The Treatment of Cycloidal Pendulum Motion in Newton’s Principia

The discovery of the near isochrony of the simple pendulum offered the possibilityof measuring time intervals more accurately than had been possible before. However,the fact that it was not strictly isochronous for all amplitudes remained a problem. Thecycloidal pendulum provided this strict isochrony and, over a thirty year period from1659 the analysis of the motion of this pendulum was developed. Newton’s analysis inhis Principia was both elegant and comprehensive and his argument is illustratedin this paper. It provides insights into the revolutionary nature of Newton’s thinkingespecially compared to the Galilean approach to understanding the motion of the simplependulum found in early 18th century textbooks.