In his 1762 paper on sound, Lagrange treats a special case of the theorem: Lagrange (1762) "Nouvelles recherches sur la nature et la propagation du son" (New researches on the nature and propagation of sound), Miscellanea Taurinensia (also known as: Mélanges de Turin ), 2: 11-172. This article is reprinted as: "Nouvelles recherches sur la nature et la propagation du son" in: Serret, J. A., ed., Oeuvres de Lagrange (Paris: Gauthier-Villars, 1867), 1: 151-316; on pp. 263-265, Lagrange transforms triple integrals into double integrals using integration by parts.
