Front Cover -- Mathematical Methods in Science -- Copyright Page -- Contents -- INTRODUCTION -- CHAPTER 1. From the History of Astronomy: Measurement and Successive Approximation -- SECTION 1 MEASUREMENT -- 1 The Tunnel -- 2 Measuring: Triangulating -- 3 How Far Away is the Moon? -- 4 Why Teach Triangulation? -- SECTION 2 ASTRONOMICAL MEASUREMENTS -- 1 Aristarchus of Samos -- 2 Radius of Earth: Eratosthenes -- 3 Rival Cosmologies -- 4 The Orbit of Venus -- 5 Tycho Brahe and Kepler -- 6 The Mars Year -- 7 The Orbit of Mars -- 8 A Word to the Perceptive Reader -- 9 Newton's Problem of a Comet's Path -- SECTION 3 SUCCESSIVE APPROXIMATION -- 1 First Application -- 2 Extraction of Square Roots -- SECTION 4 NEWTON'S METHOD OF SUCCESSIVE APPROXIMATION -- 1 The General Method of Newton -- 2 Newton's Formula -- 3 √a -- 4 3√a -- 5 5√a -- CHAPTER 2. From the History of Statics -- SECTION 1 STEVINUS AND ARCHIMEDES -- 1 Inclined Plane -- 2 Lever -- SECTION 2 VECTORS -- 1 Inclined Plane -- 2 Pulley -- 3 Lever -- 4 Archimedes' Application of his Law of the Lever -- 5 (-) · (-) = (+) -- 6 Von Mises' Flight Triangle -- CHAPTER 3. From the History of Dynamics -- SECTION 1 GALILEO -- 1 Heavier Bodies Fall Faster? -- 2 Not "Why?", But "How?" -- 3 How do Heavy Bodies Fall? -- 4 Dynamics of the Inclined Plane -- 5 Conservation of Energy -- 6 Law of Inertia -- 7 A Cannon Ball's Trajectory -- SECTION 2 NEWTON -- 1 Apples, Cannon Balls, and the Moon -- 2 Never Smoke Without Fire -- 3 That the Planets do Accelerate Towards the Sun -- 4 What is the Law of Universal Gravitation? -- 5 Uniform Circular Motion: Hamilton's Hodograph -- 6 On Newton's Discovery of the Law of Universal Gravitation -- 7 Scientific Attitude: Verification -- 8 Hindsight and Foresight -- SECTION 3 THE PENDULUM -- 1 The Dimensions Test -- 2 Simple Pendulum's Time of Swing.

3 Determination of g by Pendulum Experiment -- 4 The Conical Pendulum -- SECTION 4 ESCAPE VELOCITY -- 1 Go-Around Velocity -- 2 Apropos Go-Away Velocity -- 3 The Force of Gravity -- 4 That Kepler's Third Law is a Consequence of Newton's Law of Gravitation -- 5 Planetary Mass -- 6 Go-Away Velocity -- 7 Ratio of Escape and Orbital Velocities -- CHAPTER 4. Physical Reasoning in Mathematics -- CHAPTER 5. Differential Equations and Their Use in Science -- SECTION 1 FIRST EXAMPLES -- 1 Rotating Fluid -- 2 Galileo: Free Fall -- 3 Catenary -- 4 Fall with Friction -- SECTION 2 APPROXIMATE FORMULAE: POWER SERIES -- Introduction -- 1 Calculation of 3√28 -- 2 Fall with Friction Again -- 3 How Deep is a Well? -- 4 Pendulum: Small Oscillations -- SECTION 3 PHYSICAL ANALOGY -- SECTION 4 WHAT IS A DIFFERENTIAL EQUATION? -- 1 Example -- 2 Vector Fields -- 3 Direction Fields.