E407 -- Problema algebraicum ob affectiones prorsus singulares memorabile

(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.

According to the records, it was presented to the St. Petersburg Academy on March 5, 1770.

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