Table of Contents

PREFACE PART ONE THE ORIGINS CHAPTER ONE. - HELLENIC SCIENCE 1. Aristotelian mechanics 2. The Statics of Archimedes CHAPTER II. - ALEXANDRIAN SOURCES AND ARABIC MANUSCRIPTS 1. "The "mechanics" of Hero of Alexandria" 2. Pappus' theories of the inclined plane and of the centre of gravity 3. The fragments attributed to Euclid in arabic writings 4. The book of Charistion CHAPTER III. - THE XIIIth CENTURY. THE SCHOOL OF JORDANUS 1. "Jordanus of Nemore and "gravitas secundum situm" 2. "The anonymous author of "Liber Jordani de ratione ponderis." The angular lever. The inclined plane" CHAPTER IV. - THE XIVth CENTURY. THE SCHOOLS OF BURIDAN AND ALBERT OF SAXONY. NICOLE ORESME AND THE OXFORD SCHOOL 1. "The doctrine of "impetus" (John Buridan)" 2. The sphericity of the earth and the oceans-Albert of Saxony and the aristotelian tradition 3. Albert of Saxony's theory of centre of gravity 4. Albert of Saxony's kinematics. The acceleration of falling bodies 5. The discussion of action at a distance 6. Nicole Oresme-a disciple of Buridan 7. Oresme's rule in kinematics. (Uniformly accelerted motion.) 8. Oresme as a predecessor of Copernicus 9. The Oxford School 10. The tradition of Albert of Saxony and of Buridan CHAPTER V. - XVth AND XVIth CENTURIES. THE ITALIAN SCHOOL. BLASIUS OF PARMA. THE OXFORD TRADITION. NICHOLAS OF CUES AND LEONARDO DA VINCI. NICHOLAS COPERNICUS. THE ITALIAN AND PARISIAN SCHOOLMEN OF THE XVIth CENTURY. DOMINIC SOTO AND THE FALL OF BODIES 1. Blasius of Parma and his treatise on weights 2. The Italian tradition of Nicole Oresme and the Oxford School 3. "Nicholas of Cues (1404-1464) and the doctrine of "impetus impressus" 4. Leonardo da Vinci's contribution to mechanics 5. Nicholas Copernicus (1472-1543). His system of the world and his ideas on attraction 6. John Fernel (1497-1558) and the figure of the earth 7. Italian scholasticism in the XVIth century 8. Parisian scholasticism in the XVIth century 9. The attack of the humanists 10. Dominic de Soto (1494-1560) and the laws of falling bodies CHAPTER VI. - XVIth CENTURY (continued) THE ITALIAN SCHOOL OF NICHOLAS TARTAGLIA AND BERNARDINO BALDI 1. Nicholas Tartaglia 2. Jerome Cardan (1501-1576) 3. Julius-Caesar Scaliger and Buridan's doctrine 4. Bento Pereira (1535-1610). The classical reaction 5. "The "Mechanicorum Liber" of Guido Ubaldo (1545-1607)" 6. J.-B. Villalpand (1552-1608) and the polygon of sustentation 7. "J.-B. Benedetti (1530-1590). Statics. Figure of the earth. Doctrine of "impetus" 8. Giordano Bruno (1548-1600) and the composition of motion 9. "Bernardino Baldi (1553-1617). Statics and gravity "exviolentia" CHAPTER VII. - XVIth CENTURY (continued). XVIIth CENTURY. TYCHO-BRAHE AND KEPLER 1. The system due to Tycho-Brahe (1546-1601) 2. Kepler (1571-1631). The general chracter of his contribution 3. The origin of the law of areas 4. Origin of the law of the ellipticity of planetary trajectories 5. Kepler's third law 6. Kepler and the concept of inertia 7. Kepler and the doctrine of attraction PART II THE FORMATION OF CLASSICAL MECHANICS CHAPTER I. - STEVIN'S STATICS. SOLOMON OF CAUX 1. The statics of Stevin (1548-1620) 2. Stevin and the principle of virtual work 3. Stevin's hydrostatics 4. Solomon of Caux (1576-1630) and the concept of work CHAPTER