Abstract

The project EUCLIDES. Euclid in the Modern Age is a scientific project funded by the ANR (Project number ANR-23-FRAL-0012) and the DFG (Project number 530000455) in the framework of the Franco-German international research program and based in Paris (CNRS-SPHère) and Wuppertal (BUW-IZWT).

This project aims at providing a wide-ranging investigation of the cultural, social, scientific and epistemological impact of the diffusion of Euclid’s Elements, the most important and widely circulated work of classical mathematics, in Europe from the 16th to the 19th century. By studying its transformations throughout its editions, translations and commentaries and its pedagogical and practical uses, the international research team involved in the project seeks to establish an overarching and interdisciplinary narrative regarding the modern tradition of the Elements and its unparalleled impact on the history of science, knowledge and culture.

The main objectives of the project are: (1) the analysis of the transformations of the text and diagrams of the Elements throughout its printed tradition and the way these reflected changes in the history of mathematics and of epistemology in the modern era; (2) the study of the diffusion and uses of the Elements in pedagogical and professional contexts in early modern Europe and their impact on the transformation of Euclid’s text; (3) the establishment of an open-access database to navigate the printed editions of Euclid’s Elements.

The analysis in (1) will show how the logical and epistemological constraints that governed the mathematical discourse (i.e. its principles, the structure of its demonstrations and its diagrams) evolved over time and transformed Euclid’s text and its role in the definition of the ideal of scientific knowledge.

The analysis in (2) will show how the interaction between the Elementsand practical mathematical knowledge, as well as the diffusion of Euclid’s work in vernacular languages throughout Europe (which was crucial to its transmission within lay and professional contexts), impacted the content and uses of the Elements as well as the image of Euclidean mathematics in different social, institutional and cultural contexts. The study of 

the adaptation and promotion of Euclid’s Elements according to new pedagogical standards will provide a better insight on the changes operated in early modern Europe in mathematics and theories of education, as on the changing place held by mathematics among the sciences.

The last objective (3) will be constituted according to the principles of “green open access” and will allow scholars as well as non-experts to gain a both detailed and large overview of how Euclid’s Elements evolved over time and to obtain quick answers to specific questions on the printed European Euclidean tradition.

Prinicpal Investigator 

Dr. Angela Axowrthy

Involved Persons 

Prof. Dr. Thomas Morel

Prof. Dr. Volker Remmert

Term

October 2024 - September 2027

Financed by German Research Foundation (DFG)

Project on GEPRIS

Activities

Workshop: Euclid's Elements and Practical Mathematics in Early Modern Europe

Workshop: Euclid in the vernacular. Cross-cultural transmission, adaptation and transformation of Euclid’s Elements in early modern Europe

Publications

- Special issue of Early Science and Medicine on the vernacular translations of Euclid’s Elements (proceedings of 2026 workshop)

- Oxford Handbook in history on the Euclidean traditions from Antiquity to the modern age (collective volume, co-edited with Vincenzo De Risi, proposal in preparation)

- Thomas Morel: “Euclid in pure, and Kästner in applied mathematics.” Pedagogical Considerations in 18th century German Universities, in Oxford Handbook (provisional)

- Volker Remmert: “The frontispieces of early modern editions of Euclid’s Elements”, in prospective volume on Euclid’s Elements and visual culture (provisional)

- Angela Axworthy: “Euclid’s Elements in early modern treatises of practical geometry”, in Oxford Handbook (provisional)

- Angela Axworthy: “Johann Scheubel, Wilhelm Xylander and the numerical treatment of Euclidean geometry in early modern Europe”, submitted to Galilaeana, Special issue Mathematical Thought in the Renaissance and the Genesis of Modern Mathematics (provisional)

- Angela Axworthy: “The quantification of magnitudes in sixteenth- and seventeenth-century commentaries on Euclid’s Elements”, to be submitted to Science in context, Special issue on Quantification in Context: Premodern Theories and Practices (provisional)

- Angela Axworthy: “The dissemination of Euclid’s Elements in seventeenth-century mathematical courses”, planned for volume Shaping Mathematical Knowledge, Shaping Mathematical public: Mathematical Courses and Textbooks in Early Modern Europe (1600–1800), eds. Monica Blanco Abellán, Davide Crippa, M. Rosa Massa Esteve.

References

https://euclides.hypotheses.org

https://anr.fr/Project-ANR-23-FRAL-0012 (French part of the project)