《自然哲学的数学原理》是第一次科学革命的集大成之作，它在物理学、数学、天文学和哲学等领域产生了巨大影响。在写作方式上，牛顿遵循古希腊的公理化模式，从定义、定律（即公理）出发，导出命题；对具体的问题（如月球的运动），把从理论导出的结果和观察结果相比较。全书共分五部分，首先“定义”，这一部分给出了物质的量、时间、空间、向心力等的定义。第二部分是“公理或运动的定律”，包括著名的运动三定律。接下来的内容分为三卷。前两卷的标题一样，都是“论物体的运动”。第一卷研究在无阻力的自由空间中物体的运动，许多命题涉及已知力解定受力物体的运动状态（轨道、速度、运动时间等），以及由物体的运动状态确定所受的力。第二卷研究在阻力给定的情况下物体的运动、流体力学以及波动理论。
- Front Matter
- PRINCIPIA
- Ode by Edmund Halley. Translated by Leon J. Richardson
- Prefaces to the first, second, and third editions
- MATHEMATICAL PRINCIPLES OF NATURAL PHILOSOPHY
- 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 focus 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 force
- IX. Motion of bodies in movable orbits
- X. Motion of bodies in given surfaces
- 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(IN RESISTING MEDIUMS)
- 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 velocities
- III. Motion of bodies that are resisted partly in the ratio of the velocities, and partly as the square of the same ratio
- IV. Circular motion of bodies in resisting mediums
- V. Density and compression of fluids
- 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
