The Principia: The Authoritative Translation and Guide

Mathematical Principles of Natural Philosophy
 
 
University of California Press
  • 1. Auflage
  • |
  • erschienen am 5. Februar 2016
  • |
  • 992 Seiten
 
E-Book | ePUB mit Adobe DRM | Systemvoraussetzungen
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978-0-520-96481-5 (ISBN)
 
In his monumental 1687 work, Philosophiae Naturalis Principia Mathematica, known familiarly as the Principia, Isaac Newton laid out in mathematical terms the principles of time, force, and motion that have guided the development of modern physical science. Even after more than three centuries and the revolutions of Einsteinian relativity and quantum mechanics, Newtonian physics continues to account for many of the phenomena of the observed world, and Newtonian celestial dynamics is used to determine the orbits of our space vehicles.

This authoritative, modern translation by I. Bernard Cohen and Anne Whitman, the first in more than 285 years, is based on the 1726 edition, the final revised version approved by Newton; it includes extracts from the earlier editions, corrects errors found in earlier versions, and replaces archaic English with contemporary prose and up-to-date mathematical forms.

Newton's principles describe acceleration, deceleration, and inertial movement; fluid dynamics; and the motions of the earth, moon, planets, and comets. A great work in itself, the Principia also revolutionized the methods of scientific investigation. It set forth the fundamental three laws of motion and the law of universal gravity, the physical principles that account for the Copernican system of the world as emended by Kepler, thus effectively ending controversy concerning the Copernican planetary system.

