An Introduction to the History of Structural Mechanics

of Part I.- I The Principles of Statics.- 1 Methodological Preliminaries.- 1.1 The Special Objects That Gave Rise to Mechanics.- 1.2 The Enigma of Force and the Foundations of Mechanics.- 1.3 Statics as "Science Subordinated to Geometry as Well as to Natural Philosophy".- 1.4 Momentum: Fixed Word, Fluid Concept.- 1.5 The Aristotelian Roots of a Vocabulary for Mechanics.- 1.6 A Short Outline of Aristotle's Physical Principles.- 1.7 Modern Metamorphoses of the Immobile Mover: Towards the Principle of Conservation.- 1.8 The "Mechanical Problems": The Peripatetic Explanation of the Law of the Lever and the Parallelogram Rule.- 2 The Law of the Lever.- 2.1 Archimedes' Demonstrations.- 2.2 Interpretations (and Improvements) of Archimedes' Proof.- 2.3 An Alternative Approach: Pseudo-Euclid and Huygens.- 2.4 Marchetti's New Approach and Daviet de Foncenex's Improvements.- 2.5 De la Hire's Proof, Lagrange's Remarks and Fourier's Contribution.- 2.6 Towards the "Dethronement" of the Law of the Lever: Saccheri and de Maupertuis.- 3 The Principle of Virtual Velocities.- 3.1 Medieval Roots.- 3.2 Guidobaldo del Monte, Galileo, and the Principle.- of Virtual Velocities.- 3.3 Descartes: "Explicatio Machinarum Unico Tantum Principio".- 3.4 Bernoulli and Varignon.- 3.5 Riccati's "Universal Principle of Statics".- 3.6 Lagrange's First Demonstration.- 3.7 The Approaches of Fossombroni and Fourier.- 3.8 The Principle of Virtual Velocities and Constraints: Poinsot's and Ampere's Contributions and Lagrange's Second Proof.- 4 The Parallelogram of Forces.- 4.1 Daniel Bernoulli's Claim.- 4.2 Daniel Bernoulli's First Geometrical Demonstration.- 4.3 Bulffinger's Paradox.- 4.4 Riccati's Solution.- 4.5 Foncenex's Memoir and Lagrange's Criticism.- 4.6 Foncenex's Fundamental Lemma.- 4.7 Foncenex's and D'Alembert's Functional Equation.- 4.8 D'Alembert's Memoir of 1769.- 4.9 Further Developments: D'Alembert, Poisson, Cauchy, Dorna and Darboux.- 4.10 Conclusion.- II De Resistentia Solidorum.- 5 Galileo and His "Problem".- 5.1 Introduction.- 5.2 Galileo: A Short Account.- 5.3 The Subtext: Galileo's Atomism.- 5.4 The Primacy of Geometry over Logic in the Discorsi.- 5.5 The First Day of the Discorsi.- 5.6 Attempts to Explain the Cause of Resistance.- 5.7 For and Against the Power of the Vacuum.- 5.8 First Intimations of an Atomistic Theory of Resistance.- 5.9 Democritus or Plato?.- 5.10 The Second Day.- 5.11 Opening Remarks.- 5.12 Corollaries.- 5.13 The Problem of Solids of Ultimate Dimensions.- 5.14 The Problem of Solids of Equal Resistance.- 6 First Studies on the Causes of Resistance.- 6.1 Experimental Confutations: The Horror Vacui.- 6.2 Mersenne and the Problem of Resistance.- 6.3 Descartes' Concept: Stasis as the Best Adhesive.- 6.4 The Atomist Rossetti and His Explanation of Resistance.- 6.5 Atomism and Vacuum: Newton, Leibniz and Clarke.- 6.6 Newton's "vis interna attrahens": Elasticity and Resistance.- 6.7 Boscovich's Reformation of the Old Atomism.- 6.8 Developments of Boscovich's Theory: Early Nineteenth-Century Research on Elasticity.- 7 The Initial Growth of Galileo's Problem.- 7.1 Introduction.- 7.2 First Steps in the Controversy about Solids of Equal Resistance: Blondel's "Evidence".- 7.3 Marchetti's "Evidence" on Solids of Equal Resistance.- 7.4 Marchetti's Axiomatic Approach to the Resistance of Solids.- 7.5 Viviani's "Evidence".- 7.6 Antony Terill and Solids of Ultimate Dimensions.- 7.7 Fabri: Elasticity as an "Intermediate Force".- 7.8 Pardies' Statics.- 8 Early Theories of the Strength of Materials.- 8.1 Elasticity Enters the Theory of Resistance.- 8.2 Mariotte's Contribution.- 8.3 Leibniz's New Demonstrations.- 8.4 New Problems: Catenaries and Elastic Curves.- 8.5 Jakob Bernoulli'of Part I.- I The Principles of Statics.- 1 Methodological Preliminaries.