Edition of Leonhard Euler’s Contributions on Perturbation Theory in the Context of the Euler-Edition.

Leonhard Euler (1707-1783), citizen of Basel, belongs - together with members of the Bernoulli family - to the outstanding scientists of the 18th century. Uncountable discoveries in the fields of Mathematics, Astronomy, and Physics have to be ascribed to him or have their origin in his works. Euler’s life and scientific achievements were acknowledged in the commemoration of the 200st anniversary of his death in 1983. Euler is considered one of the most productive scientists of all times, and he left behind an enormous work: it consists of a series of textbooks on different topics of Mathematics and its applications to Mechanics, Astronomy and Engineering, hundreds of printed papers mainly published in the journals of the Academies of St. Petersburg and Berlin, numerous manuscripts ready for printing as well as further scientific manuscripts, note books, and an enormous scientific correspondence.

The Euler Committee of the Schweizerische Naturforschende Gesellschaft SNG (today the SANW) started about 1910 with the edition of the Collected Works with the goal of making it available to the scientific community. The edition of Euler’s Collected Works is close to completion, today. The Opera Omnia will contain the following volumes:

Series Prima (Opera mathematica) : 29 in 30 volume parts

Series Secunda (Opera mechanica et astronomica) : 31 in 32 volume parts

Series Tertia (Opera physica, Miscellanea) : 12 volumes

Series Quarta A (Commercium epistolicum) : ca. 9 bis 10 volume parts

Series Quarta B (Manuscripta) : ca. 7 volumes

The ultimate goal of the Euler-Committee consists of concluding the Work Edition (without the Series Quarta) until the 300st anniversary of Euler’s birthday in the year 2007. The Naturforschende Gesellschaft in Basel is editing the Collected Works of the Bernoulli family. Together with the Euler-Edition these editions will not only represent an invaluable tool for the historiography of the Exact Sciences but they will represent in addition a significant contribution to the Swiss culture.

The goal of this project is the edition of Volumes 26 and 27 of the second series of Leonhard Euler’s Opera omnia. It has to be considered as part of the activities of the Euler Commission of the Swiss Academy of Sciences (SAS). These volumes will contain 18 works on celestial mechanics: 2 treatises on general perturbation theory, 6 treatises on the three-body-problem, 3 treatises on Lunar theory, 3 treatises on Solar theory, 2 treatises on the rotation of the Earth, and one treatise on the great inequality of Jupiter and Saturn. The most extended work concerns the celestial mechanics of finite bodies. Including the introductions, facsimiles of selected title pages, figures, and vignettes, the Volumes 26 and 27 will contain approximately 500 pages ( = about 150 pages of introductions and summaries + about 350 pages of original text) and approximately 550 pages ( = about 200 pages of introductions and summaries + about 350 pages of original text) in quarto, respectively.

Euler’s 18 works originally contain about 800 printed pages. The editorial tasks consist of the translation of the text parts written in French and Latin into German, of the linguistic and grammatical adjustment of the original treatises, of the verification of the mathematical correctness of Euler’s treatises, of the re-calculations of numerical examples and problems, of the electronic scanning of the figures, title pages and vignettes, and of the formulation of overall introductions to the Volumes 26 and 27. These introductions will not only contain summaries of and comments to each of the individual treatises, but they must provide the scientific context of each treatise, as well. The study of Euler’s and his contemporaries‘ contributions to celestial mechanics and perturbation theory (e.g., planetary, Lunar and Solar theories, methods of orbit determination, theories of Earth rotation) would, thus, actually be an essential task in order to be able to write competent introductions on a high level of historiographical research. The central issue should be the foundation for further studies (performed in a new project) to estimate and appreciate Euler’s contributions by analyzing the development of the relevant Eulerian works and by relating them to the works of Euler’s contemporaries.