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[资源] Wiley2011年英文原版A History of Mathematics, 3rd ed

1 Traces 1
Concepts and Relationships, 1 Early Number Bases, 3
Number Language and Counting, 5 Spatial Relationships, 6
2 Ancient Egypt 8
The Era and the Sources, 8 Numbers and Fractions, 10
Arithmetic Operations, 12 “Heap” Problems, 13 Geometric
Problems, 14 Slope Problems, 18 Arithmetic Pragmatism, 19
3 Mesopotamia 21
The Era and the Sources, 21 Cuneiform Writing, 22
Numbers and Fractions: Sexagesimals, 23 Positional
Numeration, 23 Sexagesimal Fractions, 25 Approximations, 25
Tables, 26 Equations, 28 Measurements: Pythagorean
Triads, 31 Polygonal Areas, 35 Geometry as Applied
Arithmetic, 36
4 Hellenic Traditions 40
The Era and the Sources, 40 Thales and Pythagoras, 42
Numeration, 52 Arithmetic and Logistic, 55
v
Fifth-Century Athens, 56 Three Classical Problems, 57
Quadrature of Lunes, 58 Hippias of Elis, 61 Philolaus
and Archytas of Tarentum, 63 Incommensurability, 65
Paradoxes of Zeno, 67 Deductive Reasoning, 70
Democritus of Abdera, 72 Mathematics and the Liberal Arts, 74
The Academy, 74 Aristotle, 88
5 Euclid of Alexandria 90
Alexandria, 90 Lost Works, 91 Extant Works, 91
The Elements, 93
6 Archimedes of Syracuse 109
The Siege of Syracuse, 109 On the Equilibriums of Planes, 110
On Floating Bodies, 111 The Sand-Reckoner, 112
Measurement of the Circle, 113 On Spirals, 113
Quadrature of the Parabola, 115 On Conoids and Spheroids, 116
On the Sphere and Cylinder, 118 Book of Lemmas, 120
Semiregular Solids and Trigonometry, 121 The Method, 122
7 Apollonius of Perge 127
Works and Tradition, 127 Lost Works, 128 Cycles
and Epicycles, 129 The Conics, 130
8 Crosscurrents 142
Changing Trends, 142 Eratosthenes, 143 Angles and
Chords, 144 Ptolemy’s Almagest, 149 Heron of Alexandria, 156
The Decline of Greek Mathematics, 159 Nicomachus of
Gerasa, 159 Diophantus of Alexandria, 160 Pappus of
Alexandria, 164 The End of Alexandrian Dominance, 170
Proclus of Alexandria, 171 Boethius, 171
Athenian Fragments, 172 Byzantine Mathematicians, 173
9 Ancient and Medieval China 175
The Oldest Known Texts, 175 The Nine Chapters, 176
Rod Numerals, 177 The Abacus and Decimal Fractions, 178
Values of Pi, 180 Thirteenth-Century Mathematics, 182
10 Ancient and Medieval India 186
Early Mathematics in India, 186 The Sulbasutras, 187
The Siddhantas, 188 Aryabhata, 189 Numerals, 191
Trigonometry, 193 Multiplication, 194 Long Division, 195
Brahmagupta, 197 Indeterminate Equations, 199 Bhaskara, 200
Madhava and the Keralese School, 202
vi Cont ent s
11 The Islamic Hegemony 203
Arabic Conquests, 203 The House of Wisdom, 205
Al-Khwarizmi, 206 ‘Abd Al-Hamid ibn-Turk, 212
Thabit ibn-Qurra, 213 Numerals, 214 Trigonometry, 216
Tenth- and Eleventh-Century Highlights, 216
Omar Khayyam, 218 The Parallel Postulate, 220
Nasir al-Din al-Tusi, 220 Al-Kashi, 221
12 The Latin West 223
Introduction, 223 Compendia of the Dark Ages, 224
Gerbert, 224 The Century of Translation, 226 Abacists
and Algorists, 227 Fibonacci, 229 Jordanus Nemorarius, 232
Campanus of Novara, 233 Learning in the Thirteenth
Century, 235 Archimedes Revived, 235 Medieval Kinematics, 236
Thomas Bradwardine, 236 Nicole Oresme, 238 The Latitude
of Forms, 239 Infinite Series, 241 Levi ben Gerson, 242
Nicholas of Cusa, 243 The Decline of Medieval Learning, 243
13 The European Renaissance 245
Overview, 245 Regiomontanus, 246 Nicolas
Chuquet’s Triparty, 249 Luca Pacioli’s Summa, 251
German Algebras and Arithmetics, 253 Cardan’s Ars Magna, 255
Rafael Bombelli, 260 Robert Recorde, 262 Trigonometry, 263
Geometry, 264 Renaissance Trends, 271 Franc¸ois Vie`te, 273
14 Early Modern Problem Solvers 282
Accessibility of Computation, 282 Decimal Fractions, 283
