Galilean velocity addition (${\mathbf{v}}_{AC}={\mathbf{v}}_{AB}+{\mathbf{v}}_{BC}$)

With parallel inertial axes and absolute time, differentiating a Galilean transformation adds relative velocities as ordinary vectors. This is the low-speed limit of relativistic velocity addition. At speeds comparable with the speed of light, absolute time is no longer the appropriate frame transformation, and the relativistic denominator cannot be neglected.