Now available in a new three-volume paperback edition, Morris Kline's monumental work presents the major creations in mathematics from its beginnings in Babylonia and Egypt through the first few decades of the twentieth century. Organized around the central ideas of mathematical thought, as well as the men responsible for them, this comprehensive history provides a broad panorama of the development of mathematics, displaying the unity behind the disconnected branches of the discipline today. Beginning with the origins of mathematics in Babylonia and Egypt, Volume One includes chapters on classical Greek and Alexandrian mathematics, Hindu and Arabic contributions, algebra in the sixteenth and seventeenth centuries, coordinate geometry, and the creation of calculus. Book jacket.

Morris Kline is Professor of Mathematics, Emeritus, at the Courant Institute of Mathematical Sciences, New York University, where he directed the Division of Electromagnetic Research for twenty years.

Mathematics in Mesopotamia	p. 3
Where Did Mathematics Begin?	p. 3
Political History in Mesopotamia	p. 4
The Number Symbols	p. 5
Arithmetic Operations	p. 7
Babylonian Algebra	p. 8
Babylonian Geometry	p. 10
The Uses of Mathematics in Babylonia	p. 11
Evaluation of Babylonian Mathematics	p. 13
Egyptian Mathematics	p. 15
Background	p. 15
The Arithmetic	p. 16
Algebra and Geometry	p. 18
Egyptian Uses of Mathematics	p. 21
Summary	p. 22
The Creation of Classical Greek Mathematics	p. 24
Background	p. 24
The General Sources	p. 25
The Major Schools of the Classical Period	p. 27
The Ionian School	p. 28
The Pythagoreans	p. 28
The Eleatic School	p. 34
The Sophist School	p. 37
The Platonic School	p. 42
The School of Eudoxus	p. 48
Aristotle and His School	p. 51
Euclid and Apollonius	p. 56
Introduction	p. 56
The Background of Euclid's Elements	p. 57
The Definitions and Axioms of the Elements	p. 58
Books I to IV of the Elements	p. 60
Book V: The Theory of Proportion	p. 68
Book VI: Similar Figures	p. 73
Books VII, VIII, and IX: The Theory of Numbers	p. 77
Book X: The Classification of Incommensurables	p. 80
Books XI, XII, and XIII: Solid Geometry and the Method of Exhaustion	p. 81
The Merits and Defects of the Elements	p. 86
Other Mathematical Works by Euclid	p. 88
The Mathematical Work of Apollonius	p. 89
The Alexandrian Greek Period: Geometry and Trigonometry	p. 101
The Founding of Alexandria	p. 101
The Character of Alexandrian Greek Mathematics	p. 103
Areas and Volumes in the Work of Archimedes	p. 105
Areas and Volumes in the Work of Heron	p. 116
Some Exceptional Curves	p. 117
The Creation of Trigonometry	p. 119
Late Alexandrian Activity in Geometry	p. 126
The Alexandrian Period: The Reemergence of Arithmetic and Algebra	p. 131
The Symbols and Operations of Greek Arithmetic	p. 131
Arithmetic and Algebra as an Independent Development	p. 135
The Greek Rationalization of Nature	p. 145
The Inspiration for Greek Mathematics	p. 145
The Beginnings of a Rational View of Nature	p. 146
The Development of the Belief in Mathematical Design	p. 147
Greek Mathematical Astronomy	p. 154
Geography	p. 160
Mechanics	p. 162
Optics	p. 166
Astrology	p. 168
The Demise of the Greek World	p. 171
A Review of the Greek Achievements	p. 171
The Limitations of Greek Mathematics	p. 173
The Problems Bequeathed by the Greeks	p. 176
The Demise of the Greek Civilization	p. 177
The Mathematics of the Hindus and Arabs	p. 183
Early Hindu Mathematics	p. 183
Hindu Arithmetic and Algebra of the Period A.D. 200-1200	p. 184
Hindu Geometry and Trigonometry of the Period A.D. 200-1200	p. 188
The Arabs	p. 190
Arabic Arithmetic and Algebra	p. 191
Arabic Geometry and Trigonometry	p. 195
Mathematics circa 1300	p. 197
The Medieval Period in Europe	p. 200
The Beginnings of a European Civilization	p. 200
The Materials Available for Learning	p. 201
The Role of Mathematics in Early Medieval Europe	p. 202
The Stagnation in Mathematics	p. 203
The First Revival of the Greek Works	p. 205
The Revival of Rationalism and Interest in Nature	p. 206
Progress in Mathematics Proper	p. 209
Progress in Physical Science	p. 211
Summary	p. 213
The Renaissance	p. 216
Revolutionary Influences in Europe	p. 216
The New Intellectual Outlook	p. 218
The Spread of Learning	p. 220
Humanistic Activity in Mathematics	p. 221
The Clamor for the Reform of Science	p. 223
The Rise of Empiricism	p. 227
Mathematical Contributions in the Renaissance	p. 231
Perspective	p. 231
Geometry Proper	p. 234
Algebra	p. 236
Trigonometry	p. 237
The Major Scientific Progress in the Renaissance	p. 240
Remarks on the Renaissance	p. 247
Arithmetic and Algebra in the Sixteenth and Seventeenth Centuries	p. 250
Introduction	p. 250
The Status of the Number System and Arithmetic	p. 251
Symbolism	p. 259
The Solution of Third and Fourth Degree Equations	p. 263
The Theory of Equations	p. 270
The Binomial Theorem and Allied Topics	p. 272
The Theory of Numbers	p. 274
The Relationship of Algebra to Geometry	p. 278
The Beginnings of Projective Geometry	p. 285
The Rebirth of Geometry	p. 285
The Problems Raised by the Work on Perspective	p. 286
The Work of Desargues	p. 288
The Work of Pascal and La Hire	p. 295
The Emergence of New Principles	p. 299
Coordinate Geometry	p. 302
The Motivation for Coordinate Geometry	p. 302
The Coordinate Geometry of Fermat	p. 303
Rene Descartes	p. 304
Descartes's Work in Coordinate Geometry	p. 308
Seventeenth-Century Extensions of Coordinate Geometry	p. 317
The Importance of Coordinate Geometry	p. 321
The Mathematization of Science	p. 325
Introduction	p. 325
Descartes's Concept of Science	p. 325
Galileo's Approach to Science	p. 327
The Function Concept	p. 335
The Creation of the Calculus	p. 342
The Motivation for the Calculus	p. 342
Early Seventeenth-Century Work on the Calculus	p. 344
The Work of Newton	p. 356
The Work of Leibniz	p. 370
A Comparison of the Work of Newton and Leibniz	p. 378
The Controversy over Priority	p. 380
Some Immediate Additions to the Calculus	p. 381
The Soundness of the Calculus	p. 383
List of Abbreviations
Index
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