Notation, 285 Logarithms, 286 Mathematical Instruments, 290
Infinitesimal Methods: Stevin, 296 Johannes Kepler, 296
15 Analysis, Synthesis, the Infinite, and Numbers 300
Galileo’s Two New Sciences, 300 Bonaventura Cavalieri, 303
Evangelista Torricelli, 306 Mersenne’s Communicants, 308
Rene′ Descartes, 309 Fermat’s Loci, 320 Gregory of
St. Vincent, 325 The Theory of Numbers, 326
Gilles Persone de Roberval, 329 Girard Desargues and
Projective Geometry, 330 Blaise Pascal, 332 Philippe
de Lahire, 337 Georg Mohr, 338 Pietro Mengoli, 338
Frans van Schooten, 339 Jan de Witt, 340 Johann Hudde, 341
Rene′ Franc¸ois de Sluse, 342 Christiaan Huygens, 342
16 British Techniques and Continental Methods 348
John Wallis, 348 James Gregory, 353 Nicolaus Mercator and
William Brouncker, 355 Barrow’s Method of Tangents, 356
Content s vii
Newton, 358 Abraham De Moivre, 372 Roger Cotes, 375
James Stirling, 376 Colin Maclaurin, 376 Textbooks, 380
Rigor and Progress, 381 Leibniz, 382 The Bernoulli
Family, 390 Tschirnhaus Transformations, 398 Solid
Analytic Geometry, 399 Michel Rolle and Pierre Varignon, 400
The Clairauts, 401 Mathematics in Italy, 402 The Parallel
Postulate, 403 Divergent Series, 404
17 Euler 406
The Life of Euler, 406 Notation, 408 Foundation of
Analysis, 409 Logarithms and the Euler Identities, 413
Differential Equations, 414 Probability, 416 The Theory of
Numbers, 417 Textbooks, 418 Analytic Geometry, 419
The Parallel Postulate: Lambert, 420
18 Pre to Postrevolutionary France 423
Men and Institutions, 423 The Committee on Weights
and Measures, 424 D’Alembert, 425 Be′zout, 427
Condorcet, 429 Lagrange, 430 Monge, 433 Carnot, 438
Laplace, 443 Legendre, 446 Aspects of Abstraction, 449
Paris in the 1820s, 449 Fourier, 450 Cauchy, 452
Diffusion, 460
19 Gauss 464
Nineteenth-Century Overview, 464 Gauss: Early Work, 465
Number Theory, 466 Reception of the Disquisitiones
Arithmeticae, 469 Astronomy, 470 Gauss’s Middle Years, 471
Differential Geometry, 472 Gauss’s Later Work, 473
Gauss’s Influence, 474
20 Geometry 483
The School of Monge, 483 Projective Geometry: Poncelet and
Chasles, 485 Synthetic Metric Geometry: Steiner, 487
Synthetic Nonmetric Geometry: von Staudt, 489 Analytic
Geometry, 489 Non-Euclidean Geometry, 494 Riemannian
Geometry, 496 Spaces of Higher Dimensions, 498
Felix Klein, 499 Post-Riemannian Algebraic Geometry, 501
21 Algebra 504
Introduction, 504 British Algebra and the Operational
Calculus of Functions, 505 Boole and the Algebra of Logic, 506
Augustus De Morgan, 509 William Rowan Hamilton, 510
Grassmann and Ausdehnungslehre, 512 Cayley and Sylvester, 515
Linear Associative Algebras, 519 Algebraic Geometry, 520
Algebraic and Arithmetic Integers, 520 Axioms of Arithmetic, 522
viii Cont ent s
22 Analysis 526
Berlin and Go¨ttingen at Midcentury, 526 Riemann in
Go¨ttingen, 527 Mathematical Physics in Germany, 528
Mathematical Physics in English-Speaking Countries, 529
Weierstrass and Students, 531 The Arithmetization of
Analysis, 533 Dedekind, 536 Cantor and Kronecker, 538
Analysis in France, 543
23 Twentieth Century Legacies 548
Overview, 548 Henri Poincare′, 549 David Hilbert, 555
Integration and Measure, 564 Functional Analysis and
General Topology, 568 Algebra, 570 Differential Geometry
and Tensor Analysis, 572 Probability, 573 Bounds and
Approximations, 575 The 1930s and World War II, 577
Nicolas Bourbaki, 578 Homological Algebra
and Category Theory, 580 Algebraic Geometry, 581
Logic and Computing, 582 The Fields Medals, 584
24 Recent Trends 586
Overview, 586 The Four-Color Conjecture, 587
Classification of Finite Simple Groups, 591 Fermat’s
Last Theorem, 593 Poincare′’s Query, 596 Future Outlook, 599
References, 601
General Bibliography, 633
Index, 647
Content s

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