The book is the Serway / Moses / Moyer Modern Physics 3rd edition. He got back to me with the following:
"The Lorenz-Transformation is based on c2t2-x2 -y2 -z2 =c2t'2-x'2 -y'2 -z'2 (A) where (x,y,z,t) and (x',y',z',t') are coordinates of a light signal (photon) with speeds ux = ux' = c in...