Euclid in the Modern Age: A History of Cross-Cultural Transmissions, Translations and Transformations of the Elements – EUCLIDES

By 1 April 2026, the bibliographical catalogue contained 1,053 editions of mathematical and related works published between 1482 and 1883. Of these, 331 had been identified as belonging to the Euclidean tradition in a broad sense. Each record includes bibliographical metadata, links to available digital facsimiles and project-specific information describing the work’s relation to the Elements, including which sections are transmitted and what additional Euclidean material is incorporated. Metadata acquisition combines automated extraction from online and printed catalogues with systematic manual verification, balancing scale with scholarly reliability.
This bibliographical layer already exceeds the scale envisaged in the initial proposal and constitutes a major research result in itself. It allows questions to be asked across chronology, geography, language, contributors and publication type. It also provides a contextual frame for the 61 editions selected as the project’s core corpus: the deeply processed texts are no longer isolated examples but can be interpreted against a much larger map of the printed tradition.
6.3 Research interface and collaborative editorial environment
The catalogue is accessible through a dedicated web platform hosted within the Huma-Num environment. The interface functions both as a public-facing research tool and as a collaborative editorial environment for the project team. It supports complex filtering, free-text queries, statistical aggregation and geographical visualisation. Project members can verify, correct and enrich records directly within the environment, making the platform part of the day-to-day scholarly workflow rather than a repository assembled only at the end of the grant.
One of the most innovative achievements is the systematic extraction of visual material. By 1 April 2026, mathematical diagrams had been automatically extracted from facsimiles of 434 editions and integrated into the online interface. This creates a new research object: a large visual corpus of Euclidean diagrams that can eventually be classified, compared and traced across editions. The scale of this corpus directly supports the objectives concerning diagrammatic reasoning and visual transmission.
The project has also implemented and tested preliminary named-entity recognition workflows on title pages. This work demonstrates the feasibility of automatically extracting structured information about persons, places and other entities from historically heterogeneous printed material. The next stage will extend such extraction to the transcribed corpus and connect named entities with bibliographical and textual data, allowing patterns of authorship, translation, publication and institutional affiliation to be studied systematically.

The central scientific ambition of EUCLIDES is to move beyond the highly fragmented historiography of Euclid’s modern reception and to establish the foundations for a genuinely comparative history of the Elements from the beginning of the printed tradition to the nineteenth century. Rather than treating national traditions, individual editions, pedagogical adaptations, practical uses, diagrams, terminology, axioms and proofs as isolated objects, EUCLIDES studies them as interacting components of a single, extraordinarily long-lived textual and scientific tradition. The project therefore combines the history of mathematics with the history of epistemology, education, the book, practical knowledge and visual culture, while also developing digital tools capable of making a large corpus of editions searchable and comparable.
After eighteen months, the project has reached a high level of scientific activity and has also undergone a significant but coherent evolution. The most important strategic development has been the strengthening of the Digital Humanities component. The database originally envisaged as one of the project’s three objectives has become a central research infrastructure and, increasingly, a scientific instrument in its own right. This development led to a reallocation of resources originally intended for a postdoctoral position in order to extend the contract of the project’s research engineer, Mia Joskowicz, and to sustain the digital work for a longer period. This was not a reduction of the historical and epistemological ambitions of EUCLIDES. On the contrary, the digital platform has begun to generate new research questions and results in precisely the areas identified by the original project: diagrams and visual transmission, bibliographical and linguistic variation, the comparative structure of editions, and the circulation of Euclidean knowledge across languages, places and institutional contexts.

