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The late Carl B. Boyer was a professor of Mathematics at Brooklyn College and the author of several classic works on the history of mathematics.
Foreword | |
Preface to the First Edition | |
Preface to the Second Edition | |
Traces | |
Concepts and Relationships | |
Early Number Bases | |
Number Language and Counting | |
Spatial Relationships | |
Ancient Egypt | |
The Era and the Sources | |
Numbers and Fractions | |
Arithmetic Operations | |
"Heap" Problems | |
Geometric Problems | |
Slope Problems | |
Arithmetic Pragmatism | |
Mesopotamia | |
The Era and the Sources | |
Cuneiform Writing | |
Numbers and Fractions; Sexagesimals | |
Positional Numeration | |
Sexagesimal Fractions | |
Approximations | |
Tables | |
Equations | |
Measurements: Pythagorean Triads | |
Polygonal Areas | |
Geometry as Applied Arithmetic | |
Hellenic Traditions | |
The Era and the Sources | |
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 | |
Alexandria | |
Lost Works | |
Extant Works | |
The Elements | |
Archimedes of Syracuse | |
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 | |
Works and Tradition | |
Lost Works | |
Cycles and Epicycles | |
The Conics | |
Cross-Currents | |
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 | |
The Oldest Known Texts | |
The Nine Chapters | |
Rod Numerals | |
The Abacus and Decimal Fractions | |
Values of Pi | |
Thirteenth-Century Mathematics | |
Ancient and Medieval India | |
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 | |
Arabic Conquests | |
The House of Wisdom | |
al-Khwarizmi | |
'Abd Al-Hamid ibn-Turk | |
Thabit ibn Qurra | |
Numerals | |
Trigonometry | |
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 | |
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 | |
Overview | |
Regiomontanus | |
Nicolas Chuquet's Triparty | |
Luca Pacioli's Summa | |
German Algebras and Arithmetics | |
Cardan's Ars Magna | |
Rafael Bombelli | |
Robert Recorde | |
Trigonometry | |
Geometry | |
Renaissance Trends | |
François Viète | |
Early Modern Problem Solvers | |
Accessibility of Computation | |
Decimal Fractions | |
Notation | |
Logarithms | |
Mathematical Instruments | |
The Infinite and Italian Curves | |
Infinitesimal Methods: Stevin | |
Johannes Kepler | |
Galileo's Two New Sciences | |
Bonaventura Cavalieri | |
Evangelista Torricelli | |
Analysis, Synthesis, and Numbers | |
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 | |
John Wallis | |
James Gregory | |
Nicolaus Mercator and William Brouncker | |
Barrow's Method of Tangents | |
Newton | |
Abraham De Moivre | |
Leibniz and Continental Methods | |
Leibniz: Early Career and Travels | |
The Bernoulli Family | |
Tschirnhaus Transformations | |
Solid Analytic Geometry | |
Michel Rolle and Pierre Varignon | |
The Clairauts | |
Mathematics in Italy | |
The Parallel Postulate | |
Divergent Series | |
Euler | |
Life of Euler | |
Notation | |
Foundation of Analysis | |
Logarithms and the Euler Identities | |
Differential Equations | |
Probability | |
Theory of Numbers | |
Textbooks | |
Analytic Geometry | |
The Parallel Postulate: Lambert | |
Pre- to Post-Revolutionary France | |
Men and Institutions | |
The Committee on Weights and Measures | |
D?Alembert | |
B‚zout | |
Condorcet | |
Lagrange | |
Monge | |
Carnot | |
Laplace | |
Legendre | |
Aspects of Abstraction | |
Paris in the 1820s | |
Fourier | |
Cauchy | |
Diffusion | |
Gauss | |
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 | |
Geometry | |
The School of Monge | |
Projective Geometry: Poncelet and Chasles | |
Synthetic Metric Geometry: Steiner | |
Synthetic Nonmetric Geometry: von Staudt | |
Analytic Geometry | |
Non-Euclidean Geometry | |
Riemannian Geometry | |
Spaces of Higher Dimensions | |
Felix Klein | |
Post-Riemannian Algebraic Geometry | |
Algebra | |
Introduction | |
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 | |
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 | |
Turn-of-the-Century Overview | |
Poincar‚ | |
Hilbert | |
Twentieth Century Legacies: Pre-1930 | |
General Overview | |
Integration and Measure | |
Functional Analysis and General Topology | |
Algebra | |
Differential Geometry and Tensor Analysis | |
Probability | |
Bounds and Approximations | |
Twentieth Century Legacies: Post-1930 | |
The 1930s and World War II | |
Homological Algebra and Category Theory | |
Bourbaki | |
Algebraic Geometry | |
Logic and Computing | |
Recent Trends | |
Overview | |
The Four Color Conjecture | |
Classification of Finite Simple Groups | |
Fermat's Last Theorem | |
Poincaré's Query | |
Future Outlook | |
References | |
General Bibliography | |
Index | |
Table of Contents provided by Publisher. All Rights Reserved. |