Angela Axworthy

Angela Axworthy is a Postdoctoral Fellow at the Bergische Universität Wuppertal within the IZWT as one of the Principal investigators of the Franco-German project EUCLIDES, Euclid in the Modern Age: A History of Cross-Cultural Transmissions, Translations and Transformations of the Elements funded by the ANR and the DFG (2024-2027). She is also an associated researcher of CNRS-SPHère. She was previously a postdoctoral fellow of the ERC Group TACITROOTS at the University of Milan, of the Gerda Henkel Stiftung, of the Max-Planck-Institut für Wissenschaftsgeschichte (MPIWG), and of the Technical University of Berlin (Dept. of History of Science). Her research deals with the history and epistemology of sixteenth- and seventeenth-century mathematics, most of all of geometry and astronomy.

Awards & Fellowships

10/2024-09/2027 Wissenschaftliche Mitarbeiterin. Bergische Universität Wuppertal, IZWT, as Principal Investigator of the German part of the international ANR-DFG project EUCLIDES: Euclid in the Modern Age: A History of Cross-Cultural Transmissions, Translations and Transformations of the Elements.
10/2023-09/2024 Postdoctoral fellow. University of Milan, Department of Historical Studies, ERC Research Group TACITROOTS, dir. Giulia Giannini. Research project: The mathematical work and thought of Giovanni Alfonso Borelli, Carlo Rinaldini, Vincenzo Viviani, members of the Accademia del Cimento.
08/2021-07/2023 Research fellow. Gerda Henkel Stiftung. Research project: Making Euclid practical: The impact of practical geometry on the Euclidean tradition in the sixteenth century.
Since 01/2019 Visiting scholar. Max-Planck-Institut für Wissenschaftsgeschichte, Berlin (MPIWG, Department I).
01/2017-12/2018 Postdoctoral fellow at the Department of History of Science of the Technischer Universität in the framework of the Berlin Center for the History of Knowledge. Research project on: The status of practical geometry and its relations to theoretical and applied geometrical knowledge in sixteenth-century treatises of practical geometry.
01/2015-12/2016 Postdoctoral fellow at the MPIWG (Department I) and the University of Oklahoma. Research project: The 1531 Edition of the Commentaries on Sacrobosco’s Tractatus de Sphaera of Prosdocimo de’ Beldomandi and Bartolomeo Vespucci.
09/2012-08/2014 Postdoctoral fellow at the MPIWG (Vincenzo De Risi’s group on Modern geometry and the Concept of Space). Research project: The ontological status of geometrical objects in the commentary on the Elements of Euclid of Jacques Peletier du Mans (1517-1582). Funding 2012-2013: “Fernand Braudel – IFER outgoing” fellowship from the “Fondation Maison des sciences de l’homme” (Paris), Fritz Thyssen Stiftung and Programme Action Marie Curie of the European Commission.
2012 PhD dissertation Prize of the Société Française d’Histoire des Sciences et Techniques (S.F.H.S.T.).
2005 MA dissertation prize of the S.F.H.S.T..

Education and Qualifications

2012 Qualification by the C.N.U. (French national council of universities) to teach as a lecturer in philosophy and history of science (sections 17 and 72).
2011 (December 5) PhD in philosophy (First class honours), Centre d’Études Supérieures de la Renaissance (C.E.S.R.), Université François-Rabelais, Tours, France. Thesis written under the supervision of Joël Biard on The Status of Mathematics in Sixteenth-century France : The Case of Oronce Fine (Le statut des mathématiques en France au XVI^e siècle : le cas d’Oronce Fine).
2005 Master’s degree in philosophy (First class honours), C.E.S.R., Tours, France. Thesis written under the supervision of Joël Biard on The Status of the Mathematical Object according to Federico Commandino (Le statut de l’objet mathématique chez Federico Commandino).
