V.J. Katz in <A HREF="https://books.google.nl/books?id=7iRijkz0rrUC">History of Topology</A>:

> Although Cartan realized that the three theorems of vector calculus
> (Gauss, Green, Stokes) could be easily stated using differential
> forms, it was Edouard Goursat (1858-1936) who in 1917 [1] first noted that
> these three theorems were all special cases of a generalised Stokes
> theorem for differential forms (first stated, in coordinate free form,
> by Volterra in 1889 [2]).
> 
> [1] E. Goursat, *Sur certains systèmes d'équations aux différentielles totales et sur une généralisation du problème de Pfaff*, Ann. Fac. Sci. Toulouse (3) **7** (1917), 1--58.
> 
> [2] V. Volterra, Sulle funzioni coniugate, Rendiconti Accademia dei Licei (4) **5** (1889), 599--611.