Lagrange, in his paper “Solutions analytiques de quelques problèmes sur les pyramides triangulaires,” Nouv. Mém. de l'Acad. Roy. … (de Berlin), Ann. 1773, pp. 149–176, gives unintentionally the following expression of the relationship between the mutual distances of five points in space, viz.

where, if the points be called 1, 2, 3, 4, 5, the letters

and Δ, α, α′, α″, β, β′, β″, are certain functions of the said distances.