# Why is there a Lagrangian? [duplicate]

In all discussions regarding the Lagrangian formulation it has always been said that $$L = T - V$$, only is a correct guess that when operated via through the Euler -Lagrange equation yields something similar to the newtons law of motion. But if we are to consider yourselves at the position of Lagrange himself, how are we to guess the correct form of the Lagrangian, using physical arguments only. Even considering that nature is always trying to minimizing something, How do we say it is the action that it must, not something else?