The first priority is to continue the transition from corpus-building to comparative historical analysis. The database has now reached sufficient scale to support questions that were previously impracticable. Research should increasingly exploit the relationships between metadata, transcriptions and visual elements rather than treating these as separate resources.
The second priority is to complete the planned digital functions and guarantee sustainability. This includes continued processing of the 61 core editions, refinement of multilingual and historically aware search, development of passage-comparison tools, expansion of named-entity recognition, systematic work on diagrams, and deposit of datasets and software in long-term repositories.
The third priority is to consolidate the project’s collective scholarly outputs. The CIRM conference and the Oxford Handbook provide a framework for this synthesis. The Handbook, if successfully contracted with Oxford University Press, will be especially important because it can bring the project’s different chronological, geographical and disciplinary strands into a single reference work and ensure that the research network survives beyond the funding period.
The fourth priority is the completion and dissemination of individual research programmes, including De Risi’s work on the history of axioms and the Euclidean dimension of Leibniz and Newton, Axworthy’s research on practical adaptations, Goldstein’s work on Euclidean arithmetic, Malet’s studies of Tartaglia and the Spanish tradition, Morel’s work on eighteenth-century teaching, Wardhaugh’s book project, Rommevaux-Tani’s work on medieval educational backgrounds, Joskowicz’s visual and digital studies, and Schmidt’s doctoral dissertation.
Finally, the project should continue to exploit the productive widening of its original scope without losing coherence. The Lusophone and Brazilian research, the enlarged bibliographical corpus and the generic digital methods all show that the Euclidean tradition can serve as a point of convergence for histories of texts, institutions, languages, images, practices and epistemologies. The remaining period should use these developments to articulate the overarching narrative that was the defining ambition of EUCLIDES from the outset.

9.1 Vincenzo De Risi
• “The Derivability Theory of Axioms. Logic and Mistranslation in the Middle Ages and the Renaissance”, in Pre-Modern Mathematical Thought. The Latin Discussion (13th–16th Century), ed. Clelia V. Crialesi, Brill, Leiden, 2025, pp. 237–288.
• “Leibniz and the Logic of Geometry: The Specimen analyseos figuratae, 1686”, The Leibniz Review 35 (2025), pp. 31–44.
• “The Disgrace of Geometry. Newton on Postulates and the Mechanical Foundations of Mathematics”, accepted for publication in Annals of Science.
9.2 Catherine Goldstein
• “Nombres et combinaisons dans les cercles malebranchistes”, Revue d’histoire des sciences 78 (2025), pp. 329–365.
• “Networking Jean Prestet’s mathematics”, forthcoming in Studia Leibnitiana.
9.3 Sabine Rommevaux-Tani
• “L’enseignement de la géométrie des figures planes à l’université de Paris aux XIIIe et XIVe siècles”, in C. Crialesi and F. Galli (eds.), Surveying the Realm of Medieval Geometry (12th–15th Centuries), SISMEL–Edizioni del Galluzzo, 2026, pp. 25–50, forthcoming.
9.4 Benjamin Wardhaugh
• “Euclidean terms in European languages, 1482–1703”, Historia Mathematica 68 (2024), pp. 22–37.
• “François de Foix de Candalle: Euclidean authorship in the sixteenth century”, British Journal for the History of Mathematics 39 (2024), pp. 177–192.
• Euclid in print, 1482–1703. A catalogue of the editions of theElementsand other Euclidean works, revised edition with Philip Beeley and Yelda Nasifoglu, Bibliographical Society, online, 2025.
• Ancient Greek Mathematics in print, 1475–1703. A bibliography of the editions of works other than those of Euclid, Bibliographical Society, online, 2025.
• “Euclid’s Elements in Latin, 1482–1703: Vocabulary and classification”, Revue d’histoire des mathématiques 31 (2025), pp. 69–106.
9.5 Antoni Malet
• “The arithmetic of a 16th-century mathematical practitioner: Tartaglia’s numbers and ‘negatives’”, forthcoming.
9.6 Thomas Morel
• “‘Yet you know that there is only one Euler’. Andreas Böhm (1720–1784) and the Practice of Mathematics at German Universities”, Revue d’histoire des mathématiques 31(1), 2025, pp. 1–67.
9.7 Angela Axworthy
• “Johann Scheubel, Wilhelm Xylander and the numerical treatment of Euclidean geometry in early modern Europe”, submitted in November 2025 to Galilæana.
• “The quantification of magnitudes in sixteenth- and seventeenth-century commentaries on Euclid’s Elements”, developed during the reporting period; work in progress during the reporting period, intended for submission to Science in Context.
• “The dissemination of Euclid’s Elements in seventeenth-century mathematical courses”, forthcoming book chapter in Shaping Mathematical Knowledge, Shaping Mathematical Public: Mathematical Courses and Textbooks in Early Modern Europe (1600–1800).
9.8 Mia Joskowicz
• “Dotted Lines and the Reconceptualization of Quantity in Early Modern Editions of Euclid’s Elements”, forthcoming in Historia Mathematica.

Euclid in the Modern Age 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 (based at Paris and Wuppertal) 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 Elements and 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.