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| Mathematics in Mesopotamia | |
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| Where Did Mathematics Begin? | |
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| Political History in Mesopotamia | |
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| The Number Symbols | |
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| Arithmetic Operations | |
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| Babylonian Algebra | |
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| Babylonian Geometry | |
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| The Uses of Mathematics in Babylonia | |
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| Evaluation of Babylonian Mathematics | |
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| Egyptian Mathematics | |
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| Background | |
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| The Arithmetic | |
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| Algebra and Geometry | |
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| Egyptian Uses of Mathematics | |
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| Summary | |
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| The Creation of Classical Greek Mathematics | |
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| Background | |
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| The General Sources | |
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| The Major Schools of the Classical Period | |
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| The Ionian School | |
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| The Pythagoreans | |
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| The Eleatic School | |
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| The Sophist School | |
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| The Platonic School | |
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| The School of Eudoxus | |
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| Aristotle and His School | |
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| Euclid and Apollonius | |
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| Introduction | |
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| The Background of Euclid's Elements | |
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| The Definitions and Axioms of the Elements | |
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| Books I to IV of the Elements | |
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| Book V: The Theory of Proportion | |
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| Book VI: Similar Figures | |
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| Books VII, VIII, and IX: The Theory of Numbers | |
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| Book X: The Classification of Incommensurables | |
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| Books XI, XII, and XIII: Solid Geometry and the Method of Exhaustion | |
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| The Merits and Defects of the Elements | |
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| Other Mathematical Works by Euclid | |
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| The Mathematical Work of Apollonius | |
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| The Alexandrian Greek Period: Geometry and Trigonometry | |
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| The Founding of Alexandria | |
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| The Character of Alexandrian Greek Mathematics | |
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| Areas and Volumes in the Work of Archimedes | |
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| Areas and Volumes in the Work of Heron | |
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| Some Exceptional Curves | |
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| The Creation of Trigonometry | |
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| Late Alexandrian Activity in Geometry | |
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| The Alexandrian Period: The Reemergence of Arithmetic and Algebra | |
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| The Symbols and Operations of Greek Arithmetic | |
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| Arithmetic and Algebra as an Independent Development | |
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| The Greek Rationalization of Nature | |
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| The Inspiration for Greek Mathematics | |
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| The Beginnings of a Rational View of Nature | |
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| The Development of the Belief in Mathematical Design | |
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| Greek Mathematical Astronomy | |
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| Geography | |
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| Mechanics | |
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| Optics | |
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| Astrology | |
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| The Demise of the Greek World | |
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| A Review of the Greek Achievements | |
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| The Limitations of Greek Mathematics | |
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| The Problems Bequeathed by the Greeks | |
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| The Demise of the Greek Civilization | |
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| The Mathematics of the Hindus and Arabs | |
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| Early Hindu Mathematics | |
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| Hindu Arithmetic and Algebra of the Period A.D. 200-1200 | |
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| Hindu Geometry and Trigonometry of the Period A.D. 200-1200 | |
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| The Arabs | |
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| Arabic Arithmetic and Algebra | |
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| Arabic Geometry and Trigonometry | |
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| Mathematics circa 1300 | |
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| The Medieval Period in Europe | |
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| The Beginnings of a European Civilization | |
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| The Materials Available for Learning | |
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| The Role of Mathematics in Early Medieval Europe | |
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| The Stagnation in Mathematics | |
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| The First Revival of the Greek Works | |
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| The Revival of Rationalism and Interest in Nature | |
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| Progress in Mathematics Proper | |
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| Progress in Physical Science | |
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| Summary | |
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| The Renaissance | |
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| Revolutionary Influences in Europe | |
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| The New Intellectual Outlook | |
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| The Spread of Learning | |
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| Humanistic Activity in Mathematics | |
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| The Clamor for the Reform of Science | |
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| The Rise of Empiricism | |
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| Mathematical Contributions in the Renaissance | |
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| Perspective | |
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| Geometry Proper | |
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| Algebra | |
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| Trigonometry | |
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| The Major Scientific Progress in the Renaissance | |
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| Remarks on the Renaissance | |
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| Arithmetic and Algebra in the Sixteenth and Seventeenth Centuries | |
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| Introduction | |
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| The Status of the Number System and Arithmetic | |
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| Symbolism | |
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| The Solution of Third and Fourth Degree Equations | |
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| The Theory of Equations | |
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| The Binomial Theorem and Allied Topics | |
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| The Theory of Numbers | |
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| The Relationship of Algebra to Geometry | |
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| The Beginnings of Projective Geometry | |
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| The Rebirth of Geometry | |
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| The Problems Raised by the Work on Perspective | |
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| The Work of Desargues | |
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| The Work of Pascal and La Hire | |
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| The Emergence of New Principles | |
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| Coordinate Geometry | |
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| The Motivation for Coordinate Geometry | |
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| The Coordinate Geometry of Fermat | |
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| Rene Descartes | |
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| Descartes's Work in Coordinate Geometry | |
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| Seventeenth-Century Extensions of Coordinate Geometry | |
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| The Importance of Coordinate Geometry | |
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| The Mathematization of Science | |
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| Introduction | |
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| Descartes's Concept of Science | |
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| Galileo's Approach to Science | |
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| The Function Concept | |
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| The Creation of the Calculus | |
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| The Motivation for the Calculus | |
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| Early Seventeenth-Century Work on the Calculus | |
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| The Work of Newton | |
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| The Work of Leibniz | |
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| A Comparison of the Work of Newton and Leibniz | |
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| The Controversy over Priority | |
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| Some Immediate Additions to the Calculus | |
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| The Soundness of the Calculus | |
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| List of Abbreviations | |
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| Index | |