We show that the issue of the drag exerted by an incompressible fluid on a body in uniform motion has played a major role in the early development of fluid dynamics. In 1745 Euler came close, technically, to proving the vanishing of the drag for a body of arbitrary shape; for this he exploited and significantly extended existing ideas on decomposing the flow into thin fillets; he did not however have a correct picture of the global structure of the flow around a body. Borda in 1766 showed that the principle of live forces implied the vanishing of the drag and should thus be inapplicable to the problem. After having at first refused the possibility of a vanishing drag, d'Alembert in 1768 established the paradox, but only for bodies with a head-tail symmetry. A full understanding of the paradox, as due to the neglect of viscous forces, had to wait until the work of Saint-Venant in 1846. * Electronic address: gerard.emile@terra.com.br 1 Kelvin's name of an incompressible inviscid fluid.

The present paper is a companion to the paper by Villone and Rampf (2017), titled "Hermann Hankel's On the general theory of motion of fluids, an essay including an English translation of the complete Preisschrift from 1861" together with connected documents. Here we give a critical assessment of Hankel's work, which covers many important aspects of fluid dynamics considered from a Lagrangian-coordinates point of view: variational formulation in the spirit of Hamilton for elastic (barotropic) fluids, transport (we would now say Lie transport) of vorticity, the Lagrangian significance of Clebsch variables, etc. Hankel's work is also put in the perspective of previous and future work. Hence, the action spans about two centuries: from Lagrange's 1760-1761 Turin paper on variational approaches to mechanics and fluid mechanics problems to Arnold's 1966 founding paper on the geometrical/variational formulation of incompressible flow. The 22-year old Hankel -who was to die 12 years later -emerges as a highly innovative master of mathematical fluid dynamics, fully deserving Riemann's assessment that his Preisschrift contains "all manner of good things."

The present paper is a companion of two translated articles by Alfred Clebsch, titled "On a general transformation of the hydrodynamical equations" and "On the integration of the hydrodynamical equations". The originals were published in the Journal für die reine and angewandte Mathematik" (1857 and 1859). Here we provide a detailed critical reading of these articles, which analyzes methods, and results of Clebsch. In the first place, we try to elucidate the algebraic calculus used by Clebsch in several parts of the two articles that we believe to be the most significant ones. We also provide some proofs that Clebsch did not find necessary to explain, in particular concerning the variational principles stated in his two articles and the use of the method of Jacobi's Last Multiplier. When possible, we reformulate the original expressions by Clebsch in the language of vector analysis, which should be more familiar to the reader. The connections of the results and methods by Clebsch with his scientific context, in particular with the works of Carl Jacobi, are briefly discussed. We emphasize how the representations of the velocity vector field conceived by Clebsch in his two articles, allow for a variational formulation of hydrodynamics equations in the steady and unsteady case. In particular, we stress that what is nowadays known as the "Clebsch variables", permit to give a canonical Hamiltonian formulation of the equations of fluid mechanics. We also list a number of further developments of the theory initiated by Clebsch, which had an impact on presently active areas of research, within such fields as hydrodynamics and plasma physics.