This essay explores the research practice of French geometer Michel Chasles (1793–1880), from his 1837 Aperçu historique up to the preparation of his courses on ‘higher geometry’ between 1846 and 1852. It argues that this scientific pursuit was jointly carried out on a historiographical and a mathematical terrain. Epistemic techniques such as the archival search for and comparison of manuscripts, the deconstructive historiography of past geometrical methods, and the epistemologically motivated periodization of the history of mathematics are shown to have played a crucial role in the shaping of Chasles's own theories. In particular, we present Chasles's approach to the ‘material history’ of algebraic symbolism and argue that it motivated and informed his subsequent invention of a novel notational technology for the writing of geometrical proofs and propositions. In return, this technology allowed Chasles to carry out a programme for the modernization of geometry in keeping with epistemic requirements he had also delineated via a form of historical writing.

本文探讨了法国几何学家 Michel Chasles (1793–1880) 的研究实践，从他 1837 年的Aperçu historique直到 1846 年至 1852 年间准备他的“高等几何”课程。它认为，这种科学追求是在史学和数学领域共同进行的。诸如对手稿的档案搜索和比较、过去几何方法的解构史学以及基于认识论动机的数学史分期等认识论技术在 Chasles 自己的理论的形成中发挥了至关重要的作用。特别是，我们展示了 Chasles 对代数象征主义的“物质历史”的研究方法，并认为它激发并启发了他随后发明一种用于编写几何证明和命题的新型符号技术。作为回报，