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Correspondence with P.-L. M. de Maupertuis and Frédéric II. Edited by Pierre Costabel, Eduard Winter, Ašot T. Grigorijan (Ashot T. Grigoriyan) and Adolf P. Juškevič (A. P. Jushkevich). With the collaboration of Emil A. Fellmann. (Correspondance avec P.-L. M. de Maupertuis et Frédéric II.) (French) Zbl 0587.01022

Leonhardi Euleri Opera Omnia. Series Quarta A: Commercium Epistolicum 6. Basel: Birkhäuser Verlag (ISBN 978-3-7643-1184-1/hbk). xi, 454 p. (1986).
[As of today only vol. I (1975) and vol. V (1980) have appeared, cf. Zbl 0323.01018 and Zbl 0462.01022.]
Of the 134 extant letters of the correspondence between Euler and Maupertuis, only 5 are by Maupertuis. Euler left nothing of the correspondence, while Maupertuis instructed La Condamine to destroy all his autograph manuscripts after his death. Since 1960, photocopies have been preserved at the Académie des Sciences in Paris, the majority of the documents themselves being in private possession, and the complete texts, published here for the first time, have been taken from these photocopies. The correspondence of Euler with Frederick the Great has been published previously in the Oeuvres de Fréderic le Grand (Berlin, 1852), vol. 20. For the present edition, comprising 87 letters, of which 28 were written by Euler, and 17 appended documents, all the texts have been verified and corrected, and four new letters added. In both sets of correspondence, the letters are reproduced in the original languages (French, German or Latin) and the Latin letters are accompanied by a French translation prepared by Robert Halleux. Commentaries and notes throughout are in French.
In 1738, three years before Euler departed from St. Petersburg for Berlin, Maupertuis initiated the correspondence, which continued until 1759 when Maupertuis died in Basel. The early letters concerned Euler’s mechanics and Maupertuis’ book on the figure of the earth. Having developed the expression for the flattening towards the poles as a series, whereas Newton had used only an approximation, Euler welcomed the prospect of a collaboration with Maupertuis that would enable him to determine the law of density of the earth by a comparison of theory and observation, but he had overestimated Maupertuis’ capacity as a mathematician and the correspondence soon oriented itself towards the affairs of the Berlin Academy, of which Maupertuis became the president in 1746.
As director of the mathematical class, Euler collaborated closely with Maupertuis in the direction of the Academy, and in effect acted as president when Maupertuis was absent from Berlin, either with the king in Potsdam or in France on account of his health. Besides such things as the nomination of new members and the choice of subjects for prizes, scientific questions were also discussed. In some cases Euler’s letters contain supplements to his published memoirs. The topic of greatest interest to the historian, which figures prominently in the correspondence, is that of the principle of least action. For the history of this principle in the eighteenth century, the correspondence is an essential supplement to the documents cited in volume 5 of Series II of the Opera omnia.
Although Euler had little personal contact with Frederick the Great, their correspondence lasted from 1741 to 1777, with a long gap after 1766 when Euler returned to St. Petersburg. On occasions, the king sought the advice of Euler on important appointments, such as that of a successor to Wolff at Halle and the nomination of Albrecht von Haller as chancellor of the University. The correspondence also contains much of scientific interest, such as the responses of Euler to practical questions posed by the king. These included problems of navigation in the Finow canal, the working of a hydraulic machine, the improvement of windmills and plans for a lottery in five classes. These replies are to be found not in the letters themselves but in the appended documents, which are printed immediately after the letters, except for those already published in other volumes of the Opera omnia.
Each set of letters is preceded by an introduction, giving a general description of the contents and the historical background, while the commentary notes appended to each document are detiled, comprehensive and informative. A set of carefully prepared indexes enables the reader to locate the texts relevant to any particular topic without difficulty.
Reviewer: E.J.Aiton

MSC:

01A75 Collected or selected works; reprintings or translations of classics
01A50 History of mathematics in the 18th century
01A70 Biographies, obituaries, personalia, bibliographies

Biographic References:

de Maupertuis, P.-L. M.; Friedrich II
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