A theory of magnitudes involves criteria for their equivalence, comparison and addition. In this article we examine these aspects from an abstract viewpoint, by focusing on the so-called De Zolt’s postulate in the theory of equivalence of plane polygons (“If a polygon is divided into polygonal parts in any given way, then the union of all but one of these parts is not equivalent to the given polygon”). We formulate an abstract version of this postulate and derive it from some selected principles for magnitudes. We also formulate and derive an abstract version of Euclid’s Common Notion 5 (“The whole is greater than the part”), and analyze its logical relation to the former proposition. These results prove to be relevant for the clarification of some key conceptual aspects of Hilbert’s proof of De Zolt’s postulate, in his classical Foundations of Geometry (1899). Furthermore, our abstract treatment of this central proposition provides interesting insights for the development of a well-behaved theory of compatible magnitudes.

量值理论涉及它们的等价、比较和相加的标准。在这篇文章中，我们从一个抽象的角度来研究这些方面，通过关注平面多边形等价理论中所谓的德佐尔特假设（“如果一个多边形以任何给定的方式划分为多边形部分，那么所有多边形的并集但这些部分之一不等同于给定的多边形”）。我们制定了这个假设的抽象版本，并从一些选定的量级原则中推导出它。我们还制定和推导了欧几里得公用概念 5（“整体大于部分”）的抽象版本，并分析了它与前一个命题的逻辑关系。这些结果证明与阐明希尔伯特证明德佐尔特公设的一些关键概念方面有关，在他的经典著作中几何基础（1899）。此外，我们对这一中心命题的抽象处理为发展良好的相容量级理论提供了有趣的见解。