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The Nodding Sphere and the Bird's Beak: D'Alembert's Dispute with Euler

Robert E. Bradley

1749 was a typically productive year in the middle period of Leonhard Euler’s career.  Among the many articles he prepared for publication that year, five were destined for the journal of the Berlin Academy, where he was the director of the mathematics department.  However, four of these provoked controversy with Jean le Rond d’Alembert, who believed that one of the articles was mistaken and the other three contained results that he himself had first discovered and for which Euler had not given him due credit.

The purpose of this article is to explain this controversy between Euler and d’Alembert and to provide links to English translations of all four of the offending articles, as well as of the brief notice that Euler inserted in the 1750 volume of the Academy’s journal, where he acknowledged d’Alembert’s priority for two of the papers in question.

Leonhard Euler


Jean le Rond d'Alembert


If you want to go directly to the translations, here are the links:

"On the Controversy between Messrs. Leibniz and Bernoulli concerning Logarithms of Negative and Imaginary Numbers"

"Research on the Precession of the Equinoxes and on the Nutation of the Earth's Axis"

"On the Cuspidal Point of the second kind of Monsieur le Marquis de l'Hospital"

"Investigations on the Imaginary Roots of Equations"

"Notice on the Subject of Recherches sur la précession des équinoxes"

Robert E. Bradley, "The Nodding Sphere and the Bird's Beak: D'Alembert's Dispute with Euler," Convergence (July 2012)