  There are significant differences between Helmholtz and Hodge's decomposition
theorems, but both share a common flavor. This paper is a first step to bring
them together.
  We here produce Helmholtz theorems for differential 1-forms and 2-forms in
3-D Euclidean space. We emphasize their common structure in order to facilitate
the understanding of another paper, soon to be made public, where a Helmholtz
theorem for arbitrary differential forms in arbitrary Euclidean space is
presented and which allows one to connect (actually to derive from it) an
improvement of Hodge's decomposition theorem.
