In this paper we shall present, like in Euclidean space, in hyperbolic space H3 all spatial objects by projecting them in the plane of image by the use of some mapping methods. In that case we shall solve the space problems by solving the corresponding problems in a plane. We shall present some proofs, different from the proofs given by Z. A. Skopec [4], [2], related to the characteristics of projecting H3 space onto orisphere. The advantage of Skopec’s method [5] will be also emphasized. By the use of analogy with the Euclidean space we shall define, in H3 space, the distance method.