On the integration of the differential equations (m dx)/√(1–x4) = (n dy)/√(1–y4)
An Italian translation of this work has been done by Carmine Suriano.
Euler takes it for granted that the values of m and n in the title are such that m/n is rational. Euler also handles the cases where there is an arbitrary whole fourth-degree function or a special 6th-degree function under the radical sign.
Original Source Citation
Novi Commentarii academiae scientiarum Petropolitanae, Volume 6, pp. 37-57.
Opera Omnia Citation
Series 1, Volume 20, pp.58-79.