The calculus of variations is a key part of his geometry-free explanation of mechanics based on the function of kinetic and potential energy bearing his name.  
His early work on isoperimetrical problems impressed Euler and his theorem states that the order of a subgroup of a finite group is a factor of the group's order.  The calculus of variations is a key part of his geometry-free explanation of mechanics based on the function of kinetic and potential energy bearing his name.  For ten points, identify this French-Italian author of M?anique analytique.
His early work on isoperimetrical problems impressed Euler and his theorem states that the order of a subgroup of a finite group is a factor of the group's order.  
Joseph Louis Lagrange