II. - GALILEO AND TORRICELLI 1. Galileo's statics 2. Galileo and the fall of bodies 3. Galileo and the motion of projectiles 4. Galileo and the hydrostatics 5. Galileo and the Copernican system 6. Torricelli's principle 7. Torricelli and the motion of projectiles 8. Torricelli's experiment 9. Torricelli's law flow through an orifice CHAPTER III. - MERSENNE (1588-1648) AS AN INTERNATIONAL GO-BETWEEN IN MECHANICS. ROBERVAL (1602-1675) 1. The arrival of foreign theories in France. The part played by Mersenne 2. Roberval and compound motion 3. Roberval's treatise on mechanics 4. Roberval and the law of composition of forces CHAPTER IV. - DESCARTES' MECHANICS. PASCAL'S HYDROSTATICS 1. Descartes' statics 2. Descartes and the fall of heavy bodies 3. Descartes and the conservation of quantities of motion 4. Descartes and the impact of bodies 5. The discussion between Descartes and Roberval on the centre of agitation 6. The quarrel about geostatics 7. Pascal's hydrostatics "CHAPTER V. - THE LAWS OF IMPACT (WALLIS, WREN, HUYGHENS, MARIOTTE). THE MECHANICS OF HUYGHENS (1629-1697)" 1. The mechanics of Wallis (1616-1703) 2. Wren (1632-1723) and the laws of elastic impact 3. Huyghens (1629-1697) and the laws of impact 4. The plan of Huyghens' fundamental treatise 5. Huyghens and the fall of bodies 6. The isochronism of the cycloidal pendulum 7. The theory of the centre of oscillation 8. The theory of centrifugal force 9. Huyghens and the principle of relativity 10. Mariotte and the laws of impact CHAPTER VI. - NEWTON (1642-1727) 1. The newtonian method 2. The newtonian concepts 3. The newtonian laws of motion 4. Newton and the dynamical law of composition of forces 5. The motion of a point under the action of a central force 6. Newton's explanation of the motion of the planets 7. The universal attraction CHAPTER VII. - LEIBNIZ AND LIVING FORCE 1. "The "vis motrix" in the sense of Leibniz" 2. Leibniz and the laws of impact 3. Living and dead forces CHAPTER VIII. - THE FRENCH-ITALIAN SCHOOL OF ZACCHI AND VARIGNON 1. Zacchi and Saccheri. Lamy and the composition of forces 2. The statics of Varignon (1654-1722) 3. Varignon and Torricelli's law of flow PART III THE ORGANISATION AND DEVELOPMENT OF THE PRINCIPLES OF CLASSICAL MECHANICS IN THE XVIIIth CENTURY CHAPTER I. - JEAN BERNOULLI AND THE PRINCIPLE OF VIRTUAL WORK (1717). DANIEL BERNOULLI AND THE COMPOSITION OF FORCES (1726) 1. Jean Bernoulli and the principle of virtual work 2. Daniel Bernoulli and the composition of forces CHAPTER II. - THE CONTROVERSY ABOUT LIVING FORCES CHAPTER III. - EULER AND THE MECHANICS OF A PARTICLE (1736) CHAPTER IV. - JACQUES BERNOULLI AND THE CENTRE OF OSCILLATION (1703). D'ALEMBERT'S TREATISE ON DYNAMICS (1743) 1. Jacques Bernoulli and the centre of oscillation 2. The introductory argument of d'Alembert's Treatise on dynamics 3. D'Alembert and the concept of accelerating force 4. D'Alembert's principle 5. D'Alembert's solution of the problem of the centre of oscillation 6. The priority of Herman and Euler in the matter of d'Alembert's principle 7. D'Alembert and the laws of impact 8. D'Alembert and the principle of living forces CHAPTER V. - THE PRINCIPLE OF LEAST ACTION 1. Return to Fermat 2. Cartesian objections to Fermat's principle 3. "Leibniz and the path of "least