Complex sentence: The orthogonal transformations in the space are those automorphisms which preserve the value of the bilinear form between every pair of vectors; in Euclidean space, this corresponds to preserving distances and angles.
Split into simpler sentences: The orthogonal transformations in the space are those automorphisms which preserve the bilinear form between any pair of vectors. In Euclidean space, this corresponds to preserving distances and angles.