PORTRAIT OF NEWTON IN THE PEPYSIAN COLLECTION EDITOR'S NOTE. By R. T. Crawlord TITLE PAGE OF THE FIRST EDITION OF THE Principia PRINCIPIA ODE BY EDMUND HALLEY. Translated by Leon I. Richardson PRFACES TO THE FIRST, SECOND, AND THIRD EDITIONS DEFINITIONS AXIOMS,OR LAWS OF MOTION BOOK I. THE MOTION OF BODIES SECTION I. Method of first and last ratios II. Determination of centripetal forces III. Motion of bodies in eccentric conic sections IV. Determination of elliptic, parabolic, and hyperbolic orbits, from the locus given V. Determination of orbits when neither focus is given VI. Determination of motions in given orbits VII. Rectilinear ascent and descent of bodies . VIII. Determination of orbits in which bodies will revolve, being acted upon by any sort of centripetal lorce IX. Motion of bodies in movable orbits; and the motion of the apsides X. Motion of bodies in given surfaces; and the oscillating pendu-lous motion of bodies XI. Motion of bodies tending to each other with centripetal forces XII. Attractive forces of spherical bodies XIII. Attractive forces of bodies which are not spherical XIV. Motion of very small bodies when agitated by centripetal forces tending to the several parts of any very great body BOOK II. THE MOTION OF BODIES SECTION I. Motion of bodies that are resisted in the ratio of the velocity II. Motion of bodies that are resisted as the square of their velocitieJ III. Motion of bodies that are resisted partly in the ratio of the ve-locities, and partly as the square of the same ratio IV. Circular motion of bodies in resisting mediums V. Density and compression of fluids; hydrostatics VI. Motion and resistance of pendulous bodies VII. Motion of fluids, and the resistance made to.projected bodies VIII. Motion propagated through fluids IX. Circular motion of fluids BOOK III. THE SYSTEM OF THE WORLD RULES OF REASONING IN PHILOSOPHY PHENOMENA PROPOSITIONS MOTION OF THE MOON'S NODES GENERAL SCHOLIUM THE SYSTEM OF THE WORLD SYSTEM OF THE WORLD APPENDIX NOTES,HISTORICAL AND EXPLANATORY,PREPARED BY THE REVISER