On the role of virtual work in Levi-Civita’s parallel transport

The current literature on history of science reports that Levi-Civita’s parallel transport was motivated by his attempt to provide the covariant derivative of absolute differential calculus with a geometrical interpretation.1 Levi-Civita’s memoir on the subject was explicitly aimed at simplifying the geometrical computation of the curvature of a Riemannian manifold. In the present paper we wish to point out the possible role implicitly played by the principle of virtual work in Levi-Civita’s conceptual reasoning to formulate parallel transport.