Newton's unpublished dynamical principles: A study in simplicity

Abstract

Summary Contrary to the received opinion, the fundamentals of Newton's dynamics can be set forth quite simply. In the first edition of the Principia, Newton employs a device (the linear dynamics ratio) that relates to Galileo's analysis of uniform rectilinear motion. In the second and third editions, Newton introduces an alternate device (the circular dynamics ratio) that relates to Huygens's analysis of uniform circular motion. A third device (the comparison dynamics ratio) is also introduced but is hidden away as a corollary to a problem rather than set forth clearly as a theorem. Following the appearance of the first edition, Newton proposed, but never published, a grand new scheme for revising his dynamics in which he clearly set forth each dynamics ratio with a complementary set of solutions to the problems. As published, however, the alternate methods are not clear and are a source more of confusion than of clarification.

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