2004 “Maîtrise” in philosophy (First class honours), C.E.S.R., Tours, France. Thesis written under the supervision of Joël Biard on The Status of Mathematics in the Sixteenth Century in the light of the prefaces to the commentaries on Euclid’s Elements of Niccolò Tartaglia and Christophorus Clavius (Le statut des disciplines mathématiques au XVI^e siècle au regard des préfaces aux Éléments d’Euclide de Niccolò Tartaglia et de Christophe Clavius).
2002 Bachelor of Arts in philosophy, Université François-Rabelais, Tours, France.

Talks, teaching and conference organization

Since June 2023 Coorganisation of the monthly seminar Mathématiques de l’Antiquité à l’Age classique, with Sandra Bella, Pascal Crozet and Vincenzo De Risi, for the CNRS laboratory SPHère – Université Paris Cité (UMR 7219) in Paris, and the Archives Poincaré in Nancy.
2025 “On Jungius’ Phoranomica: from the first lecture notes to the 1691 published version ”, Workshop Mathematical Notes: Materiality and Epistemology organised by Matthias Schemmel and Stefano Farinella, University of Hamburg, Centre for the Study of Manuscript Cultures (CSMC), 6-7 February.
2024 “Making Euclid practical in the seventeenth century: a preliminary outlook”, Conference Euclid in the modern age. A History of Cross-Cultural Transmissions, Translations and Transformations of the Elements organised by Vincenzo De Risi (funded by ANR-DFG Project EUCLIDES, Paris-Wuppertal), Paris, CNRS-SPHère UMR 7219, 18-19 November.
2024 “On the project EUCLIDES (Wuppertal-Paris, 2024-2027): The modern tradition of Euclid’s Elements and its scientific, epistemological, social, and cultural impact”, Oberseminar zur Geschichte der Mathematik organised by Thomas Morel and Ralf Krömer, Bergische Universität Wuppertal, 4 December.
2024 “The turn to practice in the sixteenth-century transmission of Euclid’s Elements ”, Conference The Premodern Reception of Euclid’s Elements: Current perspectives and future directions in research organised by Ofer Elior, Ruth Glasner and Reimund Leicht, Jerusalem, 2-4 September.
2024 “Géométrie théorique et géométrie pratique dans le commentaire des Éléments d’Euclide et l’Arpanterie d’Élie Vinet ”, Conference Sciences et savoirs en Aquitaine à l’époque de Montaigne organised by Anne Bouscharain, Violaine Giacomotto-Charra et Sabine Rommevaux-Tani, Bordeaux, 23-24 May.
2023 “The Transformation of Euclidean Geometry in the Universities of Sixteenth-century Tübingen and Heidelberg: The Practical Treatment of the Elements by Johannes Scheubel (1494-1570) and Wilhelm Xylander (1532-1576) ”, panel The evolution of the new sciences within early modern formal education organised by David McOmish, Scientiae, Prague, 7 June.
2023 “Practical translations, adaptations and interpretations of Euclid’s propositions in the sixteenth-century tradition of the Elements ”, panel Éditions et traductions renaissantes de traités géométriques et astronomiques de l’Antiquité: entre restitution et adaptation organised by Carole Hofstetter and Angela Axworthy, Congress of the S.F.H.S.T. (Société Française d’Histoire des Sciences et Techniques), Bordeaux, 19 April.
2023 “Theoretical and practical geometry in Élie Vinet’s commentary on Euclid’s Elements (1575) and in his L’Arpenterie (1577)”, seminar Mathématiques de l’Antiquité à l’âge classique organised by Vincenzo De Risi and Pascal Crozet, SPHère–CNRS (UMR 7219), Paris, 17 March.
2022 “Making Euclid practical in the 16th Century ”, panel Scholarly and Artisanal Mathematics in the Early Modern Period organised by Thomas Morel & Michael Friedman, ESHS, Brussels, 10 September.
2022 “The practical treatment of Euclid’s Elements in the sixteenth century: from Niccolò Tartaglia to Christoph Clavius”, seminar Mathématiques de l’Antiquité à l’âge classique organised by Vincenzo De Risi and Sabine Rommevaux, SPHère–CNRS (UMR 7219), Paris, 10 June.
