## Table of Contents

**1. Egyptian Mathematics.**

Numeration. Arithmetic Operations. Problem Solving. Geometry.

**2. Babylonian Mathematics.**

Numeration and Computation. Problem Solving. Geometry.

**3. Greek Arithmetic.**

Numeration and Computation. The Pythagoreans. The Irrational.

**4. Pre-Euclidean Geometry.**

Thales and Pythagoras. The Athenian Empire. The Age of Plato.

**5. The**

*Elements*.

Deductive Geometry. Rectilinear Figures. Parallel Lines. Geometric Algebra. Circles. Ratio and Proportion. The Quadratic Equation. Number Theory. The Method of Exhaustion. Book XIII.

**6. Archimedes and Apollonius.**

Circles. Spheres, Cones, and Cylinders. Quadratures. Large Numbers. Vergings and Loci. Apollonius's

*Conics*. Loci and Extrema.**7. Roman Era.**

Numeration and Computation. Geometry and Trigonometry. Heron of Alexandria. Diophantus. The Decline of Classical Learning.

**8. China and India.**

Chinese Numeration and Computation. Practical Mathematics in China. Indian Problem Solving. Indian Geometry.

**9. The Islamic World.**

Numeration and Computation. Al Khwarizami. Other Algebras. Geometry and Trigonometry.

**10. Medieval Europe.**

The Early Medieval Period. Leonardo of Pisa. The High Middle Ages. Nicholas Oresme.

**11. Renaissance.**

Trigonometry. The Rise of Algebra. The Cossists. Simon Stevin. Francois Viete. The Development of Logarithms.

**12. The Era of Descartes and Fermat.**

Algebra and Geometry. Number Theory. The Infinite and Infinitesimals. The Tangent and Quadrature Problems. Probability. The Sums of Powers. Projective Geometry.

**13. The Era of Newton and Leibniz.**

John Wallis. Issac Barrow. The Low Countries. Isaac Newton. Fluxions. Leibniz. Johann Bernoulli.

**14. Probability and Statistics.**

Jakob Bernoulli. Abraham De Moivre. Daniel Bernoulli. Paradoxes and Fallacies. Simpson. Bayes's Theorem.

**15. Analysis.**

Leonhard Euler. Calculus Textbooks. Mathematical Physics. Trigonometric Series.

**16. Algebra.**

Newton and Algebra. Maclaurin. Euler and Algebra.

**17. Number Theory.**

Euler and Fermat's Conjectures. The Berlin Years. Return to St. Petersburg.

**18. The Revolutionary Era.**

Analysis. Algebra and Number Theory. Probability and Statistics. Mathematics of Society.

**19. The Age of Gauss.**

The Roots of Equations. Solvability of Equations. The Method of Least Squares. Number Theory. Geometry.

**20. Analysis to Midcentury.**

Foundation of Analysis. Abel. Fourier Series. Transcendental Numbers. Chebyshev.

**21. Geometry.**

Analytic and Projective Geometry. Differential Geometry. The Fifth Postulate. Consistency of Geometry.

**22. Analysis After Midcentury.**

Analysis in Germany. The Real Numbers. The Natural Numbers. The Infinite. Dynamical Systems.

**23. Algebras.**

The Algebra of Logic. Vector Algebra. Matrix Algebra. Groups. Algebra in Paris.

**24. The Twentieth Century.**

The Hilbert Problems. The Consistency of Arithmetic. Real Analysis. Topology. The Theory of Games. Computer Science. Solved Problems. Unsolved Problems.

**Appendix A: Answers to Selected Exercises.**

**Appendix B: Select Bibliography.**

**Index.**

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