On Euclidean diagrams and geometrical knowledge



Published 25-09-2019
Tamires Dal Magro Manuel J. García-Perez


We argue against the claim that the employment of diagrams in Euclidean geometry gives rise to gaps in the proofs. First, we argue that it is a mistake to evaluate its merits through the lenses of Hilbert's formal reconstruction. Second, we elucidate the abilities employed in diagram-based inferences in the Elements and show that diagrams are mathematically reputable tools. Finally, we complement our analysis with a review of recent experimental results purporting to show that, not only is the Euclidean diagram-based practice strictly regimented, it is rooted in cognitive abilities that are universally shared.

How to Cite

Dal Magro, T., & García-Perez, M. J. (2019). On Euclidean diagrams and geometrical knowledge. THEORIA. An International Journal for Theory, History and Foundations of Science, 34(2), 255–276. https://doi.org/10.1387/theoria.20026
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mathematical practice, Euclidean geometry, diagrammatic reasoning, cognitive abilities