2022 “Practical approaches to Euclidean geometry in the 16th century”, On Trading Zones between Scholars and Craftsmen: Artisanal Practices and Mathematics in the Early Modern Period, Princeton-Bucharest Early Modern Virtual Seminar (online), 10 May.
2022 “Practical Geometry and the Elements of Euclid in the Sixteenth Century”, panel Mathematical Practices and Practical Mathematics in Renaissance Europe organised by Adam Mosley, Renaissance Society of America 2022 conference, Dublin, 1 April.
2021 “Readers of Classics. Sixteenth-century commentators of Euclid’s Elements”, Oberwolfach Workshop Mathematics and its Ancient Classics Worldwide: Translations, Appropriations, Reconstructions, Roles organised by Karine Chemla, Vincenzo De Risi and Antoni Malet, Oberwolfach Research Institute for Mathematics (MFO), 30.05. – 05.06.2021.
2020 “The transformation of Euclidean geometry in early modern European practical geometry”, 31st Novembertagung on the History and Philosophy of Mathematics, Humboldt-Universität, Berlin (online), 28 November.
2020 “Geometrical models of the universe in the fifteenth century: the case of Prosdocimo de’ Beldomandi”, panel The practice of geometry in medieval Alfonsine astronomy organised by Matthieu Husson, Samuel Gessner and Richard Kremer, ESHS, Bologna (online) 3 September.
2020 “Unity and diversity of practical geometry in sixteenth-century France”, Seminar The History of the Exact Sciences organised by Benjamin Wardhaugh, Philip Beeley and Chris Hollings, University of Oxford, All Souls College, 28 January.
2019 “Sixteenth century French practical geometry treatises”. Workshop on early modern geometry treatises, organised by Christina Lechtermann and Jan Habermehl, Goethe University, Frankfurt am-Main, 5 – 6 December.
2019 “The Geometrisation of the Heavens in Pre- and Early Modern Europe”,
Workshop Exceeding Nature, Summer School Structuring Nature. An Interdisciplinary and Intercultural Summer School on Premodern Science and Philosophy, organised by Nicholas Aubin, Vincenzo Carlotta, Mattia Cipriani, Katja Krause, Nicola Polloni, Humboldt-Universität zu Berlin, Max-Planck-Institut für Wissenschaftsgeschichte, Freie Universität, Berlin, 28 July – 3 August 2019.
2018 “The transformation of Euclid’s Elements in sixteenth-century treatises of practical geometry”, Workshop Euclid on the Road. Cross-cultural transmission, translation and transformation of the Elements organised by Vincenzo De Risi (Paris, CNRS–SPHERE), M.P.I.W.G., Berlin.
2018 “Paper instruments and Euclidean geometry in the sixteenth century”, Round table Paper Instruments as Tools of Unification in Early Modern Practical Mathematics, organised by Kevin Tracey, ESHS 2018, London, 16 September.
2018 “Practical geometry in sixteenth-century France”, “Oberseminar” in History of mathematics organised by Volker Remmert, University of Wuppertal.
2018 (summer semester) Teaching seminar (Hauptseminar) on Practical mathematics in early modern Europe, Technische Universität Berlin, History of Science department.
2018 Masterclass (lecture and seminar) with Filippo Camerota (Museo Galileo, Florence): “The Intrinsic Place. Space as a Measurable Entity in Early Modern Art and Science”, M.P.I.W.G., Berlin, co-organised by Angela Axworthy and Elizabeth Merrill and introduced by Matteo Valleriani, Berlin Center for the History of Knowledge, M.P.I.W.G.
2018 Presentation and discussion of the pre-circulating paper “Oronce Fine: from the edition of Sacrobosco’s Sphaera (1516) to the Cosmographia, sive sphaera mundi (1532)”, Workshop on The Authors of the Early Modern Commentaries on De sphaera organised by Matteo Valleriani, M.P.I.W.G., Berlin.
2017 “Practical geometry in sixteenth-century France”, Research colloquium organised par Friedrich Steinle, Technische Universität Berlin, History of Science department.
