Elsevier S & T

Leonhard Euler: Life, Work and Legacy

Bradley, Robert E.; Sandifer, Ed

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Table of contents
  • Front CoverCover
  • Leonhard Euler: Life, Work and Legacyiii
  • Copyright Pageiv
  • Table of Contentsvii
  • Forewordv
  • Chapter 1 Introduction1
  • Chapter 2 Leonhard Euler: Life and Thought5
  • 1. Lineage, Youth, and Formal Education7
  • 2. Into the Colossus of the North: The Groundwork of Euler’s Research10
  • 3. In Frederician Berlin: At the Apex of His Career18
  • 4. During the Reign of Catherine the Great: The Second St. Petersburg Years50
  • Acknowledgments57
  • References57
  • Chapter 3 Leonhard Euler and Russia61
  • 1. Introduction61
  • 2. The First Petersburg Period62
  • 3. The Berlin Period63
  • 4. The Second Petersburg Period69
  • 5. Euler’s Legacy70
  • 6. Conclusion73
  • Chapter 4 Princess Dashkova, Euler, and the Russian Academy of Sciences75
  • 1. Princess Dashkova: Life in Brief to 178376
  • 2. Academic Governance: Euler, Orlov, and Domashnev80
  • 3. Princess Dashkova as Imperial Academy Director84
  • Acknowledgements95
  • Chapter 5 Leonhard Euler and Philosophy97
  • Chapter 6 Images of Euler109
  • 1. Introduction109
  • 2. Maria Sibylla Merian110
  • 3. Sokolov’s mezzotint of Euler112
  • 4. Handmann’s Pastel Painting of 1753113
  • 5. Handmann’s oil painting of 1756115
  • 6. Handmann’s large oil painting of 1756 (?)116
  • 7. Darbes’ Painting of 1778117
  • 8. Further Study120
  • Chapter 7 Euler and Applications of Analytical Mathematics to Astronomy121
  • Introduction121
  • 1. Euler’s first lunar tables, 1746123
  • 2. Mutual perturbations of Jupiter and Saturn, 1748124
  • 3. The precession of the Equinoxes and the mechanics of rigid bodies, 1751-1765134
  • 4. The inverse-square law and the motion of the lunar apse137
  • 5. Euler’s later thoughts on celestial mechanics; his Third Lunar Theory140
  • Chapter 8 Euler and Indian Astronomy147
  • 1. Introduction: Indian astronomy in the Enlightenment147
  • 2. T. S. Bayer and his work148
  • 3. Euler and Bayer150
  • 4. Indian calendrical methods and their representation in the appendices to Bayer’s Historia151
  • 5. Euler’s interpretations in the “De Indorum anno”158
  • 6. The impact of Euler’s work163
  • References165
  • Chapter 9 Euler and Kinematics167
  • 1. Introduction167
  • 2. Euler and instantaneous planar kinematics171
  • 3. Euler, acceleration, spherical and spatial kinematics175
  • 4. Final remarks192
  • Chapter 10 Euler on Rigid Bodies195
  • 1. Introduction195
  • 2. Cancellation of forces196
  • 3. An Error of Euler on Rigid Bodies206
  • References210
  • Chapter 11 Euler’s Analysis Textbooks213
  • 1. Introduction to Analysis of the Infinite214
  • 2. Basic Principles of the Differential Calculus223
  • 3. Basic Principles of the Integral Calculus228
  • 4. Conclusions231
  • References232
  • Chapter 12 Euler and the Calculus of Variations235
  • 1. Expository remarks235
  • 2. Prehistory240
  • 3. General remarks on Euler’s work241
  • 4. First period242
  • 5. Second period246
  • 6. Third period249
  • References251
  • Chapter 13 Euler, D’Alembert and the Logarithm Function255
  • 1. Introduction255
  • 2. Euler and D’Alembert256
  • 3. A History of the Logarithm Function259
  • 4. The Introductio261
  • 5. The Debate between Euler and d’Alembert263
  • 6. Euler’s First Memoir269
  • 7. Euler’s Second Memoir272
  • 8. Conclusion: D’Alembert’s Memoir273
  • Acknowledgement275
  • References275
  • Chapter 14 Some Facets of Euler’s Work on Series279
  • 1. Introduction279
  • 2. Euler and the Bernoulli numbers281
  • 3. Euler and the lack of subscripts288
  • References299
  • Chapter 15 The Geometry of Leonhard Euler303
  • 1. Introduction303
  • 2. The Tour304
  • 3. Conclusion320
  • Acknowledgements321
  • References321
  • Chapter 16 Cyclotomy: From Euler through Vandermonde to Gauss323
  • 1. Euler325
  • 2. Vandermonde331
  • 3. Gauss347
  • Acknowledgement357
  • References357
  • Chapter 17 Euler and Number Theory: A Study in Mathematical Invention363
  • 1. Introduction363
  • 2. Fermat and Number Theory363
  • 3. Goldbach and Euler367
  • 4. Fermat’s Little Theorem: First Proof371
  • 5. Fermat’s Little Theorem: Second Proof373
