Keyword: «lobachevskian geometry»

The paper is devoted to the historical development of geometry. The purpose of the research is to show that apart from the geometry, which is taught in schools and universities, there is another geometry, called Lobachevskian geometry. It significantly differs from the Euclidean geometry. Coming from delivered purposes, the following major objectives are identified in this work: the main provisions of Euclidean geometry and the foundations of the Lobachevskian geometry, the consistency of Lobachevskian geometry. The paper will be useful to students of physical and mathematical departments of universities and pedagogic institutions of higher education. It can be used by lecturers and students in classes with profound study of mathematics.