D   Lorentz Transformations, Velocity Addition and Doppler Effect

We examine the transformation of coordinates between different inertial frames in the mechanics of Galileo and Newton and deduce the old formula for the addition of velocities. Then we do the same considering the 3 fundamental effects of STR. We deduce the so-called Lorentz transformations twice: First with assistance of Epstein diagrams and a second time only using the formulas from section B. From the Lorentz transformations we obtain the relativistic formula for the addition of velocities. Finally we deduce the optical Doppler formula.