E808 -- Problema algebraicum de inveniendis quatuor numeris ex datis totidem productis uniuscuiusque horum numerorum in summas trium reliquorum

(An algebraic problem of finding four numbers, given the products of each of the numbers with the sum of the three others)

(based on Jordan Bell's abstract)
Euler considers the following problem: Given a, b, c, d with a = v(x + y + z), b = x(v + y + z), c = y(v + x + z), and d = z(v + x + y), determine v, x, y, and z. He changes variables to arrive at four "nice" equations, each in terms of a new variable u and the constants a, b, c, and d.

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