Isaac Newton, The Mathematical Principles of Natural Philosophy

PREFACE

DEFINITIONS

AXIOMS, OR LAWS OF MOTION

BOOK I. 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

II. Of the invention of centripetal forces

III. Of the motion of bodies in eccentric conic sections

IV. Of the finding of elliptic, parabolic, and hyperbolic orbits, from the focus given

V. How the orbits are to be found when neither focus is given

VI. How the motions are to be found in given orbits

VII. Concerning the rectilinear ascent and descent of bodies

VIII. Of the invention of orbits wherein bodies will revolve, being acted upon by any sort of centripetal force

IX. Of the motion of bodies in moveable orbits, and of the motion of the apsides

X. Of the motion of bodies in given superficies, and of the reciprocal motion of funependulous bodies

XI. Of the motion of bodies to each other with centripetal forces

XII. Of the attractive forces of spherical bodies

XIII. Of the attractive forces of bodies which are not of a spherical figure

XIV. Of the motion of very small bodies when agitated by centripetal forces tending to the several parts of any very great body

BOOK II. OF THE MOTION OF BODIES

SECTION

I. Of the motion of bodies that are resisted in the ratio of velocity

II. Of the motion of bodies that are resisted in the duplicate ratio of their velocities

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

IV. Of the circular motion of bodies in resisting mediums

V. Of the density and compression of fluids; and of hydrostatics

VI. Of the motion and resistance of funependulous bodies

VII. Of the motion of fluids and the resistance made to projected bodies

VIII. Of motion propagated through fluids

IX. Of the circular motion of fluids

BOOK III. THE SYSTEM OF THE WORLD

RULES OF REASONING IN PHILOSOPHY

Rule I. We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances. For nature is simple and does not luxuriate in superfluous causes of things. [added in 1726 3rd edition:] To this purpose the philosophers say: Nature does nothing in vain, and it is in vain to do by more that which can be done by fewer.

Rule II. Therefore the causes of natural effects of the same kind are the same. [added in 3rd ed.:] And so to natural effects of the same kind are assigned the same causes, as far as they can be.

Rule III. The qualities of bodies which admit neither intention nor remission, and which belong to all bodies on which one can make experiments, are to be taken as the qualities of all bodies whatsoever.

[Explained in the discussion:] The qualities of bodies are known to us only by experiments…we are certainly not to relinquish the evidence of experiments for the sake of dreams and vain fictions of our own devising; nor ought we to recede from the analogy of Nature, which is wont to be simple, and always consonant to itself. . . . The extension, hardness, impenetrability, mobility, and inertia of the whole result from the extension, hardness, impenetrability, mobility, and inertia of the parts; hence we conclude that all the smallest parts of all bodies are also extended, and hard and impenetrable, and movable, and endowed with the force of inertia. And this is the foundation of all philosophy. . . . Not that I affirm gravity to be essential to all bodies. By their Vis inertiae I mean nothing but their inertia. This is immutable. Their gravity is diminished as they recede from the earth.

Rule IV. [added in 3rd ed.:] In experimental philosophy we are to look upon propositions inferred by general induction from phenomena as accurately or very nearly true, notwithstanding any contrary hypotheses that may be imagined, till such time as other phenomena occur, by which they may either be made more accurate, or liable to exceptions. This rule we must follow, that the argument of induction may not be evaded by hypotheses.

PHÆNOMENA, OR APPEARANCES

PROPOSITIONS I-XXXIII

OF THE MOTION OF THE MOON’S NODES

GENERAL SCHOLIUM

But hitherto I have not been able to discover the cause of those properties of gravity from phenomena, and I feign no hypotheses [hypotheses non fingo in the original Latin]; for whatever is not deduced from the phenomena is to be called an hypothesis; and hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy. In this philosophy particular propositions are inferred from the phenomena, and afterwards rendered general by induction. Thus it was that the impenetrability, the mobility, and the impulsive force of bodies, and the laws of motion and of gravitation, were discovered. And to us it is enough that gravity does really exist, and act according to the laws which we have explained, and abundantly serves to account for all the motions of the celestial bodies, and of our sea.