This paper presents the contents, the scientific progress and the differences with respect to Genocchi's lectures and the debates that surrounded the writing of the Genocchi-Peano treatise (1884). The study of the correspondence between Genocchi and his contemporaries sheds light on the context of the publication of the volume (Genocchi at first refused to put his name on it) and how Genocchi's behaviour changed after comments were received from abroad. An examination of three manuscript versions of Genocchi's unpublished lectures, conserved in the archives of Piacenza and Torino, shows the extent of the influence exerted on Peano by his master, the differences between the teachings of the two mathematicians, and the accurate studies by Peano of the most important treatises of his time. Thanks to the marginalia, noted by Peano on his copy, it is possible to follow the development of the research undertaken by Peano in the years 1884-1899, when the German version was published, and the progression to the logical notations in his research and teaching in the field of analysis.

Category	Quartile
哲学	4
哲学, 科学史与科学哲学	4
哲学, 数学跨学科应用	4

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Category	Quartile
MATHEMATICS, INTERDISCIPLINARY APPLICATIONS	4