An easy resolution to a most difficult question, where this most general form vvzz(axx+byy)2 + Δxxyy(avv+bzz)2 is required to be reduced to a square
Euler considers quadratic forms axx+2bxy+cyy, a little more general than his usual form. Biquadratic forms didn't seem to take off, though.
Original Source Citation
Mémoires de l'académie des sciences de St.-Petersbourg, Volume 9, pp. 14-19.
Opera Omnia Citation
Series 1, Volume 5, pp.71-76.