- 1.1 The Special Objects That Gave Rise to Mechanics.- 1.2 The Enigma of Force and the Foundations of Mechanics.- 1.3 Statics as "Science Subordinated to Geometry as Well as to Natural Philosophy".- 1.4 Momentum: Fixed Word, Fluid Concept.- 1.5 The Aristotelian Roots of a Vocabulary for Mechanics.- 1.6 A Short Outline of Aristotle's Physical Principles.- 1.7 Modern Metamorphoses of the Immobile Mover: Towards the Principle of Conservation.- 1.8 The "Mechanical Problems": The Peripatetic Explanation of the Law of the Lever and the Parallelogram Rule.- 2 The Law of the Lever.- 2.1 Archimedes' Demonstrations.- 2.2 Interpretations (and Improvements) of Archimedes' Proof.- 2.3 An Alternative Approach: Pseudo-Euclid and Huygens.- 2.4 Marchetti's New Approach and Daviet de Foncenex's Improvements.- 2.5 De la Hire's Proof, Lagrange's Remarks and Fourier's Contribution.- 2.6 Towards the "Dethronement" of the Law of the Lever: Saccheri and de Maupertuis.- 3 The Principle of Virtual Velocities.- 3.1 Medieval Roots.- 3.2 Guidobaldo del Monte, Galileo, and the Principle.- of Virtual Velocities.- 3.3 Descartes: "Explicatio Machinarum Unico Tantum Principio".- 3.4 Bernoulli and Varignon.- 3.5 Riccati's "Universal Principle of Statics".- 3.6 Lagrange's First Demonstration.- 3.7 The Approaches of Fossombroni and Fourier.- 3.8 The Principle of Virtual Velocities and Constraints: Poinsot's and Ampere's Contributions and Lagrange's Second Proof.- 4 The Parallelogram of Forces.- 4.1 Daniel Bernoulli's Claim.- 4.2 Daniel Bernoulli's First Geometrical Demonstration.- 4.3 Bulffinger's Paradox.- 4.4 Riccati's Solution.- 4.5 Foncenex's Memoir and Lagrange's Criticism.- 4.6 Foncenex's Fundamental Lemma.- 4.7 Foncenex's and D'Alembert's Functional Equation.- 4.8 D'Alembert's Memoir of 1769.- 4.9 Further Developments: D'Alembert, Poisson, Cauchy, Dorna and Darboux.- 4.10 Conclusion.- II De Resistentia Solidorum.- 5 Galileo and His "Problem".- 5.1 Introduction.- 5.2 Galileo: A Short Account.- 5.3 The Subtext: Galileo's Atomism.- 5.4 The Primacy of Geometry over Logic in the Discorsi.- 5.5 The First Day of the Discorsi.- 5.6 Attempts to Explain the Cause of Resistance.- 5.7 For and Against the Power of the Vacuum.- 5.8 First Intimations of an Atomistic Theory of Resistance.- 5.9 Democritus or Plato?.- 5.10 The Second Day.- 5.11 Opening Remarks.- 5.12 Corollaries.- 5.13 The Problem of Solids of Ultimate Dimensions.- 5.14 The Problem of Solids of Equal Resistance.- 6 First Studies on the Causes of Resistance.- 6.1 Experimental Confutations: The Horror Vacui.- 6.2 Mersenne and the Problem of Resistance.- 6.3 Descartes' Concept: Stasis as the Best Adhesive.- 6.4 The Atomist Rossetti and His Explanation of Resistance.- 6.5 Atomism and Vacuum: Newton, Leibniz and Clarke.- 6.6 Newton's "vis interna attrahens": Elasticity and Resistance.- 6.7 Boscovich's Reformation of the Old Atomism.- 6.8 Developments of Boscovich's Theory: Early Nineteenth-Century Research on Elasticity.- 7 The Initial Growth of Galileo's Problem.- 7.1 Introduction.- 7.2 First Steps in the Controversy about Solids of Equal Resistance: Blondel's "Evidence".- 7.3 Marchetti's "Evidence" on Solids of Equal Resistance.- 7.4 Marchetti's Axiomatic Approach to the Resistance of Solids.- 7.5 Viviani's "Evidence".- 7.6 Antony Terill and Solids of Ultimate Dimensions.- 7.7 Fabri: Elasticity as an "Intermediate Force".- 7.8 Pardies' Statics.- 8 Early Theories of the Strength of Materials.- 8.1 Elasticity Enters the Theory of Resistance.- 8.2 Mariotte's Contribution.- 8.3 Leibniz's New Demonstrations.- 8.4 New Problems: Catenaries and Elastic Curves.- 8.5 Jakob Bernoulli's Fundamental Work.- 8.6 Varignon and the Galileo-Mariotte Dichotomy.- 8.7 Musschenbroek and the Imperfections of Matter.- 8.8 The Last of the Eighteenth-Century Treatises on Resistance.- Author Index.