The following translations are part of the Euler Project.
1. "On Transcendental Progressions, that is, those whose General Terms cannot be given Algebraically" (Postscript)(PDF) (E19, OO I_14, 1--24). This is the paper in which Euler first introduced the "gamma function".
2. "On the Controversy between Messrs. Leibniz and Bernoulli concerning Logarithms of Negative and Imaginary Numbers" (Postscript)(PDF) (E168, OO I_17, 195--232). Euler resolves the paradoxes by revealing that the complex logarithm is a multiple-valued function.
3. "On the Integration of the Differential Equation m dx/sqrt(1 - x^4)
= n dy/sqrt(1 - y^4)" (Postscript)(PDF)
(E251, OO I_20, 58--79). One of Euler's first major papers on elliptic
integrals. Euler derives the addition formula for the lemniscatic integral.
The expanded text of my talk "Gauss, recurrence relations, and the agM" at the session "Mathematics in the Age of Euler", Joint Mathematics Meetings, New Orleans, Lousiana, 11 January 2001. (Postscript)(PDF)
Last updated: 1-Mar-2007