## Leonhard Euler: Life, Work and LegacyThe 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 |

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### Contents

1 | |

5 | |

Leonhard Euler and Russia | 61 |

Princess Dashkova Euler and the Russian Academy of Sciences | 75 |

Leonhard Euler and Philosophy | 97 |

Images of Euler | 109 |

Euler and Applications of Analytical Mathematics to Astronomy | 121 |

Euler and Indian Astronomy | 147 |

The Geometry of Leonhard Euler | 303 |

From Euler through Vandermonde to Gauss | 323 |

A Study in Mathematical Invention | 363 |

Euler and Lotteries | 385 |

Eulers Science of Combinations | 395 |

The Truth about Königsberg | 409 |

The Polyhedral Formula | 421 |

On the Recognition of Euler among the French 1790 1830 | 441 |

Euler and Kinematics | 167 |

Euler on Rigid Bodies | 195 |

Eulers Analysis Textbooks | 213 |

Euler and the Calculus of Variations | 235 |

Euler DAlembert and the Logarithm Function | 255 |

Some Facets of Eulers Work on Series | 279 |

### Common terms and phrases

Acad algebraic analysis astronomer axes axis Basel Basel problem Berlin Academy Bernoulli numbers Calculus of Variations Cauchy century Christian Goldbach Clairaut coefficients coordinate correspondence curve cyclotomy d’Alembert Daniel Bernoulli derived differential equations Euler wrote example expression Fermat’s function Gauss geometrical Goldbach infinite infinitesimal integral Introductio inverse-square law Jakob Bernoulli Johann Johann Bernoulli kinematics l’Académie Lagrange Laplace later Leibniz Leonhard Euler letter logarithms lottery lunar mathematical mathematicians mathématiques Maupertuis mechanics Mémoires method Monge motion Newton notation nth roots number theory Opera omnia paper Paris Petersburg Petersburg Academy Petropolitanae plane Poinsot polyhedra polyhedral formula polyhedron polynomial position prime Princess Dashkova principle prize problem proof published quantities Reichsthaler relation Reprinted in OO rigid body roots of unity rotation Russian Saturn Schrödinger Sciences sequence solution square surface theorem tion translation values Vandermonde vector velocity volume