The illuminating Guide to Newton's Principia by I. Bernard Cohen makes this preeminent work truly accessible for today's scientists, scholars, and students.
1. Auflage
  • Englisch
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978-0-520-96481-5 (9780520964815)
0520964810 (0520964810)
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I. Bernard Cohen (1914-2003) was Victor S. Thomas Professor of the History of Science at Harvard University. He was the author of Benjamin Franklin's Science, Interactions, and Science and the Founding Fathers. Anne Whitman (1937-1984) was coeditor (with I. Bernard Cohen and Alexander Koyré) of the Latin edition, with variant readings, of the Principia. Julia Budenz, author of From the Gardens of Flora Baum, is a multilingual classicist and poet.
  • Cover
  • Contents
  • Preface
  • A GUIDE TO NEWTON'S PRINCIPIA
  • Contents of the Guide
  • Abbreviations
  • CHAPTER ONE: A Brief History of the Principia
  • 1.1 The Origins of the Principia
  • 1.2 Steps Leading to the Composition and Publication of the Principia
  • 1.3 Revisions and Later Editions
  • CHAPTER TWO: Translating the Principia
  • 2.1 Translations of the Principia: English Versions by Andrew Motte (1729), Henry Pemberton (1729-?), and Thomas Thorp (1777)
  • 2.2 Motte's English Translation
  • 2.3 The Motte-Cajori Version
  • The Need for a New Translation
  • 2.4 A Problem in Translation: Passive or Active Voice in Book 1, Secs. 2 and 3
  • The Sense of "Acta" in Book 1, Prop. 1
  • 2.5 "Continuous" versus "Continual"
  • The Problem of "Infinite
  • CHAPTER THREE: Some General Aspects of the Principia
  • 3.1 The Title of Newton's Principia
  • The Influence of Descartes
  • 3.2 Newton's Goals: An Unpublished Preface to the Principia
  • 3.3 Varieties of Newton's Concepts of Force in the Principia
  • 3.4 The Reorientation of Newton's Philosophy of Nature
  • Alchemy and the Principia
  • 3.5 The Reality of Forces of Attraction
  • The Newtonian Style
  • 3.6 Did Newton Make the Famous Moon Test of the Theory of Gravity in the 1660s?
  • 3.7 The Continuity in Newton's Methods of Studying Orbital Motion: The Three Approximations (Polygonal, Parabolic, Circular)
  • 3.8 Hooke's Contribution to Newton's Thinking about Orbital Motion
  • 3.9 Newton's Curvature Measure of Force: New Findings (by Michael Nauenberg)
  • 3.10 Newton's Use of "Centrifugal Force" in the Principia
  • CHAPTER FOUR: Some Fundamental Concepts of the Principia
  • 4.1 Newton's Definitions
  • 4.2 Quantity of Matter: Mass (Def. 1)
  • 4.3 Is Newton's Definition of Mass Circular?
  • 4.4 Newton's Determination of Masses
  • 4.5 Newton's Concept of Density
  • 4.6 Quantity of Motion: Momentum (Def. 2)
  • 4.7 "Vis Insita": Inherent Force and the Force of Inertia (Def. 3)
  • 4.8 Newton's Acquaintance with "Vis Insita" and "Inertia
  • 4.9 Impressed Force
  • Anticipations of Laws of Motion (Def. 4)
  • 4.10 Centripetal Force and Its Three Measures (Defs. 5, 6-8)
  • 4.11 Time and Space in the Principia
  • Newton's Concept of Absolute and Relative Space and Time and of Absolute Motion
  • The Rotating-Bucket Experiment
  • CHAPTER FIVE: Axioms, or the Laws of Motion
  • 5.1 Newton's Laws of Motion or Laws of Nature
  • 5.2 The First Law
  • Why Both a First Law and a Second Law?
  • 5.3 The Second Law: Force and Change in Motion
  • 5.4 From Impulsive Forces to Continually Acting Forces: Book 1, Prop. 1
  • Is the Principia Written in the Manner of Greek Geometry?
  • 5.5 The Third Law: Action and Reaction
  • 5.6 Corollaries and Scholium: The Parallelogram Rule, Simple Machines, Elastic and Inelastic Impact
  • 5.7 Does the Concept of Energy and Its Conservation Appear in the Principia?
  • 5.8 Methods of Proof versus Method of Discovery
