| Foreword |
| Preface to the First Edition |
| Preface to the Second Edition |
| Traces / 1： |
| Concepts and Relationships |
| Early Number Bases |
| Number Language and Counting |
| Spatial Relationships |
| Ancient Egypt / 2： |
| The Era and the Sources |
| Numbers and Fractions |
| Arithmetic Operations |
| "Heap" Problems |
| Geometric Problems |
| Slope Problems |
| Arithmetic Pragmatism |
| Mesopotamia / 3： |
| Cuneiform Writing |
| Numbers and Fractions; Sexagesimals |
| Positional Numeration |
| Sexagesimal Fractions |
| Approximations |
| Tables |
| Equations |
| Measurements: Pythagorean Triads |
| Polygonal Areas |
| Geometry as Applied Arithmetic |
| Hellenic Traditions / 4： |
| Thales and Pythagoras |
| Numeration |
| Arithmetic and Logistic |
| Fifth Century Athens |
| Three Classical Problems |
| Incommensurability |
| Paradoxes of Zeno |
| Deductive Reasoning |
| Democritus of Abdera |
| Mathematics and the Liberal Arts |
| The Academy |
| Aristotle |
| Euclid of Alexandria / 5： |
| Alexandria |
| Lost Works |
| Extant Works |
| The Elements |
| Archimedes of Syracuse / 6： |
| The Siege of Syracuse |
| On the Equilibriums of Planes |
| On Floating Bodies |
| The Sand-Reckoner |
| Measurement of the Circle |
| On Spirals |
| Quadrature of the Parabola |
| On Conoids and Spheroids |
| On the Sphere and Cylinder |
| Book of Lemmas |
| Semiregular Solids and Trigonometry |
| The Method |
| Apollonius of Perge / 7： |
| Works and Tradition |
| Cycles and Epicycles |
| The Conics |
| Cross-Currents / 8： |
| Changing Trends |
| Eratosthenes |
| Angles and Chords |
| Ptolemy's Almagest |
| Heron of Alexandria |
| Decline of Greek Mathematics |
| Nichomachus of Gerasa |
| Diophantus of Alexandria |
| Pappus of Alexandria |
| The End of Alexandrian Dominance |
| Proclus of Alexandria |
| Boethius |
| Athenian Fragments |
| Byzantine Mathematicians |
| Ancient and Medieval China / 9： |
| The Oldest Known Texts |
| The Nine Chapters |
| Rod Numerals |
| The Abacus and Decimal Fractions |
| Values of Pi |
| Thirteenth-Century Mathematics |
| Ancient and Medieval India / 10： |
| Early Mathematics in India |
| The Sulbasutras |
| The Siddhantas |
| Aryabhata |
| Numerals |
| Trigonometry |
| Multiplication |
| Long Division |
| Brahmagupta |
| Indeterminate Equations |
| Bhaskara |
| Madhava and the Keralese School |
| The Islamic Hegemony / 11： |
| Arabic Conquests |
| The House of Wisdom |
| al-Khwarizmi |
| 'Abd Al-Hamid ibn-Turk |
| Thabit ibn Qurra |
| Abu'l-Wefa and Al-Karkhi |
| Al-Biruni and Alhazen |
| Omar Khayyam |
| The Parallel Postulate |
| Nasir al-Din al-Tusi |
| Al-Kashi |
| The Latin West / 12： |
| Introduction |
| Compendia of the Dark Ages |
| Gerbert |
| The Century of Translation |
| Abacists and Algorists |
| Fibonacci |
| Jordanus Nemorarius |
| Campanus of Novara |
| Learning in the Thirteenth Century |
| Archimedes Revived |
| Medieval Kinematics |
| Thomas Bradwardine |
| Nicole Oresme |
| The Latitude of Forms |
| Infinite Series |
| Levi ben Gerson |
| Nicholas of Cusa |
| Decline of Medieval Learning |
| The European Renaissance / 13： |
| Overview |
| Regiomontanus |
| Nicolas Chuquet's Triparty |
| Luca Pacioli's Summa |
| German Algebras and Arithmetics |
| Cardan's Ars Magna |
| Rafael Bombelli |
| Robert Recorde |
| Geometry |
| Renaissance Trends |
| François Viète |
| Early Modern Problem Solvers / 14： |
| Accessibility of Computation |
| Decimal Fractions |
| Notation |
| Logarithms |
| Mathematical Instruments |
| The Infinite and Italian Curves / 15： |
