《122 Translation of E 105 Final Nov 10 09》.pdf

1 Translation of Euler’s paper E105 -- Memoire sur la plus grande equation des planetes (Memoir on the Maximum value of an Equation of the Planets) Originally published in Memoires de lacademie des sciences de Berlin 2, 1748, pp. 225-248 Opera Omnia: Series 2, Volume 28, pp. 252 – 268 Reviewed in Nouvelle bibliothèque Germanique 5, 1749, pp. 18-19 Translated by Jasen A. Scaramazza and Thomas J. Osler Mathematics Department Rowan University Glassboro, NJ 08028 Osler@rowan.edu Introduction to the translation: This translation is the result of a fortunate collaboration between student and professor. Jasen Scaramazza is an undergraduate mathematics and physics major at Rowan University. Tom Osler has been a mathematics professor for 49 years. Together we struggled to understand this astronomical work. Jasen translated Euler’s paper from French to English and both he and Tom worked to comprehend Euler’s achievement. When translating Euler’s words, we tried to imagine how he would have written had he been fluent in modern English and familiar with today’s mathematical jargon. Often he used very long sentences, and we sometimes converted these to several shorter ones. However, in almost all cases we kept his original notation, even though some is very dated. We thought this added to the charm of the paper. Euler was very careful in proof reading his work, and we found few typos. When we found an error, we called a