  • The "New Analysis" and Newton's Allegations about How the Principia Was Produced
  • The Use of Fluxions in the Principia
  • CHAPTER SIX: The Structure of Book 1
  • 6.1 The General Structure of the Principia
  • 6.2 Sec. 1: First and Ultimate Ratios
  • 6.3 Secs. 2-3: The Law of Areas, Circular Motion, Newton's Dynamical Measure of Force
  • The Centripetal Force in Motion on an Ellipse, on a Hyperbola, and on a Parabola
  • 6.4 The Inverse Problem: The Orbit Produced by an Inverse-Square Centripetal Force
  • 6.5 Secs. 4-5: The Geometry of Conics
  • 6.6 Problems of Elliptical Motion (Sec. 6)
  • Kepler's Problem
  • 6.7 The Rectilinear Ascent and Descent of Bodies (Sec. 7)
  • 6.8 Motion under the Action of Any Centripetal Forces (Sec. 8)
  • Prop. 41
  • 6.9 Specifying the Initial Velocity in Prop. 41
  • The Galileo-Plato Problem
  • 6.10 Moving Orbits (Sec. 9) and Motions on Smooth Planes and Surfaces (Sec. 10)
  • 6.11 The Mutual Attractions of Bodies (Sec. 11) and the Newtonian Style
  • 6.12 Sec. 11: The Theory of Perturbations (Prop. 66 and Its Twenty-Two Corollaries)
  • 6.13 Sec. 12 (Some Aspects of the Dynamics of Spherical Bodies)
  • Sec. 13 (The Attraction of Nonspherical Bodies)
  • Sec. 14 (The Motion of "Minimally Small" Bodies)
  • CHAPTER SEVEN: The Structure of Book 2
  • 7.1 Some Aspects of Book 2
  • 7.2 Secs. 1, 2, and 3 of Book 2: Motion under Various Conditions of Resistance
  • 7.3 Problems with Prop. 10
  • 7.4 Problems with the Diagram for the Scholium to Prop. 10
  • 7.5 Secs. 4 and 5: Definition of a Fluid
  • Newton on Boyle's Law
  • The Definition of "Simple Pendulum
  • 7.6 Secs. 6 and 7: The Motion of Pendulums and the Resistance of Fluids to the Motions of Pendulums and Projectiles
  • A General Scholium (Experiments on Resistance to Motion)
  • 7.7 The Solid of Least Resistance
  • The Design of Ships
  • The Efflux of Water
  • 7.8 Sec. 8: Wave Motion and the Motion of Sound
  • 7.9 The Physics of Vortices (Sec. 9, Props. 51-53)
  • Vortices Shown to Be Inconsistent with Keplerian Planetary Motion
  • 7.10 Another Way of Considering Book 2: Some Achievements of Book 2 (by George E. Smith)
  • CHAPTER EIGHT: The Structure of Book 3
  • The System of the World
  • 8.1 The Structure of Book 3
  • 8.2 From Hypotheses to Rules and Phenomena
  • 8.3 Newton's "Rules for Natural Philosophy
  • 8.4 Newton's "Phenomena
  • 8.5 Newton's Hyp. 3
  • 8.6 Props. 1-5: The Principles of Motion of Planets and of Their Satellites
  • The First Moon Test
  • 8.7 Jupiter's Perturbation of Saturn as Evidence for Universal Gravity
  • 8.8 Planetary Perturbations: The Interaction of Jupiter and Saturn (by George E. Smith)
  • 8.9 Props. 6 and 7: Mass and Weight
  • 8.10 Prop. 8 and Its Corollaries (The Masses and Densities of the Sun, Jupiter, Saturn, and the Earth)
  • 8.11 Props. 9-20: The Force of Gravity within Planets, the Duration of the Solar System, the Effects of the Inverse-Square Force of Gravity (Further Aspects of Gravity and the System of the World): Newton's Hyp. 1
  • 8.12 Prop. 24: Theory of the Tides
  • The First Enunciation of the Principle of Interference
  • 8.13 Props. 36-38: The Tidal Force of the Sun and the Moon
  • The Mass and Density (and Dimensions) of the Moon
  • 8.14 Props. 22, 25-35: The Motion of the Moon
  • 8.15 Newton and the Problem of the Moon's Motion (by George E. Smith)
  • 8.16 The Motion of the Lunar Apsis (by George E. Smith)
  • 8.17 Prop. 39: The Shape of the Earth and the Precession of the Equinoxes
  • 8.18 Comets (The Concluding Portion of Book 3)
  • CHAPTER NINE: The Concluding General Scholium
  • 9.1 The General Scholium: "Hypotheses non fingo
  • 9.2 "Satis est": Is It Enough?
  • 9.3 Newton's "Electric and Elastic" Spirit
