  In fact, there is a deep mistake in Newton's approach to resistance forces that came to be understood only at the beginning of the twentieth century. Resistance forces do not arise from independent contributions made by such factors as the viscosity and inertia of the fluid. Consequently, no polynomial consisting of a few always positive terms in powers of velocity can ever be adequate for resistance forces. The first indication of this came when d'Alembert, unhappy with Newton's ad hoc theory for the inertial contribution, analyzed the flow of what we now call a perfect fluid about spheres and bodies of other shapes, discovering in all cases that the net force of the fluid is exactly zero. Consequently, contrary to Newton, there is no such thing as the contribution made to resistance purely by the inertia of the fluid. Resistance forces always arise from a combination of viscous and inertial effects, however low the viscosity of the fluid may be. Newton's assumption that resistance forces can be represented as a sum, one term of which gives the contribution made purely by the inertia of the fluid, was wrong empirically, much as his assumptions about simultaneity and space being Euclidean turned out to be wrong. Unlike the latter assumptions, however, the assumption about resistance amounted to a dead end. All Newton achieved in Book 2 with resistance forces was merely a curve-fit.