  I argue that in the Lagrangian formulation of standard, Galilei-invariant
Newtonian mechanics there are subtle but concrete signs of {\em Lorentz}
invariance. In fact, in a specific sense made explicit in the paper, Newtonian
mechanics is more Lorentz-invariant than Galilei-invariant. So, special
relativity could have been discovered deductively, before there were any
indications---such as Maxwell's equations---that Galilei relativity had to be
modified. To make this anti-historical exercise less academic, I derive certain
velocity-dependent corrections to long-range interactions between spinless
point particles. Such corrections are universal; in particular, they do not
depend on the spin of the field mediating such interactions or on how strongly
coupled such a field is. I discuss potential applications to the post-Newtonian
expansion of general relativity.
