Definition:Euler-Lagrange Equation/Historical Note

Historical Note on Euler-Lagrange Equation
The Euler-Lagrange equation was developed in the $1750$s by and  in connection with their studies of the Tautochrone Problem.

solved it in $1755$ and sent the solution to.

They further developed 's method and applied it to mechanics.

This led to the formulation of Lagrangian mechanics.

Their correspondence ultimately led to the calculus of variations.