Axioms, or Laws of Motion 83 OF THE MOTION OF BODIES Section I: Of the method of first and last ratios of quantities, by the help whereof we demonstrate the propositions that follow 95 Section II: Of the Invention of Centripetal Forces 103 Section III: Of the motion of bodies in eccentric conic sections 116 Section IV: Of the finding of elliptic, parabolic, and hyperbolic orbits, from the focus given 125 Section V: How the orbits are to be found when neither focus is given 131 Section VI: How the motions are to be found in given orbits 153 Section VII: Concerning the rectilinear ascent and descent of bodies 159 Section VIII: Of the invention of orbits wherein bodies will revolve, being acted upon by any sort of centripetal force 168 Section IX: Of the motion of bodies in movable orbits; and of the motion of the apsides 172 Section X: Of the motion of bodies in given superficies; and of the reciprocal motion of funependulous bodies 182 Section XI: Of the motions of bodies tending to each other with centripetal forces 194 Section XII: Of the attractive forces of sphærical bodies 218 Section XIII: Of the attractive forces of bodies which are not of a sphærical figure 233 Section XIV: Of the motion of very small bodies when agitated by centripetal forces tending to the several parts of any very great body 243 BOOK II. OF THE MOTION OF BODIES Section I: Of the motion of bodies that are resisted in the ratio of the velocity 251 Section II: Of the motion of bodies that are resisted in the duplicate ratio of their velocities 258 Section III: Of the motions of bodies which are resisted partly in the ratio of the velocities, and partly in the duplicate of the same ratio 279 Section IV: Of the circular motion of bodies in resisting mediums 287 Section V: Of the density and compression of fluids; and of hydrostatics 293 Section VI: Of the motion and resistance of funependulous bodies 303 Section VII: Of the motion of fluids and the resistance made to projected bodies 323 Section VIII: Of motion propagated through fluids 356 Section IX: Of the circular motion of fluids 370 BOOK III. Book III 383 Rules of Reasoning in Philosophy 384 Phænomena, or Appearances 386 Propositions I-IX (Force of gravity) 390 Propositions X-XXIV (Motions of celestial bodies and the sea) 400 Propositions XXV-XXXIII (Quantity of lunar motions) 419 Propositions XXXVI-XXXVIII (Forces to move the sea) 449 Lemmas I-III, Proposition XXXIX (Precession of equinoxes) 455 Lemmas IV-XI, Propositions XL-XLII (Comets) 460 General Scholium 503 The System of the World. 511 Index to the Principia. 575 [Pg 9] LIFE OF SIR ISAAC NEWTON. Nec fas est proprius mortali attingere Divos.-HALLEY.