Foundations of geometry in the works of B.F. Kagan (1869-1953)

At the end of the nineteenth century, the attention of many mathematicians around the world was focused on the foundations of mathematics in general and geometry in particular. T. Levi-Civita (Levi-Civita Tullio, 1873-1941), M. Pieri (Pieri Mario, 1860-1913), F. Shur (Schur Friedrich, 1856-1932) and many others offered their geometric systems. D. Hilbert (David Hilbert, 1862-1943) also was interested in questions of foundations of geometry. In 1899 he published the work "Foundations of geometry", in which he sets out his version of the axioms, and built on its base geometry.
D. Hilbert's work caused a great discussion among mathematicians from different countries. The mathematicians of Novorossiysk University also did not stand aside. Since the late 80's of the nineteenth century B. F. Kagan (Kagan Benjamin Fedorovich, 1869-1953) and S. O. Shatunovsky (Shatunovsky Samuel Osipovich, 1859-1929) were working on the foundations of mathematics.
In his works [1]-[4] B.F,Kagan proposed his own axiomatics of geometry, based not on the concept of congruence, as in Hilbert, but on the concept of distance.
1) Kagan V. F., Etudes on the foundations of geometry. Bulletin of experimental physics and elementary mathematics, Odessa, 1901, vol. №308, p. 174-185, №311 p. 254-260, № 312 p. 186-192
2) Kagan V. F. System of premises defining Euclidean geometry // Notes of the Mathematical Department of the Novorossiysk society of natural scientists. — 1902. — Vol. XX. — P. 67-105.
3) V. F. Kagan, Foundations of geometry. Vol.1. Experience of justification of Euclidean geometry. — Odessa: Economic printing house, 1905. — 794 p.
4) V. F. Kagan, Foundations of geometry. Vol.2. Historical sketch of the development of the doctrine of the foundations of geometry. — Odessa: Economic printing house, 1907. — 556 p.