Abstract
Let ⊓(So) be the set of rectilinear congruences in Euclidean space E3 which have a common middle enveloppe with a given congruence So. In this paper we supply the set ⊓(So) with the structure of a vector space and prove that it is a real infinite dimensional vector space. Some properties of subspaces of ⊓(So) are also discussed.
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