# Did Hooke's law come from experiments, or was it mathematically derived from Newtonian mechanics?

Was Hooke's law first coming from experiment or from math derivation of which Newtonian mechanical laws are the only prerequisite? Also can the law itself be reinvented in this way, or is it impossible to derive it mathematically from Newton's fundamental laws?

I want to know if Hooke's law is an axiom or a theorem, even though it was called a law...

• The second part of the question is really about physics, not the history of physics. Once you have Newton's laws and calculus available (which, as Conifold points out, was later), Hooke's law is derivable under the assumption that the force F is a well-behaved function of the position x. Without loss of generality, suppose we define the coordinate x such that the equilibrium position is x=0. Then we have F(0)=0. If F is analytic at 0, then near 0 it converges to its Taylor series, so F(x)=-kx+..., where the minus sign is if k>0 and the equilibrium is stable. – Ben Crowell Aug 23 '15 at 14:28