Axiomatizations of Euclidean geometry in terms of points, equilateral triangles or squares, and incidence. (Q1890449)

In this paper the axiomatization of dimension-free Euclidean geometry is discussed. Primitive notions are point and equilateral triangle and the incidence of point and (side of) triangle. Some predicates and axioms are given such that one gets an equivalent formulation of an axiom system of \textit{W. Schwabhäuser, W. Szmielew} and \textit{A. Tarski} [Metamathematische Methoden in der Geometrie. Teil I: Ein axiomatischer Aufbau der euklidischen Geometrie. Springer-Verlag (1983; Zbl 0564.51001)]. Similar results are given for point, square and incidence as primitive notions.