On hexagonal three-webs formed by Cartesian net and a family of circles
By the Elie Cartan's method we prove that there are only two types of regular three-webs formed by the Cartesian net and a family of circles: three-webs ( C 1), in which the family is formed by concentric circles, and the three-webs ( C 2), where all circles of the family have the same radius, and their centers lie on a line.