An algebraic problem that is notable for some quite extraordinary relations
Eneström says that this work contains orthogonality conditions for rectangular corrdinates in space. He also says that Euler will express the coefficients of linear homogeneous transformations that let a sum of n square numbers remain constant using trigonometric functions for n = 3, 4, and 5, and also using rational parametric functions for n = 3 and 4.
Original Source Citation
Novi Commentarii academiae scientiarum Petropolitanae, Volume 15, pp. 75-106.
Opera Omnia Citation
Series 1, Volume 6, pp.287-315.