Lorenzo Mascheroni's 1797 work La geometria del compasso, which develops a geometry based solely on compass constructions, is considered by the author as stepping back behind the “demarcation line” of Euclidean geometry. In this work Mascheroni emphasizes the practical aspects of this geometry over a theoretical approach. A century later, in 1899, David Hilbert and his student Michael Feldblum proposed a totally different approach – algebraic and axiomatic – concerning geometric constructions based on various instruments. Taking into account that, at the end of the 18th century, straightedge geometry was also developed, one may ask what happened to the image of instrument-based geometry during the 19th century? By focusing on Mascheroni's book and its reception, this article aims to examine the various views and conceptions of mathematicians with respect to this geometry.

Lorenzo Mascheroni 1797 年的作品La geometria del compasso，它开发了一种完全基于罗盘结构的几何，被作者认为是退到了欧几里得几何的“分界线”后面。在这项工作中，Mascheroni 强调了这种几何学的实际方面而不是理论方法。一个世纪后的 1899 年，大卫希尔伯特和他的学生迈克尔费尔德布鲁姆提出了一种完全不同的方法——代数和公理——关于基于各种仪器的几何构造。考虑到18世纪末也发展了直尺几何，不禁要问19世纪仪器几何的形象发生了什么变化？通过关注 Mascheroni 的书及其接受度，本文旨在检验数学家对这种几何学的各种观点和概念。