  • 6. The Sum of Four Squares375
  • 7. Fermat’s Little Theorem: Third Proof376
  • 8. Fermat’s Little Theorem: Fourth Proof377
  • 9. Results on Quadratic Forms379
  • 10. Fermat’s Last Theorem381
  • References383
  • Chapter 18 Euler and Lotteries385
  • 1. Introduction385
  • 2. Euler’s First Analysis387
  • 3. Euler’s Later Analyses390
  • References393
  • Chapter 19 Euler’s Science of Combinations395
  • 1. Partitions395
  • 2. Squares400
  • 3. Other Topics403
  • References407
  • Chapter 20 The Truth about Konigsberg409
  • 1. What Euler didn’t do409
  • 2. The Konigsberg bridges problem411
  • 3. Euler’s Konigsberg letters413
  • 4. Euler’s 1736 paper415
  • 5. The modern solution418
  • References420
  • Chapter 21 The Polyhedral Formula421
  • 1. The polyhedral formula422
  • 2. The flaw and the repair425
  • 3. Legendre’s proof428
  • 4. The exceptions of Lhuilier, Hessel, and Poinsot429
  • 5. Cauchy’s proof431
  • 6. Von Staudt’s proof434
  • 7. Prehistory of the polyhedral formula: Descartes’ lost notes435
  • 8. After 1850436
  • References437
  • Chapter 22 On the Recognition of Euler among the French, 1790 - 1830441
  • 1. The rise of Paris to mathematical eminence441
  • 2. Varieties in the calculus and mechanics442
  • 3. Euler’s place: preliminary remarks443
  • 4. Euler or Lagrange in the calculus and analysis?444
  • 5. Euler or Lagrange in mechanics?446
  • 6. On Laplace and his own place448
  • 7. Laplace’s programme of molecular physics, and the alternatives449
  • 8. Continuum mechanics, molecular and otherwise451
  • 9. A new tradition for the calculus: the impact of Cauchy452
  • 10. Three smaller topics452
  • 11. Three general surveys453
  • 12. Concluding remark455
  • References455
  • Chapter 23 Euler’s Influence on the Birth of Vector Mechanics459
  • 1. Introduction459
  • 2. On Euler’s conception of vectors460
  • 3. Euler’s first memoir: the solution by pure geometry464
  • 4. Euler’s second memoir: the solution by the first principles of statics467
  • 5. Impact and influence of the work468
  • Acknowledgments472
  • References473
  • Chapter 24 Euler’s Contribution to Differential Geometry and its Reception479
  • 1. Leonhard Euler’s various contributions to differential geometry479
  • 2. Reception487
  • 3. Final Remarks498
  • References499
  • Chapter 25 Euler’s Mechanics as a Foundation of Quantum Mechanics503
  • 1. Introduction503
  • 2. The contribution of Euler to mechanics504
  • 3. From Euler’s mechanics to Schrodinger’s wave function507
  • 4. Energy, paths and configurations511
  • 5. Euler’s method of maxima and minima, generalized516
  • 6. Derivation of the Schrodinger equation518
  • 7. Summary523
  • References524
  • Index527
Book details
  • Vendor Elsevier S & T
  • SKU 9780444527288
  • ISBN-13 9780080471297
  • Author Bradley, Robert E.; Sandifer, Ed
  • Category Mathematics
  • Subject History & Philosophy

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The year 2007 marks the 300th anniversary of the birth of one of the Enlightenment’s most important mathematicians and scientists, Leonhard Euler. This volume is a collection of 24 essays by some of the world’s best Eulerian scholars from seven different countries about Euler, his life and his work.

Some of the essays are historical, including much previously unknown information about Euler’s life, his activities in the St. Petersburg Academy, the influence of the Russian Princess Dashkova, and Euler’s philosophy. Others describe his influence on the subsequent growth of European mathematics and physics in the 19th century. Still others give technical details of Euler’s innovations in probability, number theory, geometry, analysis, astronomy, mechanics and other fields of mathematics and science.

- Over 20 essays by some of the best historians of mathematics and science, including Ronald Calinger, Peter Hoffmann, Curtis Wilson, Kim Plofker, Victor Katz, Ruediger Thiele, David Richeson, Robin Wilson, Ivor Grattan-Guinness and Karin Reich
- New details of Euler's life in two essays, one by Ronald Calinger and one he co-authored with Elena Polyakhova
- New information on Euler's work in differential geometry, series, mechanics, and other important topics including his influence in the early 19th century