resistance" for light" 4. Maupertuis' law of rest 5. The principle of least action in Maupertuis' sense (1744) 6. The application of the principle of least action to the direct impact of two bodies 7. The principle of least action in Maupertuis' work 8. D'Alembert's condemnation of final causes 9. The polemic on the principle of least action 10. Euler's judgment on the controversy on least action 11. Euler and the law of the extremum of ? mvds 12. Final remark CHAPTER VI. - EULER AND THE MECHANICS OF SOLID BODIES (1760) CHAPTER VII. -CLAIRAUT AND THE FUNDAMENTAL LAW OF HYDROSTATICS 1. Clairaut's principle of the duct 2. The condition to be satisfied by the law of gravity to assure the conservation of the shape of a rotating fluid mass 3. CHAPTER VIII. - DANIEL BERNOULLI'S HYDRODYNAMICS. D'ALEMBERT AND THE RESISTANCE OF FLUIDS. EULER'S HYDRODYNAMICAL EQUATIONS. BORDA AND THE LOSSES OF KINETIC ENERGY IN FLUIDS 1. Return to the hydrodynamics of the XVIIth century 2. Daniel Bernoulli's hydrodynamics 3. D'Alembert and the motion of fluids 4. D'Alembert and the resistance of fluids - His paradox 5. Euler and the equilibrium of fluids 6. Euler and the general equations of hydrodynamics 7. Borda and the losses of kinetic energy in fluids "CHAPTER IX. - EXPERIMENTS ON THE RESISTANCE OF FLUIDS (BORDA, BOSSUT, DU BUAT). COULOMB AND THE LAWS OF FRICTION" 1. Borda's experiments and newtonian theories 2. The abbe Bossut's expriments 3. Du Buat (1734-1809) : Hydraulics and the resistance of fluids 4. Coulomb's work on friction CHAPTER X. - LAZARE CARNOT'S MECHANICS 1. Carnot and the experimental character of mechanics 2. The concepts and postulates of Carnot's mechanics 3. Carnot's theorem "CHAPTER XI. - THE "MECANIQUE ANALYTIQUE" OF LAGRANGE" 1. "The content and purpose of Lagrange's "Mecanique analytique" 2. Lagrange's statics 3. Lagrange and the history of dynamics 4. Lagrange's equations 5. The conservation of living forces as a corollary of Lagrange's equations 6. The principle of least action as a corollary of Lagrange's equations 7. "On some problems treated in the "Mecanique analytique" 8. Lagrange's hydrodynamics PART IV SOME CHARACTERISTIC FEATURES OF THE EVOLUTION OF CLASSICAL MECHANICS AFTER LAGRANCE FOREWARD CHAPTER I. - LAPLACE'S MECHANICS (1799) 1. Laplace and the principles of dynamics 2. "The general mechanics compatible with an arbitrary relation between the "force" and the velocity" 3. Laplace and the significance of the law of universal gravitation CHAPTER II. - FOURIER AND THE PRINCIPLE OF VIRTUAL WORKS (1798) CHAPTER III. - THE PRINCIPLE OF LEAST CONSTRAINT (1829) CHAPTER IV. - RELATIVE MOTION: RETURN TO A PRINCIPLE OF CLAIRAUT. CORIOLIS' THEOREMS. FOUCAULT'S EXPERIMENTS 1. Return to a principle of Clairaut (1742) 2. Coriolis' first theorem 3. Coriolis' second theorem 4. The experiments of Foucault (1819-1868) CHAPTER V. - POISSON'S THEOREM (1809) 1. Poisson's theorem and brackets 2. The Lagrange-Poisson square brackets CHAPTER VI. - ANALYTICAL DYNAMICS IN THE SENSE OF HAMILTON AND JACOBI 1. Hamilton's optics. Its double interpretation in terms of emision and wave propagation 2. The dynamical law of varying action in Hamilton's sense 3. The significance of the hamiltonian dynamics 4. Jacobi's criticism 5. Jacobi's fundamental theorem 