Geodesic
Tangency vis-à-vis Differentiability by Peano, Severi and Guareschi
Journal of convex analysis, Tome 18 (2011) no. 2, pp. 301-339
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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. 
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     title = {Tangency vis-\`a-vis {Differentiability} by {Peano,} {Severi} and {Guareschi}},
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S. Dolecki; G. H. Greco. Tangency vis-à-vis Differentiability by Peano, Severi and Guareschi. Journal of convex analysis, Tome 18 (2011) no. 2, pp. 301-339. http://geodesic.mathdoc.fr/item/JCA_2011_18_2_JCA_2011_18_2_a0/