Part I. Ancient Mathematics
1. Egypt and Mesopotamia
1.1 Egypt
1.2 Mesopotamia
2. The Beginnings of Mathematics in Greece
2.1 The Earliest Greek Mathematics
2.2 The Time of Plato
2.3 Aristotle
3. Euclid
3.1 Introduction to the Elements
3.2 Book I and the Pythagorean Theorem
3.3 Book II and Geometric Algebra
3.4 Circles and the Pentagon
3.5 Ratio and Proportion
3.6 Number Theory
3.7 Irrational Magnitudes
3.8 Solid Geometry and the Method of Exhaustion
3.9 Euclid's Data
4. Archimedes and Apollonius
4.1 Archimedes and Physics
4.2 Archimedes and Numerical Calculations
4.3 Archimedes and Geometry
4.4 Conic Sections Before Apollonius
4.5 The Conics of Apollonius
5. Mathematical Methods in Hellenistic Times
5.1 Astronomy Before Ptolemy
5.2 Ptolemy and The Almagest
5.3 Practical Mathematics
6. The Final Chapter of Greek Mathematics
6.1 Nichomachus and Elementary Number Theory
6.2 Diophantus and Greek Algebra
6.3 Pappus and Analysis
Part II. Medieval Mathematics
7. Ancient and Medieval China
7.1 Introduction to Mathematics in China
7.2 Calculations
7.3 Geometry
7.4 Solving Equations
7.5 Indeterminate Analysis
7.6 Transmission to and from China
8. Ancient and Medieval India
8.1 Introduction to Mathematics in India
8.2 Calculations
8.3 Geometry
8.4 Equation Solving
8.5 Indeterminate Analysis
8.6 Combinatorics
8.7 Trigonometry
8.8 Transmission to and from India
9. The Mathematics of Islam
9.1 Introduction to Mathematics in Islam
9.2 Decimal Arithmetic
9.3 Algebra
9.4 Combinatorics
9.5 Geometry
9.6 Trigonometry
9.7 Transmission of Islamic Mathematics
10. Medieval Europe
10.1 Introduction to the Mathematics of Medieval Europe
10.2 Geometry and Trigonometry
10.3 Combinatorics
10.4 Medieval Algebra
10.5 The Mathematics of Kinematics
11. Mathematics Elsewhere
11.1 Mathematics at the Turn of the Fourteenth Century
11.2 Mathematics in America, Africa, and the Pacific
Part III. Early Modern Mathematics
12. Algebra in the Renaissance
12.1 The Italian Abacists
12.2 Algebra in France, Germany, England, and Portugal
12.3 The Solution of the Cubic Equation
12.4 Viete, Algebraic Symbolism, and Analysis
12.5 Simon Stevin and Decimal Analysis
13. Mathematical Methods in the Renaissance
13.1 Perspective
13.2 Navigation and Geography
13.3 Astronomy and Trigonometry
13.4 Logarithms
13.5 Kinematics
14. Geometry, Algebra and Probability in the Seventeenth Century
14.1 The Theory of Equations
14.2 Analytic Geometry
14.3 Elementary Probability
14.4 Number Theory
14.5 Projective Geometry
15. The Beginnings of Calculus
15.1 Tangents and Extrema
15.2 Areas and Volumes
15.3 Rectification of Curves and the Fundamental Theorem
16. Newton and Leibniz
16.1 Isaac Newton
16.2 Gottfried Wilhelm Leibniz
16.3 First Calculus Texts
Part IV. Modern Mathematics
17. Analysis in the Eighteenth Century
17.1 Differential Equations
17.2 The Calculus of Several Variables
17.3 Calculus Texts
17.4 The Foundations of Calculus
18. Probability and Statistics in
