWP) a new retarded potential of
two moving charges, the Common Retarded Electric Potential (CREP) is introduced
which depends on the velocities of both interacting charges. The sought after
force law is determined by means of the second order approximation of CREP. The
law obtained is the Galilean invariant Weber's force law, surprisingly. Its
rediscovery from the second order approximation of a retarded electric
potential confirms the significance of Weber's force law and proves it to be a
retarded and approximative law. The fact that Weber's force law implies even
the magnetic forces tells us that magnetic phenomena are a manifestation of the
retarded electric interaction exclusively. The third order approximation of the
CREP opens the possibility of EM waves, and the creation of a complete,
Euclidean electrodynamics.
