The summation of an innumerable progression
This paper concerns the sum of reciprocal squares, which equals π2/6. Euler does not yet have the tools to find this value directly, but instead approximates it as 1.644934. He says this follows from E25 and E19, and also refers us forward to E736. Euler also brings in the harmonic series: let f(x) be the x-th partial sum of the harmonic series. He approximates this as an integral and defines the now-named Euler-Mascheroni constant g as the limit of f(x)-log(x).
Original Source Citation
Commentarii academiae scientiarum Petropolitanae, Volume 5, pp. 91-105.
Opera Omnia Citation
Series 1, Volume 14, pp.25-41.