 Bolzano began his mathematical investigations with a work in geometry (Bolzano 1804) and continued with publications in the area of analysis. He essentially formulated the modern criterion of convergence in his Purely Analytic Proof (Bolzano 1817, 11 f.) already four years prior to Cauchy’s Course d’analyse (1821). This work already contains the so-called Bolzano-Weierstrass theorem, which again occurs in Bolzano’s posthumously edited Theory of Functions (Bolzano 1930, 28 f., BGA IIA, 10/1: 47 f.). Here (Bolzano 1930, 66–70, 98 f., BGA IIA, 10/1: 79–82, 103) we find also for the first time an example of a continuous and still non-differentiable function; for a long time, Weierstrass had been regarded as the first one who discovered such functions, until historical justice was done by Karel Rychlík’s investigations.