I have been reading DF Lawden's nice book on tensor calculus and relativity. I keep going back to first chapter (p 9-11) as I did not 100% get his derivation of the "special" Lorentz transformation. He writes about a rotational transformation in one plane and then writes about a translational transformation, and then out pops the Lorentz transforms. The math in each step is easy but I am missing the logic of his argument and have never seen the Lorentz transformation derived in this fashion. How does the rotation lead to equations of translation? What exactly is he doing here?