Abstract:
Leibniz formulated the idea of constructing a special geometry - geometria situs, where the basic relation is mutual arrangement of figures. He named the corresponding calculus as analysis situs. In the 19th century, Leibniz’s ideas on the analysis situs were developed and implemented in graph theory, combinatorics, projective geometry, and the theory of finite groups. The second of Leibniz's idea relates to the construction of symbolic logic. Both ideas were developed in the XIX and XX centuries.
Euler was the first who refered to the analysis situs in his article on Konigsberg bridges (Euler L. Solutio problematis ad geometriam situs pertinentis, 1736). Euler is a founder of graph theory. The ideas of Leibniz were putted into practice in the XIX century in projective geometry. L. Carnot called the projective geometry “Géométrie de position” (1803). K.G.C. von Staudt in “Geometrie der Lage” (1847) revealed that projective geometry is the study of the relative position of points, lines and planes. Louis Poinsot constructed new star polyhedra, referring to the ideas of Leibniz.
The Leibniz's idea about analysis situs was the common source of the theory of geometric and combinatorial configurations.
In his master’s thesis of 1666 (Dissertatio de arte combinatoria), Leibniz expounded the idea of a combinatorial research method. The Leibniz's views on the high importance of combinatorial art were shared by J.J. Sylvester and A. Cayley. Sylvester coined the term "Tactic" for the part of mathematics which studies order. He attributed combinatorics, group theory, and syntax to this section.
In 1896, the American mathematician E.H. Moore introduced the term "tactical configuration" to the article "Tactical memoranda". Moore reviewed numerous examples of tactical systems and investigated their properties. The generalization of the concept "tactical configuration" was the concept "block design".
