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Foreword | |

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Preface to the First Edition | |

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Preface to the Second Edition | |

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Traces | |

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Concepts and Relationships | |

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Early Number Bases | |

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Number Language and Counting | |

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Spatial Relationships | |

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Ancient Egypt | |

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The Era and the Sources | |

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Numbers and Fractions | |

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Arithmetic Operations | |

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"Heap" Problems | |

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Geometric Problems | |

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Slope Problems | |

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Arithmetic Pragmatism | |

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Mesopotamia | |

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The Era and the Sources | |

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Cuneiform Writing | |

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Numbers and Fractions; Sexagesimals | |

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Positional Numeration | |

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Sexagesimal Fractions | |

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Approximations | |

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Tables | |

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Equations | |

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Measurements: Pythagorean Triads | |

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Polygonal Areas | |

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Geometry as Applied Arithmetic | |

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Hellenic Traditions | |

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The Era and the Sources | |

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Thales and Pythagoras | |

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Numeration | |

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Arithmetic and Logistic | |

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Fifth Century Athens | |

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Three Classical Problems | |

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Incommensurability | |

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Paradoxes of Zeno | |

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Deductive Reasoning | |

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Democritus of Abdera | |

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Mathematics and the Liberal Arts | |

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The Academy | |

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Aristotle | |

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Euclid of Alexandria | |

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Alexandria | |

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Lost Works | |

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Extant Works | |

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The Elements | |

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Archimedes of Syracuse | |

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The Siege of Syracuse | |

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On the Equilibriums of Planes | |

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On Floating Bodies | |

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The Sand-Reckoner | |

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Measurement of the Circle | |

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On Spirals | |

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Quadrature of the Parabola | |

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On Conoids and Spheroids | |

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On the Sphere and Cylinder | |

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Book of Lemmas | |

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Semiregular Solids and Trigonometry | |

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The Method | |

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Apollonius of Perge | |

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Works and Tradition | |

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Lost Works | |

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Cycles and Epicycles | |

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The Conics | |

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Cross-Currents | |

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Changing Trends | |

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Eratosthenes | |

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Angles and Chords | |

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Ptolemy's Almagest | |

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Heron of Alexandria | |

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Decline of Greek Mathematics | |

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Nichomachus of Gerasa | |

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Diophantus of Alexandria | |

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Pappus of Alexandria | |

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The End of Alexandrian Dominance | |

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Proclus of Alexandria | |

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Boethius | |

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Athenian Fragments | |

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Byzantine Mathematicians | |

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Ancient and Medieval China | |

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The Oldest Known Texts | |

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The Nine Chapters | |

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Rod Numerals | |

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The Abacus and Decimal Fractions | |

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Values of Pi | |

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Thirteenth-Century Mathematics | |

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Ancient and Medieval India | |

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Early Mathematics in India | |

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The Sulbasutras | |

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The Siddhantas | |

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Aryabhata | |

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Numerals | |

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Trigonometry | |

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Multiplication | |

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Long Division | |

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Brahmagupta | |

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Indeterminate Equations | |

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Bhaskara | |

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Madhava and the Keralese School | |

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The Islamic Hegemony | |

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Arabic Conquests | |

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The House of Wisdom | |

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al-Khwarizmi | |

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'Abd Al-Hamid ibn-Turk | |

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Thabit ibn Qurra | |

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Numerals | |

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Trigonometry | |

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Abu'l-Wefa and Al-Karkhi | |

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Al-Biruni and Alhazen | |

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Omar Khayyam | |

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The Parallel Postulate | |

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Nasir al-Din al-Tusi | |

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Al-Kashi | |

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The Latin West | |

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Introduction | |

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Compendia of the Dark Ages | |

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Gerbert | |

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The Century of Translation | |

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Abacists and Algorists | |

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Fibonacci | |

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Jordanus Nemorarius | |

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Campanus of Novara | |

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Learning in the Thirteenth Century | |

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Archimedes Revived | |

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Medieval Kinematics | |

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Thomas Bradwardine | |

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Nicole Oresme | |

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The Latitude of Forms | |

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Infinite Series | |

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Levi ben Gerson | |

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Nicholas of Cusa | |

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Decline of Medieval Learning | |

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The European Renaissance | |

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Overview | |

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Regiomontanus | |

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Nicolas Chuquet's Triparty | |

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Luca Pacioli's Summa | |

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German Algebras and Arithmetics | |

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Cardan's Ars Magna | |

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Rafael Bombelli | |

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Robert Recorde | |

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Trigonometry | |

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Geometry | |

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Renaissance Trends | |

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Franï¿½ois Viï¿½te | |

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Early Modern Problem Solvers | |

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Accessibility of Computation | |