| Infinitesimal Methods: Stevin |
| Johannes Kepler |
| Galileo's Two New Sciences |
| Bonaventura Cavalieri |
| Evangelista Torricelli |
| Analysis, Synthesis, and Numbers / 16： |
| Mersenne's Communicants |
| Descartes |
| Fermat's Loci |
| Gregory of St. Vincent |
| Theory of Numbers |
| Gilles Persone de Roberval |
| Girard Desargues and Projective Geometry |
| Blaise Pascal |
| Philippe de Lahire |
| Georg Mohr |
| Pietro Mengoli |
| Frans van Schooten |
| Jan de Witt |
| Johann Hudde |
| René François de Sluse |
| Christiaan Huygens |
| Newton and British Techniques / 17： |
| John Wallis |
| James Gregory |
| Nicolaus Mercator and William Brouncker |
| Barrow's Method of Tangents |
| Newton |
| Abraham De Moivre |
| Leibniz and Continental Methods / 18： |
| Leibniz: Early Career and Travels |
| The Bernoulli Family |
| Tschirnhaus Transformations |
| Solid Analytic Geometry |
| Michel Rolle and Pierre Varignon |
| The Clairauts |
| Mathematics in Italy |
| Divergent Series |
| Euler / 19： |
| Life of Euler |
| Foundation of Analysis |
| Logarithms and the Euler Identities |
| Differential Equations |
| Probability |
| Textbooks |
| Analytic Geometry |
| The Parallel Postulate: Lambert |
| Pre- to Post-Revolutionary France / 20： |
| Men and Institutions |
| The Committee on Weights and Measures |
| D?Alembert |
| B\x{0082}zout |
| Condorcet |
| Lagrange |
| Monge |
| Carnot |
| Laplace |
| Legendre |
| Aspects of Abstraction |
| Paris in the 1820s |
| Fourier |
| Cauchy |
| Diffusion |
| Gauss / 21： |
| Nineteenth-Century Overview |
| Gauss: Early Work |
| Number Theory |
| Reception of the Disquisitiones Arithmeticae |
| Astronomy |
| Gauss's Middle Years |
| Differential Geometry |
| Gauss's Later Work |
| Gauss's Influence |
| The School of Monge / 22： |
| Projective Geometry: Poncelet and Chasles |
| Synthetic Metric Geometry: Steiner |
| Synthetic Nonmetric Geometry: von Staudt |
| Non-Euclidean Geometry |
| Riemannian Geometry |
| Spaces of Higher Dimensions |
| Felix Klein |
| Post-Riemannian Algebraic Geometry |
| Algebra / 23： |
| British Algebra and the Operational Calculus of Functions |
| Boole and the Algebra of Logic |
| Augustus De Morgan |
| William Rowan Hamilton |
| Grassmann and Ausdehnungslehre |
| Cayley and Sylvester |
| Linear Associative Algebras |
| Algebraic Geometry |
| Algebraic and Arithmetic Integers |
| Axioms of Arithmetic |
| Analysis / 24： |
| Berlin and Göttingen at Mid-Century |
| Riemann in Göttingen |
| Mathematical Physics in Germany |
| Mathematical Physics in English-Speaking Countries |
| Weierstrass and Students |
| The Arithmetization of Analysis |
| Dedekind |
| Cantor and Kronecker |
| Analysis in France |
| Poincaé and Hilbert / 25： |
| Turn-of-the-Century Overview |
| Poincar\x{0082} |
| Hilbert |
| Twentieth Century Legacies: Pre-1930 / 26： |
| General Overview |
| Integration and Measure |
| Functional Analysis and General Topology |
| Differential Geometry and Tensor Analysis |
| Bounds and Approximations |
| Twentieth Century Legacies: Post-1930 / 27： |
| The 1930s and World War II |
| Homological Algebra and Category Theory |
| Bourbaki |
| Logic and Computing |
| Recent Trends / 28： |
| The Four Color Conjecture |
| Classification of Finite Simple Groups |
| Fermat's Last Theorem |
| Poincaré's Query |
| Future Outlook |
| References |
| General Bibliography |
| Index |
| Foreword |
| Preface to the First Edition |
| Preface to the Second Edition |
| Traces / 1： |
| Concepts and Relationships |
| Early Number Bases |
