I understand French. I looked through the document. I could not find any place where Coriolis derived kinetic energy. He was apparently using someone else's derivation.

By simple substitution, anyone can easily derive E = mv² from Newtonian equations. One starts with W = Fd = mad, and go from there. There is no need to integrate the difference in initial and final velocities (as is currently being done) because this is already assumed in the definition of acceleration. The 1/2 is a mistake and I stand by it.