2017 (summer semester) Teaching seminar (Hauptseminar) on The status of mathematics from Antiquity to the Renaissance, Technische Universität Berlin, History of Science department.
2017 “Jacques Peletier du Mans’s Conception of Practical Geometry in the
De usu geometriae (1572) and De l’usage de geometrie (1573)”, Workshop Beyond the Academy. The Practice of Mathematics from the Renaissance to the Nineteenth Century, organised by Philip Beeley and Christopher Hollings, British Society of History of Mathematics, York.
2017 “The ontological status of geometrical objects in the commentary on the Elements of Euclid of Jacques Peletier du Mans (1517-1582)”, Seminar “Concepts and methods in philosophy and history of science” organised by Delphine Bellis and Charles Wolfe, Sarton Centre for History of Science, University of Ghent.
2016 “Oronce Fine’s project for the revival of mathematics in sixteenth-century Paris”, Workshop Teaching mathematics in the early modern world organised by Benjamin Wardhaugh, All Souls College, University of Oxford.
2016 “La forme, le contenu et la finalité de la géométrie pratique d’Oronce Fine”, History of mathematics seminar organised by Rossana Tazzioli, University of Lille 1.
2016 “Conceptions of motion in geometrical definitions according to sixteenth-century commentators of Euclid”, Harriot seminar organised by Stephen Clucas, Birkbeck College, London.
2016 “Mathematical teaching from the Faculty of Arts to the Institution of the Royal Lecturers in early sixteenth-century France”, Three Societies Conference, Edmonton (Alberta).
2016 “Prosdocimo de’ Beldomandi and Bartolomeo Vespucci on the geometrical definitions of the sphere in Sacrobosco’s Sphaera”, Lunch talk organised by Peter Barker, University of Oklahoma, History of Science Department, Norman (Oklahoma).
2016 Lecture on Francis Bacon’s New Atlantis, Liberal Arts course on “Early Modern Science” organised by Ewa Atanassow and Michael Weinman, Bard College, Berlin.
2015 Teaching session on “the uses and rejection of starless mobile spheres above the Firmament in sixteenth century cosmology”, Hauptseminar on Late medieval geocentric cosmology taught by Matteo Valleriani (M.P.I.W.G.), Technische Universität, Berlin.
2015 “The geometrical definition of the sphere in Sacrobosco’s Sphaera according to Prosdocimo de’ Beldomandi (1370/80-1428) and Bartolomeo Vespucci (1479-1527)”, research seminar organised by Anna Jerratsch and Pietro D. Omodeo on the transformations of cosmology, M.P.I.W.G., Department I
2015 “Jacques Peletier du Mans (1517-1582) and Christoph Clavius (1538-1612) on the superposition of geometrical figures: a sixteenth-century debate on the ontological and epistemological status of geometrical objects and procedures”, Lunch talk organised by the interdisciplinary laboratory “Bild Wissen Gestaltung” of the Humboldt-Universität in Berlin.
2015 “The Euclidean Definition of the Sphere in the Middle Ages and in the Renaissance: from the commentaries on Sacrobosco’s Sphere to the commentaries on Euclid’s Elements”, Geometry and Space in the Early Modern Age, conference organised by Vincenzo De Risi, Independent research group “Modern geometry and the concept of space”, Max-Planck-Institut für Wissenschaftsgeschichte, Berlin.
2015 “La forme des traités de mathématiques pratiques d’Oronce Fine”, Seminar Formes du savoir) organised by Violaine Giacomotto-Charra and Pascal Duris, Université Bordeaux-Montaigne.
2014 “The epistemological and ontological background of the debate on superposition between Jacques Peletier du Mans (1517-1582) and Christophorus Clavius (1538-1612)”, HOPOS 2014, Ghent, Belgium.
2014 “Sixteenth-century Interpretations of the Nature and Use of Motion in Geometry”, conference The Mechanization of Geometry. From Antiquity to the Modern Age organised by Vincenzo De Risi, Independent research group “Modern geometry and the concept of space”, Max-Planck-Institut für Wissenschaftsgeschichte, Berlin.
