Sulla ricezione del Theorema Egregium, 1828-1868

The article aims to analyze the history of the reception of Theorema Egregium in the time span between the publication of Gauss’s Disquisitiones and about 1870. Some contributions by Liouville, Bertrand, Puiseux, Chelini, Brioschi and Beltrami are carefully analyzed, by showing how the authors proposed to demonstrate this fundamental result of surface theory in a manner that highlighted its geometric content in a more satisfactory way than Gauss’s original treatment. In actual fact, most part of the ideas underlying these reformulations was already contained in the research (private and published only posthu- mously) of Gauss. Curiously, the history of the reception of Theorema Egregium in the period considered was littered with attempts, certainly unaware, to rediscover demonstrations and procedures that Gauss had deemed inadequate and that he had definitively discarded when drafting the text of the Disquisitiones. As will be shown, the reception of Gauss’s ideas produced a fruitful and in-depth debate concerning the methods and techniques that should be considered most suitable to deal with problems in the realm of the theory of surfaces.