  The thrust of the argument in Section 9 is that fluid vortices are incompatible with Kepler's area and 3/2 power rules. The argument has two shortcomings, both of them recognized by Newton's opponents at the time. First, the entire argument is predicated on a hypothesis: “The resistance that arises from want of slipperiness of the parts of the fluid is, ceteris paribus, proportional to the velocity with which the parts of the fluid are separated from one another.” Fluids of this sort are now called “Newtonian.” The absence of evidence for the hypothesis left Newton's opponents free to adopt other rules for the velocity gradient in a vortex generated around a rotating cylinder or sphere, rules that could undercut his conclusions. Second, his analysis of the vortex generated around a rotating cylinder or sphere involves fundamentally wrong physics: it defines steady state in terms of a balance of forces instead of torques across each shell element comprising the vortex. To use Johann Bernoulli's words from 1730, Newton “completely neglects to take into account the action of the lever, the consideration of which however is absolutely necessary here, it being obvious that the same force, applied along the tangent to the circumference of a large wheel, has a greater efficacity for making it turn than it has when applied to the circumference of a smaller  radius.”[38] (This is not the only place in the Principia where it is clear that Newton had not thought through the mechanics of angular motion.)