Lagrange’s observation
After Newton, the Bernoulli family and Euler the next great contribution was made by Lagrange who stated that optimal motion is achieved if in any given moment the effect causing the motion and the motion itself is in equilibrium; that is the motion is lossless. Lagrange derived the differential equation of this condition, the equilibrium condition of change in time and space. From here it took only a step for Hamilton to generalise this fundamental rule and create the basic equation for all equilibrium processes which is not only valid in the directly observable and controllable world but also in the micro world of quantum phenomena.