Tangency vis-à-vis Differentiability by Peano, Severi and Guareschi

G. Peano defined differentiability of functions and lower tangent cones in 1887, and upper tangent cones in 1903, but uses the latter concept already in 1887 without giving a formal definition. Both cones were defined for arbitrary sets, as certain limits of appropriate homothetic relations. Around 1930 F. Severi and G. Guareschi, in a series of mutually fecundating individual papers, characterized differentiability in terms of lower tangent cones and strict differentiability in terms of lower paratangent cones, a notion introduced, independently, by Severi and G. Bouligand in 1928. Severi and Guareschi graduated about 1900 from the University of Turin, where Peano taught till his demise in 1932