  • 9.4 A Gloss on Newton's "Electric and Elastic" Spirit: An Electrical Conclusion to the Principia
  • CHAPTER TEN: How to Read the Principia
  • 10.1 Some Useful Commentaries and Reference Works
  • Newton's Directions for Reading the Principia
  • 10.2 Some Features of Our Translation
  • A Note on the Diagrams
  • 10.3 Some Technical Terms and Special Translations (including Newton's Use of "Rectangle" and "Solid")
  • 10.4 Some Trigonometric Terms ("Sine," "Cosine," "Tangent," "Versed Sine" and "Sagitta," "Subtense," "Subtangent")
  • "Ratio" versus "Proportion"
  • "Q.E.D.," "Q.E.F.," "Q.E.I.," and "Q.E.O.
  • 10.5 Newton's Way of Expressing Ratios and Proportions
  • 10.6 The Classic Ratios (as in Euclid's Elements, Book 5)
  • 10.7 Newton's Proofs
  • Limits and Quadratures
  • More on Fluxions in the Principia
  • 10.8 Example No. 1: Book 1, Prop. 6 (Newton's Dynamical Measure of Force), with Notes on Prop. 1 (A Centrally Directed Force Acting on a Body with Uniform Linear Motion Will Produce Motion according to the Law of Areas)
  • 10.9 Example No. 2: Book 1, Prop. 11 (The Direct Problem: Given an Ellipse, to Find the Force Directed toward a Focus)
  • 10.10 Example No. 3: A Theorem on Ellipses from the Theory of Conics, Needed for Book 1, Props. 10 and 11
  • 10.11 Example No. 4: Book 1, Prop. 32 (How Far a Body Will Fall under the Action of an Inverse-Square Force)
  • 10.12 Example No. 5: Book 1, Prop. 41 (To Find the Orbit in Which a Body Moves When Acted On by a Given Centripetal Force and Then to Find the Orbital Position at Any Specified Time)
  • 10.13 Example No. 6: Book 1, Lem. 29 (An Example of the Calculus or of Fluxions in Geometric Form)
  • 10.14 Example No. 7: Book 3, Prop. 19 (The Shape of the Earth)
  • 10.15 Example No. 8: A Theorem on the Variation of Weight with Latitude (from Book 3, Prop. 20)
  • 10.16 Example No. 9: Book 1 Prop. 66, Corol. 14, Needed for Book 3, Prop. 37, Corol. 3
  • 10.17 Newton's Numbers: The "Fudge Factor
  • 10.18 Newton's Measures
  • 10.19 A Puzzle in Book 1, Prop. 66, Corol. 14 (by George E. Smith)
  • CHAPTER ELEVEN: Conclusion
  • Abbreviations
  • CHAPTER ONE: A Brief History of the Principia
  • CHAPTER TWO: Translating the Principia
  • CHAPTER THREE: Some General Aspects of the Principia
  • CHAPTER FOUR: Some Fundamental Concepts of the Principia
  • CHAPTER FIVE: Axioms, or the Laws of Motion
  • CHAPTER SIX: The Structure of Book 1
  • CHAPTER SEVEN: The Structure of Book 2
  • CHAPTER EIGHT: The Structure of Book 3
  • CHAPTER NINE: The Concluding General Scholium
  • CHAPTER TEN: How to Read the Principia
  • CHAPTER ELEVEN: Conclusion
  • THE PRINCIPIA (Mathematical Principles of Natural Philosophy)
  • Halley's Ode to Newton
  • Newton's Preface to the First Edition
  • Newton's Preface to the Second Edition
  • Cotes's Preface to the Second Edition
  • Newton's Preface to the Third Edition
  • Definitions
  • Axioms, or the Laws of Motion
  • BOOK 1: THE MOTION OF BODIES
  • SECTION 1
  • SECTION 2
  • SECTION 3
  • SECTION 4[SUP(a)]
  • SECTION 5
  • SECTION 6
  • SECTION 7
  • SECTION 8
  • SECTION 9
  • SECTION 10
  • SECTION 11
  • SECTION 12
  • SECTION 13
  • BOOK 2: THE MOTION OF BODIES
  • SECTION 1
  • SECTION 2
  • SECTION 3
  • SECTION 4
  • SECTION 5
  • SECTION 6
  • SECTION 7
  • SECTION 8
  • SECTION 9
  • BOOK 3: THE SYSTEM OF THE WORLD
  • [SUP(a)]RULES FOR THE STUDY OF NATURAL PHILOSOPHY
  • PHENOMENA
  • PROPOSITIONS
  • General Scholium[SUP(a)]
  • Notes Added in Second Printing
  • Index
  • A
  • B
  • C
  • D
  • E
  • F
  • G
  • H
  • I
  • J
  • K
  • L
  • M
  • N
  • O
  • P
  • Q
  • R
  • S
  • T
  • U
  • V
  • W
  • Y
  • Z

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