The paper is devoted to further study of a certain type of infinitesimal transformations of two-dimensional (pseudo-) Riemannian spaces, which are called rotary. An infinitesimal transformation is called rotary if it maps any geodesic on (pseudo-) Riemannian space onto an isoperimetric extremal of rotation in their principal parts on (pseudo-) Riemannian space. We study basic equations of the infinitesimal rotary transformations in detail and obtain the simpler fundamental equations of these transformations,