Composition of velocities

The Galilean sum of velocities $\vec{v}_{AC} = \vec{v}_{AB} + \vec{v}_{BC}$ stops working when the velocities involved approach that of light: two summed velocities must stay below $c$, something Galileo does not guarantee at all. This section derives the correct law with the same ingredient used for the Doppler effect — a scientist firing light signals and reasoning event by event — and shows a graphical trick for never getting the signs wrong.

• Relativistic composition of velocities
• The triangle trick