Where in Gauss's works does he derive "Gauss's Law"?

Question

Where in Gauss's works does he derive "Gauss's Law"? Or is "Gauss's Law" named after Gauss for a different reason?

Answer 1

The law was first¹ formulated by Joseph Louis Lagrange in 1773,² followed by Carl Friedrich Gauss in 1813,³ both in the context of the attraction of ellipsoids.

^{Notes
¹ Pierre Duhem's Leçons sur l'électricité et le magnétisme (liv. 1, chap. 4, p. 22-23) shows that Lagrange has priority over Gauss. Others after Gauss discovered "Gauss's Law," too.
² Lagrange, "Sur l'attraction des sphéroïdes elliptiques" , Mémoires de l'Académie de Berlin, p. 125; 1773.
³ Gauss (C.-F.) , Theoria attractionis corporum sphœroidicorum ellipticorum homogeneorum methodo nova tractata (Gauss, Werke, t. V, p. 1). Gauss mentions Newton's related Principia proposition XCI regarding finding the force exerted by a sphere on a point anywhere along an axis passing through the spehere.}

^{(source: my recent edits on the "'Gauss's' Law" page)}