The Mathematical Principles of Natural Philosophy
An Annotated Translation of Newton's Principia

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Language: Anglais
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800 p. · Hardback
Newton's Principia is perhaps the second most famous work of mathematics, after Euclid's Elements. Originally published in 1687, it gave the first systematic account of the fundamental concepts of dynamics, as well as three beautiful derivations of Newton's law of gravitation from Kepler's laws of planetary motion. As a book of great insight and ingenuity, it has raised our understanding of the power of mathematics more than any other work. This heavily annotated translation of the third and final edition (1726) of the Principia will enable any reader with a good understanding of elementary mathematics to grasp easily the meaning of the text, either from the translation itself or from the notes, and to appreciate some of its significance. All forward references are given to illuminate the structure and unity of the whole, and to clarify the parts. The mathematical prerequisites for understanding Newton's arguments are given in a brief appendix.
Definitions; The Axioms, or the Laws of Motion; Book One. On the Motion of Bodies: Section 1. On the theory of limits; Section 2. On the calculation of centripetal forces; Section 3. On the motion of particles in eccentric conic sections; Section 4. On the calculation of elliptical, parabolic, and hyperbolic orbits with a given focus; Section 5. On the calculation of orbits when neither focus is given; Section 6. On the calculation of motion in given orbits; Section 7. On the ascent and descent of particles in a straight line; Section 8. On the calculation of the orbits in which particles revolve under any centripetal forces; Section 9. On the motion of particles in moving orbits, and the motion of the apsides; Section 10. On the motion of particles on given surfaces, and the swinging motion of a string pendulum; Section 11. On the motion of particles attracting each other by centripetal forces; Section 12. On the attractive forces of spherical bodies; Section 13. On the attractive forces of non-spherical bodies; Section 14. On the motion of particles attracted by centripetal forces towards the various parts of arbitrarily large bodies; Book Two. On the Motion of Bodies: Section 1. On the motion of particles moving against a resistance that is proportional to the speed; Section 2. On the motion of particles moving against a resistance that is proportional to the square of the speed; Section. 3. On the motion of bodies to which the resistance consists of one part that is proportional to the speed, and another part that is proportional to the square of the speed; Section. 4. On the revolving motion of bodies in resisting media; Section 5. On the density and compression of fluids, and on hydrostatics; Section 6. On the motion and resistance of string pendulums; Section 7. On the motion of fluids and the resistance of projectiles; Section 8. On motion propagated through fluids; Section 9. On the circular motion of fluids; Book Three. On Celestial Mechanics: The rules of Scientific Argument; Phenomena; Propositions; On the motion of the nodes of the moon; Appendices; Glossary of Latin terms; References; Index.