Praise for the Second Edition

"An amazing assemblage of worldwide contributions in mathematics
and, in addition to use as a course book, a valuable resource . . .
essential."

--CHOICE

This Third Edition of The History of Mathematics
examines the elementary arithmetic, geometry, and algebra of
numerous cultures, tracing their usage from Mesopotamia, Egypt,
Greece, India, China, and Japan all the way to Europe during the
Medieval and Renaissance periods where calculus was developed.

Aimed primarily at undergraduate students studying the history
of mathematics for science, engineering, and secondary education,
the book focuses on three main ideas: the facts of who, what, when,
and where major advances in mathematics took place; the type of
mathematics involved at the time; and the integration of this
information into a coherent picture of the development of
mathematics. In addition, the book features carefully designed
problems that guide readers to a fuller understanding of the
relevant mathematics and its social and historical context.
Chapter-end exercises, numerous photographs, and a listing of
related websites are also included for readers who wish to pursue a
specialized topic in more depth. Additional features of The
History of Mathematics, Third Edition include:

* Material arranged in a chronological and cultural context

* Specific parts of the history of mathematics presented as
individual lessons

* New and revised exercises ranging between technical, factual,
and integrative

* Individual PowerPoint presentations for each chapter and a bank
of homework and test questions (in addition to the exercises in the
book)

* An emphasis on geography, culture, and mathematics

In addition to being an ideal coursebook for undergraduate
students, the book also serves as a fascinating reference for
mathematically inclined individuals who are interested in learning
about the history of mathematics.

ROGER L. COOKE, PhD, is Williams Professor of Mathematics at the University of Vermont. His research interests include the history of mathematics and Fourier analysis, and he has taught a general introduction to the history and development of mathematics for many years.

Praise for the Second Edition

"An amazing assemblage of worldwide contributions in mathematics and, in addition to use as a course book, a valuable resource . . . essential."
CHOICE

This Third Edition of The History of Mathematics examines the elementary arithmetic, geometry, and algebra of numerous cultures, tracing their usage from Mesopotamia, Egypt, Greece, India, China, and Japan all the way to Europe during the Medieval and Renaissance periods where calculus was developed.

Aimed primarily at undergraduate students studying the history of mathematics for science, engineering, and secondary education, the book focuses on three main ideas: the facts of who, what, when, and where major advances in mathematics took place; the type of mathematics involved at the time; and the integration of this information into a coherent picture of the development of mathematics. In addition, the book features carefully designed problems that guide readers to a fuller understanding of the relevant mathematics and its social and historical context. Chapter-end exercises, numerous photographs, and a listing of related websites are also included for readers who wish to pursue a specialized topic in more depth. Additional features of The History of Mathematics, Third Edition include:

• Material arranged in a chronological and cultural context
• Specific parts of the history of mathematics presented as individual lessons
• New and revised exercises ranging between technical, factual, and integrative
• Individual PowerPoint presentations for each chapter and a bank of homework and test questions (in addition to the exercises in the book)
• An emphasis on geography, culture, and mathematics

In addition to being an ideal coursebook for undergraduate students, the book also serves as a fascinating reference for mathematically inclined individuals who are interested in learning about the history of mathematics.

PREFACE xxiii

Changes from the Second Edition xxiii

Elementary Texts on the History of Mathematics xxiv

PART I. WHAT IS MATHEMATICS?

Contents of Part I 1

1. Mathematics and its History 3

1.1. Two Ways to Look at the History of Mathematics 3

1.2. The Origin of Mathematics 5

1.3. The Philosophy of Mathematics 8

1.4. Our Approach to the History of Mathematics 11

2. Proto-mathematics 14

2.1. Number 14

2.2. Shape 16

2.3. Symbols 18

2.4. Mathematical Reasoning 20

PART II. THE MIDDLE EAST, 2000-1500 BCE

Contents of Part II 25

3. Overview of Mesopotamian Mathematics 27

3.1. A Sketch of Two Millennia of Mesopotamian History 27

3.2. Mathematical Cuneiform Tablets 29

3.3. Systems of Measuring and Counting 30

3.4. The Mesopotamian Numbering System 31

4. Computations in Ancient Mesopotamia 38

4.1. Arithmetic 38

4.2. Algebra 40

5. Geometry in Mesopotamia 46

5.1. The Pythagorean Theorem 46

5.2. Plane Figures 48

5.3. Volumes 49

5.4. Plimpton 322 49

6. Egyptian Numerals and Arithmetic 56

6.1. Sources 56

6.2. The Rhind Papyrus 58

6.3. Egyptian Arithmetic 58

6.4. Computation 59

7. Algebra and Geometry in Ancient Egypt 66

7.1. Algebra Problems in the Rhind Papyrus 66

7.2. Geometry 68

7.3. Areas 69

PART III. GREEK MATHEMATICS FROM 500 BCE TO 500 CE

Contents of Part III 77

8. An Overview of Ancient Greek Mathematics 79

8.1. Sources 80

8.2. General Features of Greek Mathematics 82

8.3. Works and Authors 87

9. Greek Number Theory 91

9.1. The Euclidean Algorithm 92

9.2. The Arithmetica of Nicomachus 93

9.3. Euclid's Number Theory 97

9.4. The Arithmetica of Diophantus 97

10. Fifth-Century Greek Geometry 103

10.1. "Pythagorean" Geometry 103

10.2. Challenge No. 1: Unsolved Problems 106

10.3. Challenge No. 2: The Paradoxes of Zeno of Elea 107

10.4. Challenge No. 3: Irrational Numbers and Incommensurable Lines 108

11. Athenian Mathematics I: The Classical Problems 115

11.1. Squaring the Circle 116

11.2. Doubling the Cube 117

11.3. Trisecting the Angle 122

12. Athenian Mathematics II: Plato and Aristotle 128

12.1. The Influence of Plato 128

12.2. Eudoxan Geometry 130

12.3. Aristotle 134

13. Euclid of Alexandria 140

13.1. The Elements 140

13.2. The Data 144

14. Archimedes of Syracuse 148

14.1. The Works of Archimedes 149

14.2. The Surface of a Sphere 150

14.3. The Archimedes Palimpsest 153

14.4. Quadrature of the Parabola 155

15. Apollonius of Perga 160

15.1. History of the Conics 161

15.2. Contents of the Conics 162

15.3. Foci and the Three- and Four-Line Locus 165

16. Hellenistic and Roman Geometry 169

16.1. Zenodorus 169

16.2. The Parallel Postulate 171

16.3. Heron 172

16.4. Roman Civil Engineering 174

17. Ptolemy's Geography and Astronomy 177

17.1. Geography 177

17.2. Astro…