The article deals with the connection between the second postulate of Euclid and non-Euclidean geometry. It is shown that the violation of the second postulate of Euclid inevitably leads to hyperbolic geometry. This eliminates misunderstandings about the sums of some divergent series. The connection between hyperbolic geometry and relativistic computations is noted. It is stated also that there are more tight binding between the second and fifth Euclid postulates than it seemed before.