Alexander Aycock has made draft translations into German and English, available online at Euler-Kreis Mainz.
This paper contains more equations involving the Euler constant γ, relating it to logarithms, to the (now-named) Riemann zeta function, to integrals and limits, and to his function f.
Original Source Citation
Acta Academiae Scientiarum Imperialis Petropolitanae, Volume 1781: II, pp. 45-75.
Opera Omnia Citation
Series 1, Volume 15, pp.569-603.