2014 Geometrical, Astronomical and Geographical Notions of Space in the Renaissance, workshop organised by Vincenzo De Risi, Independent research group “Modern geometry and the concept of space”, Max-Planck-Institut für Wissenschaftsgeschichte, Berlin.
2014 “The notion of flow of the point as a principle of generation of the line in the Renaissance Euclidean tradition”, history of science seminar (HEST) organised by François Loget and Marc Moyon, I.R.E.M. of Limoges.
2014 “Renaissance interpretations of the geometrical notion of rhusis”, colloquium organised by Vincenzo De Risi, Independent research group “Modern geometry and the concept of space”, Max-Planck-Institut für Wissenschaftsgeschichte, Berlin
2013 “The Purpose, Modalities and Limits of the Admission of Movement in the Definition and Study of Geometrical Objects in the Sixteenth-century Euclidean Tradition: Oronce Fine (1494-1555), Jacques Peletier du Mans (1517-1582) and Christoph Clavius (1538-1611)”, colloquium organised by Vincenzo De Risi, Independent research group “Modern geometry and the concept of space”, Max-Planck-Institut für Wissenschaftsgeschichte, Berlin.
2013 “Le statut des objets géométriques dans le commentaire des Éléments d’Euclide de Jacques Peletier du Mans (1557)”, Seminar “Mathématiques à la Renaissance” organised by Sabine Rommevaux and Odile Kouteynikoff, (UMR 7219 – SPHERE), Paris.
2012 “Quelques interprétations renaissantes de l’In Euclidem de Proclus: d’Oronce Fine à Christoph Clavius”, Paris, “Neoplatonic workshop”, organised by Pierre Caye, Philippe Hoffmann, Christian Jambet and Stéphane Toulouse, Collège International de Philosophie.
2012 “Le statut épistémologique de la géométrie selon Charles de Bovelles”, conference Charles de Bovelles: philosophe et pédagogue, organised by Emmanuel Faye, Anne-Hélène Klinger-Dollé et Joël Biard, C.E.S.R., Tours.
2011 “L’influence de Proclus sur la conception du statut de la géométrie d’Oronce Fine”, IV^th congress of the Société Française d’Histoire des Sciences et Techniques (S.F.H.S.T.), Nantes.
2010 “La démonstration de l’utilité des mathématiques dans le cadre des préfaces et des prologues d’Oronce Fine”, conference “The conceptions of Renaissance authors on mathematics” organised by Sabine Rommevaux, C.E.S.R., Tours.
2008 “La reprise et la réception du discours de Proclus sur les mathématiques chez Federico Commandino et Christophe Clavius”, III^rd Congress of the S.F.H.S.T., Paris.
2007 “L’utilité des mathématiques selon Oronce Fine”, C.E.S.R., Tours
2004 “L’influence de Proclus sur Clavius concernant la question de l’utilité des mathématiques”, C.E.S.R., Tours.

Publications

Forthcoming “Practical geometry in the Latin Middle Ages”, in E. Sammarchi (dir.), History of Mathematics: Antiquity and Middle Ages / Histoire des mathématiques: Antiquité et Moyen Âge vol. 2.1 of Encyclopedia of the History of Science, Bilingual edition (French-English), London, ISTE-Wiley.
Forthcoming “Géométrie théorique et géométrie pratique dans le commentaire des Éléments d’Euclide et L’Arpanterie d’Élie Vinet”, Camenae.
2024 “Mathematics in the Accademia del Cimento: from a Language of Nature to a Language of Reason”, Physis: International Journal for the History of Science 59/2, p. 463-499, published in open access: https://www.torrossa.com/de/resources/an/5881168.
2024 “Renaissance approaches to the terminology of mathematics”, Le Français Préclassique 26, p. 61-68, https://www.honorechampion.com/fr/editions-honore-champion/13360-book-08536372-9782745363725.html.
