De Zolt’s Postulate: The Abstract Approach

A theory of magnitudes involves criteria for their equivalence, comparison and addition. In this chapter we examine these aspects from an abstract viewpoint, by focusing on a central proposition in the geometrical theory of equivalence, namely the so-called De Zolt’s postulate. This theory investigates criteria for the equality of area of polygonal figures on the basis of its decomposition and composition in polygonal components respectively congruent. We formulate an abstract version of De Zolt’s postulate and derive it from some selected principles related to the comparison, equivalence and addition of magnitudes.