 Earnshaw clearly describes Cotes's 5 cases and unnecessarily adds a 6th, which is when the force is centrifugal (repulsive).As noted above, Cotes's included this with case 5.The mistaken view that there are only 3 Cotes's spirals appears to have originated with Whittaker's "A Treatise on the Analytical Dynamics of Particles and Rigid Bodies", first published in 1904.