Dr. Angela Axworthy

Wissenschaftliche Mitarbeiterin am IZWT

Research interests

My research, broadly construed, addresses the history and philosophy of mathematics in the pre- and early modern periods. My current work explores the interactions between practical and theoretical geometry within the early modern Euclidean tradition. Among my earlier and more recent topics of research is the status and development of practical geometry in the Middle Ages and early modern era; the relationship between mathematics and natural philosophy within the Florentine Accademia del Cimento (1657-1667); the role and status of motion in Euclidean geometry from Antiquity to the early modern period; the epistemological status of mathematics in sixteenth-century France and Italy; as well as the epistemological status of astronomy in medieval and Renaissance commentaries and adaptations of Johannes Sacrobosco’s De sphaera.

Research project

My current research project is part of the Franco-German collaborative project EUCLIDES, Euclid in the Modern Age: A History of Cross-Cultural Transmissions, Translations and Transformations of the Elements, divided between Paris (CNRS-SPHère, with Dr. Vincenzo De Risi as PI) Wuppertal (IZWT) and funded by the ANR and the DFG. Members of the Wuppertal team count Prof. Dr. Volker Remmert and Prof. Dr. Thomas Morel.

The part of the project conducted in Wuppertal aims to investigate the interactions between practical mathematics, professional mathematical knowledge, and Euclid’s Elements, both within the Euclidean corpus and in practical geometry treatises and artisans' handbooks, during the early modern era.

In the 16th century, numerous editions of Euclid’s Elements (both Latin and vernacular) integrated features typical of practical mathematics, particularly practical geometry. This tradition provided a hands-on, empirical form of geometrical knowledge, allowing for a numerical and more concrete consideration of magnitudes. These characteristics contrasted with the more theoretical methods canonically associated with Euclid’s Elements, regarded since the Middle Ages as the epitome of theoretical geometry. The incorporation of practical approaches in these editions reflects a growing interest among early modern authors and their readers in more applied forms of Euclidean geometry. This interest persisted beyond the 16th century, as evidenced by 17th-century editions and commentaries of the Elements—notably in the vernacular tradition—that explicitly aimed to adapt Euclid for practical use. Examples include Pietro-Antonio Cataldi’s I primi sei libri de gl’Elementi d’Euclide ridotti alla Prattica (1620) and Lucas Brunn’s Euclidis elementa practica (1625).

One of the primary objectives of this project is to assess the extent and evolution of the practical treatment of Euclid’s Elements in the early modern era. This includes examining the motivations behind this practical adaptation and its effects on the visual and textual content of the Elements, its logical structure, epistemological status, and relationship to practical knowledge.

Given that Euclid’s Elements had been a part of elementary education since Antiquity, and considering that the rapid development of numeracy and literacy in the early modern period expanded the scope and ambitions of educational institutions, this project also aims to explore how mathematics professors—editors, translators, and commentators of Euclid—adapted their teaching of the Elements to meet the needs of these new institutions and audiences, notably by offering a more practical and reader-friendly reading of the Elements.

Simultaneously, there was a rise in early modern textbooks on practical or professional mathematics, in both printed and manuscript form, predominantly written in the vernacular. These works often incorporated selected principles and propositions from the Elements, adapting them to suit the style, purpose, and audience of these texts. This contributed to a convergence between Euclidean geometry and practical geometry that reflected changes in the role and representation of Euclidean geometry in lay and artisanal contexts. Therefore, the project also examines the dissemination of Euclidean content within practical and professional mathematical contexts, the motivations behind this integration, and the way Euclidean principles were transformed to accommodate the needs of these audiences.

Moreover, as vernacular languages increasingly replaced Latin in 17th-century editions and commentaries of Euclid’s Elements, this project seeks to establish the relationship between the use of vernacular languages and the pedagogical and professional applications of the Elements. This includes analysing the impact of vernacular diffusion on the logical structure, terminology, and readership of Euclid’s work.

Additionally, the project aims to address the evolution of the visual language used to convey Euclidean geometrical concepts in pedagogical contexts. This includes the use of geometrical diagrams, models employing folded paper to represent three-dimensional solids (as in Billingsley’s 1570 edition of the Elements), and illustrations of geometrical instruments. The visual strategies used to represent and promote Euclid’s Elements and geometry in various social and institutional contexts—such as the frontispieces of Euclidean editions and other mathematical treatises—are also essential to investigate within this framework.

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