The Mathematical Principles of Natural Philosophy

Isaac Newton

The Mathematical Principles of Natural Philosophy by Isaac Newton, often referred to as the Principia, is one of the most influential works in the history of science. In this groundbreaking treatise, Newton introduced his laws of motion and universal gravitation, providing a mathematical framework for understanding the physical forces that govern the universe. The book presents a comprehensive system of classical mechanics that has guided scientific thought for centuries. Newton's work revolutionized our understanding of the natural world, providing the foundation for much of modern physics and mathematics. The Mathematical Principles of Natural Philosophy is not only a monumental scientific achievement but also a testament to Newton's genius in synthesizing mathematical concepts with the physical observations of nature. This book is essential for anyone seeking to understand the laws that govern motion, force, and the structure of the cosmos.

Table of contents

• CONTENTS
• DEDICATION
• INTRODUCTION TO THE AMERICAN EDITION
• LIFE OF SIR ISAAC NEWTON
• THE AUTHOR'S PREFACE
• BOOK 1
• DEFINITIONS
• AXIOMS, OR LAWS OF MOTION
• OF THE MOTION OF BODIES
• SECTION 1.OF THE METHOD OF FIRST AND LAST RATIOS OF QUANTITIES, BY THE HELP WHEREOF WE DEMONSTRATE THE PROPOSITIONS THAT FOLLOW
• SECTION 2.OF THE INVENTION OF CENTRIPETAL FORCES
• SECTION 3.OF THE MOTION OF BODIES IN ECCENTRIC CONIC SECTIONS
• SECTION 4.OF THE FINDING OF ELLIPTIC, PARABOLIC, AND HYPERBOLIC ORBITS, FROM THE FOCUS GIVEN
• SECTION 5.HOW THE ORBITS ARE TO BE FOUND WHEN NEITHER FOCUS IS GIVEN
• SECTION 6.HOW THE MOTIONS ARE TO BE FOUND IN GIVEN ORBITS
• SECTION 7.CONCERNING THE RECTILINEAR ASCENT AND DESCENT OF BODIES
• SECTION 8.OF THE INVENTION OF ORBITS WHEREIN BODIES WILL REVOLVE, BEING ACTED UPON BY ANY SORT OF CENTRIPETAL FORCE
• SECTION 9.OF THE MOTION OF BODIES IN MOVEABLE ORBITS; AND OF THE MOTION OF THE APSIDES
• SECTION 10.OF THE MOTION OF BODIES IN GIVEN SUPERFICIES, AND OF THE RECIPROCAL MOTION OF FUNEPENDULOUS BODIES
• SECTION 11.OF THE MOTIONS OF BODIES TENDING TO EACH OTHER WITH CENTRIPETAL FORCES
• SECTION 12.OF THE ATTRACTIVE FORCES OF SPHAERICAL BODIES
• SECTION 13.OF THE ATTRACTIVE FORCES OF BODIES WHICH ARE NOT OF A SPHAERICAL FIGURE
• SECTION 14.OF THE MOTION OF VERY SMALL BODIES WHEN AGITATED BY CENTRIPETAL FORCES TENDING TO THE SEVERAL PARTS OF ANY VERY GREAT BODY
• BOOK 2.OF THE MOTION OF BODIES
• SECTION 1.OF THE MOTION OF BODIES THAT ARE RESISTED IN THE RATIO OF THE VELOCITY
• SECTION 2.OF THE MOTION OF BODIES THAT ARE RESISTED IN THE DUPLICATE RATIO OF THEIR VELOCITIES
• SECTION 3.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 4.OF THE CIRCULAR MOTION OF BODIES IN RESISTING MEDIUMS
• SECTION 5.OF THE DENSITY AND COMPRESSION OF FLUIDS; AND OF HYDROSTATICS
• SECTION 6.OF THE MOTION AND RESISTANCE OF FUNEPENDULOUS BODIES
• SECTION 7.OF THE MOTION OF FLUIDS, AND THE RESISTANCE MADE TO PROJECTED BODIES
• SECTION 8.OF MOTION PROPAGATED THROUGH FLUIDS
• SECTION 9.OF THE CIRCULAR MOTION OF FLUIDS
• BOOK 3
• INTRODUCTION
• 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-XXXV (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