THE MATHEMATICAL PRINCIPLES OF NATURAL PHILOSOPHY (MOTTE TRANSLATION)

Translated by Andrew Motte

CONTENTS

Introduction to the American Edition

Life of Sir Isaac Newton

The Author’s Preface

Book I. Definitions

Axioms, or Laws of Motion

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

Section II: Of the Invention of Centripetal Forces

Section III: Of the motion of bodies in eccentric conic sections

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

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

Section VI: How the motions are to be found in given orbits

Section VII: Concerning the rectilinear ascent and descent of bodies

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

Section IX: Of the motion of bodies in movable orbits; and of the motion of the apsides

Section X: Of the motion of bodies in given superficies; and of the reciprocal motion of funependulous bodies

Section XI: Of the motions of bodies tending to each other with centripetal forces

Section XII: Of the attractive forces of sphaerical bodies

Section XIII: Of the attractive forces of bodies which are not of a sphaerical figure

Section 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 the velocity

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

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

Section IV: Of the circular motion of bodies in resisting mediums

Section V: Of the density and compression of fluids; and of hydrostatics

Section VI: Of the motion and resistance of funependulous bodies

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

Section VIII: Of motion propagated through fluids

Section IX: Of the circular motion of fluids

Book III. Rules of Reasoning in Philosophy

Phaenomena, or Appearances

Propositions I-IX (Force of gravity)

Propositions X-XXIV (Motions of celestial bodies and the sea)

Propositions XXV-XXXIII (Quantity of lunar motions)

Propositions XXXVI-XXXVIII (Forces to move the sea)

Lemmas I-III, Proposition XXXIX (Precession of equinoxes)

Lemmas IV-XI, Propositions XL-XLII (Comets)

General Scholium

The System of the World.