During the first half of the 20th century the Danish geometer Johannes Hjelmslev developed what he called a geometry of reality. It was presented as an alternative to the idealized Euclidean paradigm that had recently been completed by Hilbert. Hjelmslev argued that his geometry of reality was superior to the Euclidean geometry both didactically, scientifically and in practice: Didactically, because it was closer to experience and intuition, in practice because it was in accordance with the real geometrical drawing practice of the engineer, and scientifically because it was based on a smaller axiomatic basis than Hilbertian Euclidean geometry but still included the important theorems of ordinary geometry. In this paper, I shall primarily analyze the scientific aspect of Hjelmslev's new approach to geometry that gave rise to the so-called Hjelmslev (incidence) geometry or ring geometry.

在20世纪上半叶，丹麦几何学家约翰内斯·耶姆列斯列夫（Johannes Hjelmslev）开发了他所谓的现实几何。它是希尔伯特最近完成的理想欧几里德范式的替代方案。赫耶姆斯列夫（Hjelmslev）辩称，他的现实几何无论是在理论上，科学上还是在实践上都优于欧几里得几何：在理论上，因为它更接近经验和直觉，在实践中是因为它符合工程师的真实几何图形实践，从科学上讲，因为它是基于比希尔伯特欧几里得几何学小的公理学基础，但仍然包括普通几何学的重要定理。在本文中，我将主要分析赫姆斯列夫（Hjelmslev）的科学方面。