"Let the mass of the projectile be M, and let its speed be v while being moved over an infinitesimal distance ds. The body will have a momentum Mv that, when multiplied by the distance ds, will give , the momentum of the body integrated over the distance ds. Now I assert that the curve thus described by the body to be the curve (from among all other curves connecting the same endpoints) that minimizes\int Mv\,dsor, provided that M is constant along the path,M\int v\,ds."
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Leonhard Euler, Methodus Inveniendi Lineas Curvas Maximi Minive Proprietate Gaudentes (1744) Additamentum 2
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Principle of least action
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