The Mathematical Principles of Natural Philosophy

C. R. Leedham-Green is an Emeritus Professor of Pure Mathematics at Queen Mary, University of London. He is an algebraist, working mainly in group theory, and most of his publications concern p-groups, pro-p-groups, and computation in matrix groups defined over finite fields. He is a joint author, together with Susan McKay, of The Structure of Groups of Prime Power Order (2002).

• Definitions; The Axioms, or the Laws of Motion; On the Motion of Bodies, Book One: I.1. On the theory of limits, which is used to deduce later results; I.2. On the calculation of centripetal forces; I.3. On the motion of particles in eccentric conic sections; I.4. On the calculation of elliptical, parabolic, and hyperbolic orbits; I.5. On the calculation of orbits when neither focus is given; I.6. On the calculation of motion in given orbits; I.7. On the ascent and descent of particles in a straight line; I.8. On the calculation of the orbits in which particles revolve under any centripetal forces; I.9. On the motion of particles in moving orbits, and the motion of the apsides; I.10. On the motion of particles on given surfaces, and the swinging motion of a string pendulum; I.11. On the motion of particles attracting each other by centripetal forces; I.12. On the attractive forces of spherical bodies; I.13. On the attractive forces of non-spherical bodies; I.14. On the motion of particles attracted by centripetal forces towards the various parts of arbitrarily large bodies; On the Motion of Bodies, Book Two: II.1. On the motion of particles moving against a resistance that is proportional to the speed; II.2. On the motion of bodies moving against a resistance that is proportional to the square of the speed; III.3. On the motion of bodies to which the resistance consists of one part that is proportional to the speed, and another to the square of the speed; II.4. On the circular motion of bodies in resisting media; II.5. On the density and compression of fluids, and on hydrostatics; II.6. On the motion and resistance of string pendulums; II.7. On the motion of fluids and the resistance of projectiles; II.8. On motion propagated through fluids; II.9. On the circular motion of fluids; On Celestial Mechanics, Book Three: Introduction to Book Three; The Rules of Scientific Argument; Phenomena; Propositions; On the motion of the nodes of the moon; General Scholium; A. Mathematical notation and results assumed in The Principia; B. Calculus in The Principia; C. Newton's astronomy; D. Newton's theory of tides; E. Technical terms used in the translation; F. On Newton's style, and translating The Principia; G. Some difficult words; H. Astrological symbols; I. Glossary of Latin terms; J. Technological illustrations; References; Index.