6. The canonical equations and Jacobi's multiplier 7. Geometrisation of the principle of least action CHAPTER VII. - NAVIER'S EQUATIONS 1. The molecular hypothesis 2. Equilibrium of fluids 3. The molecular forces in the motion of a fluid 4. Remark on the origin of the general equations of elasticity CHAPTER VIII. - CAUCHY AND THE FINITE DEFORMATION OF CONTINUOUS MEDIA CHAPTER IX. - HUGONIOT AND THE PROPAGATION OF MOTION IN CONTINUOUS MEDIA 1. Nature of the problem 2. Compatibility of two solutions. Velocity of propagation of one solution in another. Hugoniot's theorem 3. Discontinuities in the propagation of motion "CHAPTER X. - HELMHOLTZ AND THE ENERGETIC THESIS DISCUSSION OF THE NEWTONIAN PRINCIPLES (SAINT-VENANT, REECH, KIRCHHOF, MACH, HERTZ, POINCARE, PAINLEVE, DUHEM)" 1. Helmholtz and the energetic thesis 2. Barre de Saint-Venant 3. "Reech and the "School of the thread" 4. Kirchhoff and the logistic structure of mechanics 5. Mach 6. Hertz 7. Poincare - Criticism of the principles and discussion of the notion of absolute motion 8. Poincare and the energetic thesis 9. Painleve and the princple of causality in mechanics 10. Duhem and the evolution of mechanics 11. Conclusion of this chapter PART V THE PRINCIPLES OF THE MODERN PHYSICAL THEORIES OF MECHANICS FOREWARD CHAPTER I. - SPECIAL RELATIVITY A. PRESENTATION 1. Immediate antecedents of the special theory of relativity 2. Michelson's experiment and Lorentz's hypothesis of contraction 3. The Lorentz transformation 4. Introduction to Einstein's electrodynamics 5. Definition of simultaneity 6. Relativity of lengths and times 7. Transformation of the coordinates of space and time 8. Contraction of lengths and correlative dilation of times 9. Composition of velocities 10. Transformation of Maxwell's equations in the vacuum. Electrodynamic relativity 11. Transformation of Maxwell's equations including convection currents 12. Dynamics of the slowly accelerated electron 13. Space-time in the sense of Minkowski B. ANALYSIS AND INTERPRETATION 2a. On Michelson's experiment 3a. Dynamics of the electron in Poincare's sense 3b. From Lorentz to Einstein 4a. The ether made superfluous 5a. Difficulties of Einstein's notion of simultaneity 6a. "Field of validity of the principle of special relativity - "Galilean" systems of reference" 7a. On different mathematical ways of obtaining the Lorentz transformation 8a. Pseudo-paradoxes in special relativity 9a. Composition of velocities and Fizeau's experiment 12a. Return to the dynamics of variable mass in Painleve's sense 13a. On the meaning of space-time CHAPTER II. - GENERALISED RELATIVITY A. PRESENTATION 1. Statement of the principle of generalized relativity 2. Remark on the mathematical tools of generalised relativity 3. The equations of motion of a free particle in a gravitational field 4. Equations of the gravitational field in the absence of matter 5. General form of the equations of gravitation 6. Reversion to Newton's theory in the first approximation 7. The conduct of measurements of space and time in a static gravitational field. Deviation of light rays. Displacement of the perihelion of the planets 8. The spatially closed universe 9. Gravitation and electricity B. ANALYSIS AND INTERPRETATION &nb 6a. On the geometrisation of classical mechan