In this paper we present for the first time a part of the correspondence between Tullio Levi-Civita and Jan Arnoldus Schouten, in the period from May 1918 to April 1919. These letters recount the story of the common and independent discovery of a geometrical interpretation of the covariant derivative. Furthermore, they offer the occasion to reflect upon the quite diverging technical choices adopted by the two mathematicians. The transcription of the letters along with some commentary remarks is preceded by two introductory sections in which the relevant contributions of Levi-Civita and Schouten are dealt with. Il presente articolo offre, per la prima volta, una trascrizione di parte della corrispondenza scientifica di Tullio Levi-Civita e Jan Arnoldus Schouten. Il periodo di riferimento va dal Maggio 1918 sino all'Aprile 1919. Le lettere raccontano l'episodio della contemporanea e indipendente scoperta di una interpretazione geometrica della derivata covariante. La corrispondenza offre l'occasione per riflettere sulla diversità delle scelte tecniche operate dai due matematici. La trascrizione delle lettere, unitamente a note di commento, è preceduta da due sezioni introduttive nelle quali sono analizzati i contributi di Levi-Civita e di Schouten sull'argomento.
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