2022 “The Hybridization of Practical and Theoretical Geometry in the Sixteenth-Century Euclidean Tradition”, The Journal of Interdisciplinary History of Ideas 11 (22), p. 1-38, https://doi.org/10.13135/2280-8574/7333 (published online on 31 January 2023).
2022 “Eleanor Chan, Mathematics and the Craft of Thought in the Anglo-Dutch Renaissance, New York, Routledge, coll. Studies in Renaissance and Early Modern Worlds of Knowledge, 2022, 240 p., ill.”, Revue de Synthèse 143 (3-4), p. 529-533.
2021 Motion and Genetic Definitions in the Sixteenth-century Euclidean Tradition, Cham, Birkhäuser, Frontiers in the History of Science. A pdf of the Frontmatter (including an Erratum) may be downloaded here.
2021 “Le statut épistémologique de la géométrie d’après l’Introductio in Geometriam de Charles de Bovelles”, in Emmanuel Faye and Anne-Hélène Klinger-Dollé (eds.), Charles de Bovelles, Philosophe et Pédagogue, Paris, Beauchesne, p. 101-119.
2021 “Shin Higashi, Penser les mathématiques au xvie siècle (Paris: Classiques Garnier, 2018), 15 × 22 cm, 489 p., bibliogr., index nominum, index rerum, table, coll. Histoire et philosophie des sciences”, Revue d’Histoire des Sciences 74, 2021 (2), p. 478–479.
2020 “Oronce Fine and Sacrobosco: From the Edition of the Tractatus de sphaera (1516) to the Cosmographia (1532)”, in Matteo Valleriani (ed.), De sphaera of Johannes de Sacrobosco in the Early Modern Period, Springer Nature, p. 185-264, published in Open Access: https://link.springer.com/chapter/10.1007/978-3-030-30833-9_8#aboutcontent.
2020 “Richard J. Oosterhoff, Making mathematical culture: University and print in the circle of Lefèvre d’Étaples, Oxford, Oxford University Press, 2018, xiv + 276 pp. ISBN: 9780198823520”, Centaurus 62 (1), p. 211-213, https://doi.org/10.1111/1600-0498.12252.
2018 “Early modern conceptions and treatments of space and spatiality”, review of Koen Vermeir and Jonathan Regier (eds.), Boundaries, extents and circulations: Space and spatiality in early modern natural philosophy (Dordrecht, Springer, 2016), Metascience 27, p. 309–312 https://doi.org/10.1007/s11016-018-0294-2.
2018 “The debate between Peletier and Clavius on superposition”, Historia mathematica 45 (1), p. 1-38, https://doi.org/10.1016/j.hm.2017.09.004.
2017 “Early Modern Cosmological Debates”, review of Miguel Á. Granada, Patrick J. Boner and Dario Tessicini (eds.), Unifying Heaven and Earth: Essays in the History of Early Modern Cosmology, (Edicions de la Universitat de Barcelona, Barcelona, 2016), Journal for the History of Astronomy, 48 (4), p. 489-491, https://doi.org/10.1177/0021828617724895.
2017 “La notion géométrique de flux du point à la Renaissance et dans le commentaire des Éléments de Jacques Peletier du Mans”, in Christophe Grellard (ed.), Miroir de l’amitié. Mélanges offerts à Joël Biard à l’occasion de ses 65 ans, Paris, Vrin, p. 453-464.
2016 Le Mathématicien renaissant et son savoir. Le statut des mathématiques selon Oronce Fine, Paris, Classiques Garnier.
2013 “The ontological status of geometrical objects in the commentary on the Elements of Euclid of Jacques Peletier du Mans (1517-1582)”, Working Paper of the F.M.S.H., published on-line on hypotheses.org.
2009 “The Epistemological Foundations of the Propaedeutic Status of Mathematics according to the Epistolary and Prefatory Writings of Oronce Fine” in Alexander Marr (ed.), The Worlds of Oronce Fine: Mathematics, Instruments and Print in Renaissance France, Donington, Shaun Tyas, p. 31-51.