The paper provides an analysis of Giuseppe Vitali’s contributions to differential geometry over the period 1923–1932. In particular, Vitali’s ambitious project of elaborating a generalized differential calculus regarded as an extension of Ricci-Curbastro tensor calculus is discussed in some detail. Special attention is paid to describing the origin of Vitali’s calculus within the context of Ernesto Pascal’s theory of forms and to providing an analysis of the process leading to a fully general notion of covariant derivative. Finally, the reception of Vitali’s theory is discussed in light of Enea Bortolotti and Enrico Bompiani’s subsequent works.

本文分析了朱塞佩·维塔利 (Giuseppe Vitali) 在 1923 年至 1932 年期间对微分几何的贡献。特别是，详细讨论了维塔利的雄心勃勃的项目，即详细阐述广义微分学，将其视为 Ricci-Curbastro 张量微积分的扩展。特别注意在埃内斯托·帕斯卡形式理论的背景下描述维塔利微积分的起源，并提供对导致协变导数的完全一般概念的过程的分析。最后，结合 Enea Bortolotti 和 Enrico Bompiani 的后续作品讨论了维塔利理论的接受情况。