The History of the Priority Dispute between Newton and Leibniz: Mathematics in History and Culture

About the Author......Page 6
Preface of the Author......Page 8
Acknowledgements......Page 14
Preface of the Editors......Page 17
Contents......Page 20
1 An Attunement......Page 25
1.1 What is it All About?......Page 26
1.2 Slope, Derivative, and Differential Quotient......Page 27
1.2.1 The Product Rule......Page 31
1.2.2 The Quotient Rule......Page 32
1.2.3 The Chain Rule......Page 33
1.3 Area, Integral, and Antidifferentiation......Page 35
1.4 Indivisibles and Infinitesimals......Page 37
1.5 ... and What is it Good For?......Page 39
2 ‘On ye Shoulders of Giants’......Page 42
2.1 Who were the Giants?......Page 44
2.2 England in the 17th Century......Page 45
2.3 John Wallis......Page 56
2.4 Isaac Barrow......Page 69
2.5.1 France on its Way to Absolutism......Page 80
2.5.2 The Netherlands and the Persistent Conflict with Spain and England......Page 86
2.6 Blaise Pascal......Page 92
2.7 Christiaan Huygens......Page 103
3 The Warriors Grow Up......Page 114
3.1.1 Childhood and Youth......Page 116
3.1.2 The Lonely Student......Page 120
3.1.3 The Way to the Infinitesimal Calculus......Page 127
3.1.4 The ‘anni mirabiles’......Page 134
3.1.5 The Professor in the Lucasian Chair......Page 139
3.1.6 Till Death: The Fight with Robert Hooke......Page 144
3.2.1 Childhood and Youth......Page 149
3.2.2 The Student......Page 153
3.2.3 The Young Doctor Utriusque Iuris......Page 156
3.2.4 Lawyer and Diplomat......Page 159
4 The Cold War Begins......Page 165
4.1 The Mathematician: Leibniz in Paris......Page 166
4.1.1 The First Journey to London......Page 170
4.1.2 The Aftermath of the Pell Affair......Page 176
4.1.3 Leibniz Conquers Mathematics......Page 177
4.2.1 The Quarrel Concerning the Rectification of Curves......Page 191
4.2.2 Turbulent Times: Hooke versus Huygens......Page 195
4.2.3 Atmospheric Disturbances......Page 200
4.3 Times are Changing......Page 201
4.3.1 Leibniz’s Letter of 30th March 1675 and its Immediate Consequence......Page 202
4.3.2 Analysis Becomes Calculus......Page 206
4.3.3 Leibniz Gains a Companion......Page 210
4.4 De quadratura arithmetica......Page 214
5 The Apparent Relaxation......Page 222
5.1 The Beginning of the Correspondence: Epistola prior......Page 223
5.2 The Second Journey to London......Page 232
5.3 The Correspondence Ends: Epistola posterior......Page 238
5.4 The Front Line in the Year 1677......Page 245
6 The Aftermath of the Principia Mathematica......Page 246
6.1.1 The Privy Councillor Leibniz – Stranded in Hanover......Page 247
6.1.2 Isaac Newton – The Hermit in Cambridge......Page 262
6.2.1 The Prehistory......Page 271
6.2.2 The Formation Phase......Page 278
6.2.3 Leibniz in Newton’s Thought......Page 281
6.2.4 The Principia Published......Page 283
6.2.5 Mr Leibniz Lays a Fuse......Page 286
6.3.1 The Situation in England......Page 287
6.3.2 Huygens as Recipient......Page 290
6.3.3 Leibniz as Recipient......Page 293
6.3.5 The First Reaction in France......Page 298
6.4 The Scholium Dedicated to Leibniz......Page 300
7 The War is getting hot......Page 302
7.1 Newton in a Political Crisis......Page 303
7.2 A Friend Appeared......Page 305
7.3.1 A Strange Couple......Page 309
7.3.2 A New Crisis......Page 312
7.3.3 Leibniz Back in Newton’s Thoughts......Page 316
7.3.4 The Monkey Bites......Page 319
7.4.1 Wallis Jars on Newton’s Nerves......Page 323
7.4.2 Newton’s Quarrel with Flamsteed......Page 327
7.4.3 Newton and the Mint......Page 333
7.5.1 Leibniz again in Hanover......Page 336
7.5.2 The Bernoulli Brothers......Page 339
7.5.3 Marquis de l’Hospital......Page 344
7.6.1 Wallis’s Algebra of 1693......Page 359
7.6.2 The Aftermath of the Problem of the Brachistochrone: The Monkey is Insulted......Page 366
7.7 Fatio’s Fate......Page 375
7.8 The ‘Case Leibniz’......Page 377
7.9 Summary and the Front Line in the Year 1699......Page 382
8 War of Extermination......Page 384
8.1.1 George Cheyne and His Effect on Newton......Page 385
8.1.2 The Response to Newton’s Opticks......Page 389
8.2.1 The Last Years in Peace......Page 392
8.2.2 John Keill Appoints Himself as the Army Commander......Page 393
8.3.1 Leibniz Asks the Royal Society for Help......Page 396
8.3.2 The Royal Society Instructs Keill......Page 399
8.4.1 The Fast Track Leading to the Commercium epistolicum......Page 403
8.4.2 The Commercium epistolicum......Page 405
8.5.1 An Error in the Principia......Page 408
8.5.2 The Second Edition of the Principia Becomes Due......Page 413
8.5.3 A Flyer is Published......Page 423
8.6 The Leibniz-Clarke Controversy......Page 428
8.7 Newton’s Account and Raphson’s History of Fluxions......Page 431
9 Beyond the Grave......Page 434
9.1.2 Newton Becomes Active Again......Page 435
9.2 Leibniz Dies......Page 438
9.3.1 Bernoulli versus Keill, but in Favour of Newton......Page 443
9.3.2 Pierre des Maizeaux and His Recueil......Page 445
9.4 Newton’s Last Years......Page 448
9.5 Newton Dies......Page 452
10 The Early Challenges......Page 459
10.1.1 A Life in North Holland......Page 461
10.1.3 The Fight Against Leibniz’s Infinitesimals of Higher Order......Page 462
10.2.1 A Life between Theology, Science, and Tar Water......Page 468
10.2.2 Berkeley’s Philosophy of Mathematics......Page 476
10.2.3 Of Infinities......Page 478
10.2.4 The Analyst......Page 480
10.3 The Reactions to Berkeley’s Critique......Page 485
10.4 The Impact of Berkley’s Critique......Page 487
11 The Aftermath of the War......Page 493
11.1 De Morgan’s Work Concerning the Priority Dispute......Page 494
11.1.1 In Search of the ‘True’ Newton......Page 495
11.1.2 The Conflict with David Brewster......Page 500
11.2 England’s Long Way to Analysis......Page 502
Epilogue......Page 511
Eberhard Knobloch’s Epilogue......Page 515
References......Page 518
List of Figures......Page 529
Index of Names......Page 551
Subject Index......Page 560