This volume of the definitive series on Newton's mathematical papers focuses on the period leading up to the publication of *Principia* in 1687. Dr. Whiteside compiles significant mathematical extracts from Newton's manuscripts, particularly those related to the theory of moving bodies and gravitation. The volume highlights Newton's work on the dynamical theory of motion under central forces and his attempts to explain comet and lunar motions. It includes a Latin tract on orbital motion, translated into English, which covers Kepler's laws and the elliptical orbit. The tract was a response to a question posed by Christopher Wren and Edmund Halley, which reignited Newton's interest in the general dynamical theory. The volume also features manuscripts on specific problems, such as the solid of least resistance and the annual advance of the lunar apogee. The final section includes extracts from Newton's plan to revise *Principia* in the early 1690s. The volume maintains the high standards of annotation and printing set by previous volumes.This volume of the definitive series on Newton's mathematical papers focuses on the period leading up to the publication of *Principia* in 1687. Dr. Whiteside compiles significant mathematical extracts from Newton's manuscripts, particularly those related to the theory of moving bodies and gravitation. The volume highlights Newton's work on the dynamical theory of motion under central forces and his attempts to explain comet and lunar motions. It includes a Latin tract on orbital motion, translated into English, which covers Kepler's laws and the elliptical orbit. The tract was a response to a question posed by Christopher Wren and Edmund Halley, which reignited Newton's interest in the general dynamical theory. The volume also features manuscripts on specific problems, such as the solid of least resistance and the annual advance of the lunar apogee. The final section includes extracts from Newton's plan to revise *Principia* in the early 1690s. The volume maintains the high standards of annotation and printing set by previous volumes.