In Part I [Bal14a], we defined the notion of a modest complete descriptive axiomatization and showed that HP5 and EG are such axiomatizations of Euclid’s polygonal geometry and Euclidean circle geometry1. In this paper we argue: 1) Tarski’s axiom set E is a modest complete descriptive axiomatization of Cartesian geometry (Section 2; 2) the theories EGπ,C,A and E π,C,A are modest complete descriptive axiomatizations of Euclidean circle geometry and Cartesian geometry, respectively when extended by formulas computing the area and circumference of a circle (Section 3); and 3) that Hilbert’s system in the Grundlagen is an immodest axiomatization of any of these geometries. As part of the last claim (Section 4), we analyze the role of the Archimdedean postulate in the Grundlagen, trace the intricate relationship between alternative formulations of ‘Dedekind completeness’, and exhibit many other categorical axiomatizations of related geometries.

中文翻译：

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公理化几何连续体 II 的变化概念：阿基米德-笛卡尔-希尔伯特-塔斯基†

在第一部分 [Bal14a] 中，我们定义了适度完全描述公理化的概念，并表明 HP5 和 EG 是欧几里得多边形几何和欧几里得圆几何的公理化1。在本文中，我们认为： 1) Tarski 公理集 E 是笛卡尔几何的适度完全描述公理化（第 2 节；2）理论 EGπ,C,A 和 E π,C,A 是欧几里得圆几何的适度完全描述公理化和笛卡尔几何，分别通过计算圆的面积和周长的公式进行扩展（第 3 节）；和 3) Grundlagen 中的希尔伯特系统是这些几何中任何一个的不适当的公理化。作为最后一个主张（第 4 节）的一部分，我们分析了阿基姆德假设在 Grundlagen 中的作用，