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Decimal Fractions | |

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Notation | |

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Logarithms | |

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Mathematical Instruments | |

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The Infinite and Italian Curves | |

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Infinitesimal Methods: Stevin | |

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Johannes Kepler | |

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Galileo's Two New Sciences | |

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Bonaventura Cavalieri | |

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Evangelista Torricelli | |

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Analysis, Synthesis, and Numbers | |

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Mersenne's Communicants | |

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Descartes | |

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Fermat's Loci | |

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Gregory of St. Vincent | |

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Theory of Numbers | |

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Gilles Persone de Roberval | |

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Girard Desargues and Projective Geometry | |

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Blaise Pascal | |

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Philippe de Lahire | |

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Georg Mohr | |

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Pietro Mengoli | |

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Frans van Schooten | |

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Jan de Witt | |

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Johann Hudde | |

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Renï¿½ Franï¿½ois de Sluse | |

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Christiaan Huygens | |

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Newton and British Techniques | |

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John Wallis | |

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James Gregory | |

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Nicolaus Mercator and William Brouncker | |

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Barrow's Method of Tangents | |

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Newton | |

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Abraham De Moivre | |

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Leibniz and Continental Methods | |

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Leibniz: Early Career and Travels | |

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The Bernoulli Family | |

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Tschirnhaus Transformations | |

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Solid Analytic Geometry | |

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Michel Rolle and Pierre Varignon | |

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The Clairauts | |

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Mathematics in Italy | |

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The Parallel Postulate | |

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Divergent Series | |

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Euler | |

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Life of Euler | |

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Notation | |

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Foundation of Analysis | |

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Logarithms and the Euler Identities | |

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Differential Equations | |

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Probability | |

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Theory of Numbers | |

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Textbooks | |

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Analytic Geometry | |

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The Parallel Postulate: Lambert | |

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Pre- to Post-Revolutionary France | |

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Men and Institutions | |

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The Committee on Weights and Measures | |

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D?Alembert | |

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B‚zout | |

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Condorcet | |

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Lagrange | |

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Monge | |

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Carnot | |

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Laplace | |

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Legendre | |

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Aspects of Abstraction | |

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Paris in the 1820s | |

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Fourier | |

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Cauchy | |

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Diffusion | |

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Gauss | |

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Nineteenth-Century Overview | |

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Gauss: Early Work | |

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Number Theory | |

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Reception of the Disquisitiones Arithmeticae | |

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Astronomy | |

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Gauss's Middle Years | |

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Differential Geometry | |

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Gauss's Later Work | |

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Gauss's Influence | |

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Geometry | |

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The School of Monge | |

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Projective Geometry: Poncelet and Chasles | |

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Synthetic Metric Geometry: Steiner | |

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Synthetic Nonmetric Geometry: von Staudt | |

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Analytic Geometry | |

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Non-Euclidean Geometry | |

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Riemannian Geometry | |

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Spaces of Higher Dimensions | |

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Felix Klein | |

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Post-Riemannian Algebraic Geometry | |

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Algebra | |

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Introduction | |

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British Algebra and the Operational Calculus of Functions | |

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Boole and the Algebra of Logic | |

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Augustus De Morgan | |

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William Rowan Hamilton | |

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Grassmann and Ausdehnungslehre | |

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Cayley and Sylvester | |

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Linear Associative Algebras | |

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Algebraic Geometry | |

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Algebraic and Arithmetic Integers | |

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Axioms of Arithmetic | |

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Analysis | |

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Berlin and Gï¿½ttingen at Mid-Century | |

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Riemann in Gï¿½ttingen | |

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Mathematical Physics in Germany | |

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Mathematical Physics in English-Speaking Countries | |

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Weierstrass and Students | |

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The Arithmetization of Analysis | |

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Dedekind | |

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Cantor and Kronecker | |

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Analysis in France | |

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Poincaï¿½ and Hilbert | |

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Turn-of-the-Century Overview | |

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Poincar‚ | |

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Hilbert | |

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Twentieth Century Legacies: Pre-1930 | |

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General Overview | |

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Integration and Measure | |

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Functional Analysis and General Topology | |

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Algebra | |

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Differential Geometry and Tensor Analysis | |

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Probability | |

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Bounds and Approximations | |

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Twentieth Century Legacies: Post-1930 | |

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The 1930s and World War II | |

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Homological Algebra and Category Theory | |

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Bourbaki | |

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Algebraic Geometry | |

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Logic and Computing | |

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Recent Trends | |

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Overview | |

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The Four Color Conjecture | |

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Classification of Finite Simple Groups | |

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Fermat's Last Theorem | |

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Poincarï¿½'s Query | |

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Future Outlook | |

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References | |

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General Bibliography | |

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Index | |