He used them to transform Laplace's equation into ellipsoidal coordinates and so separate the variables and solve the resulting equation.
2.
In general, a focaloid could be understood as a shell consisting out of two closed coordinate surfaces of a confocal ellipsoidal coordinate system.
3.
However, there are other orthogonal coordinate systems in three dimensions that cannot be obtained by projecting or rotating a two-dimensional system, such as the ellipsoidal coordinates.
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