In 1905 Albert Einstein made use of the non-Galilean character of Maxwell's equations to develop his theory of special relativity. The special property embedded in Maxwell's equations is known as the Lorentz invariance. In Maxwell's equations frame, assuming that the speed of moving charges is small compared to the speed of light, it is possible to derive approximations that fulfill Galilean invariance. This approach enables the rigorous definition of two main mutually exclusive limits known as quasi- electrostatics (electrostatics with displacement currents or ohmic currents) and quasi- magnetostatics (magnetostatics with electric field caused by variation of magnetic field according to Faraday's law, or by ohmic currents). Quasi-static approximations are often poorly introduced in literature as stated for instance in Hermann A. Hauss and James R. Melcher's book. They are often presented as a single one whereas Galilean electromagnetism shows that the two regimes are in general mutually exclusive. According to Germain Rousseaux, the existence of these two exclusive limits explains why electromagnetism has long been thought to be incompatible with Galilean transformations. However Galilean transformations applying in both cases (magnetic limit and electric limit) were known by engineers before the topic was discussed by Jean-Marc Lévy-Leblond. These transformations are found in H. H. Woodson and Melcher's 1968 book.