The aim of this paper is to argue that there existed relevant interactions between mechanics and geometry during the first half of the nineteenth century, following a path that goes from Gauss to Riemann through Jacobi. By presenting a rich historical context we hope to throw light on the philosophical change of epistemological categories applied by these authors to the fundamental principles of both disciplines (which they came to regard as hypotheses or conventions). We intend to show that presentations of the changing status of the principles of mechanics as a mere epiphenomenon of the emergence of non-Euclidean geometries are inaccurate, that the relations between the two disciplines were richer than what is usually considered in the literature. These claims will be based on historical and philosophical arguments, starting from the fact that disciplinary boundaries at the time were not rigid as we are used today. It is widely known that the main figures we target worked in different areas, which is a first piece of evidence for the plausibility of our main thesis.

中文翻译：

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从高斯到黎曼通过雅可比：几何和力学认识论之间的相互作用？

本文的目的是论证在 19 世纪上半叶，沿着从高斯到黎曼再到雅可比的路径，力学和几何之间存在相关的相互作用。通过呈现丰富的历史背景，我们希望阐明这些作者应用于两个学科的基本原则（他们开始将其视为假设或约定）的认识论类别的哲学变化。我们打算表明，将力学原理的变化状态描述为非欧几何出现的仅仅是附带现象是不准确的，这两个学科之间的关系比文献中通常考虑的要丰富。这些主张将基于历史和哲学论点，从当时的学科界限并不像我们今天使用的那样严格。众所周知，我们针对的主要人物在不同领域工作过，这是我们主要论文合理性的第一个证据。