Mechanics before quantum mechanics and special relativity.

Basically the same as classical mechanics.

The idea tha taking the limit of the non-classical theories for certain parameters (relativity and quantum mechanics) should lead to the classical theory.

It appears that classical limit is only very strict for relativity. For quantum mechanics it is much more hand-wavy thing. See also: Subtle is the Lord by Abraham Pais (1982) page 55.

Basically the same as classical limit, but more for quantum mechanics.