 In the "Harmonia Mensurarum" (1722), Roger Cotes analysed a number of spirals and other curves, such as the "Lituus".He described the possible trajectories of a particle in an inverse-cube central force field, which are the Cotes's spirals.The analysis is based on the method in the Principia Book 1, Proposition 42, where the path of a body is determined under an arbitrary central force, initial speed, and direction.