ALFA symposium in HSS

Utrecht 23-27 July 2019

Org. : ALFA Advisory Board


Session Wenesday, 24 July 9h-11h45



Manuscripts, instruments, tables and computation in Alfonsine astronomy

Alfonsine astronomy flourished in Latin Europe from the second half of the 13th to the middle of the 16th century. It is arguably among the first European scientific achievements and shaped a scene for well-known actors like Regiomontanus or Copernicus. There has been, however, little detailed analysis of its comprehensive development. ALFA (2017-2022) is a European Research Council-funded research project addressing this lacuna by studying Alfonsine tables, instruments, mathematical and theoretical texts in a methodologically innovative way, drawing on approaches from the history of manuscript cultures, history of mathematics, and history of astronomy.  For example, rather than focussing simply on individual texts, we are studying manuscript codices as physical objects and computation with such objects as performance. The roles of different instruments and visual representations in relation to manuscripts in various astronomical practices is also addressed.  The goal of this symposium is to present to a wider audience some of the first results of the project.




 Laura Fernandez Fernandez; Laure Miolo; Nick Jacobson; Samuel Guesner; ; Matthieu Husson (commentary)



Laure Miolo (Postdoc ERC project ALFA)

Theory and Practice of Eclipse Computations by John of Genoa in the 1330s

Before 1332 in Paris, John of Genoa elaborated an original table of Lunar and Solar hourly velocities combined with a table of the radii of the Sun, the Moon and the shadow of the earth, including a column for the variation of the shadow of the earth – variatio umbre – used as a function of the motion in anomaly. This table was probably composed for renewing two tables embedded in John of Lingères’s set of tables (1321). It is the starting point of a whole project focused on eclipse theories and calculations. Indeed, John of Genoa wrote a canon associated with his table, and then eclipse canons entitled Canones eclipsium (1332). The climax of his work was a thorough computation of the solar eclipse of the 3rd March 1337. It is the most detailed calculation of the late Middle Ages. Three manuscripts contained this work, which is an important witness for the history of calculation practices. In this paper, I will compare the calculation provided for the 3rd March 1337 with the methods for establishing a calculation of eclipse that John of Genoa described in his Canones eclipsium. With this analysis, I will consider the link between theoretical knowledge and a real practice of computation.


Laura Fernandez Fernandez (Universidad Complutense de Madrid, Spain)

The Visual Culture of Alfonsine Astronomy: The Case of Getty Museum, Ludwig XII.7

The constellations pictured in the manuscripts commissioned by ‘Alfonso X el Sabio’ (Lapidario, El Escorial, RBME, Ms. h-I-15, Libro del saber de astrología, Madrid, UCM BH, Ms. 156, Libro de astromagia, Città del Vaticano, BAV, Ms. Reg. Lat. 1283a) stem from the figurative cycle illustrating the text of al-Sufi´s Kitab Al-Kawakeb Al-Thabita, the Book of the Fixed Stars. This repertoire adapted Classical representations of the constellations, adding specific elements from the Islamic and the Bedouin tradition. Al- Sufi´s forms also changed the Classical aesthetic and attributes and adapted them to the Eastern fashion, just as the figures of the Alfonsine manuscripts later added a Western touch, more suited to the cultural context and the audience for which this visual repertoire was designed, while simultaneously respecting al-Sufi´s iconographical structure. The Ludwig XII.7 manuscript, nowadays preserved at the Getty Museum, a scientific miscellany provably made in Oxford in the last quarter of the 14th century, has a direct relationship with the Alfonsine production. One of its parts seems to be inspired by a fragment of the Libro de las estrellas fixas, the first treatise of the Libro del saber de astrología, keeping the same iconographical features than the Alfonsine manuscript, documenting the circulation and preservation of the visual culture of Alfonsine astronomy in other territories and chronologies.

Nick Jacobson (Postdoc ERC project ALFA)

Time, Sense Perception, and Experiential Knowledge in John of Saxony’s Epochs of Nations

During the late fourteenth and early fifteenth centuries, the calculating techniques described by the canons found in the Alfonsine Tables became a topic of general epistemological interest at the University of Paris and other major centers of learning in Latin Europe. Scholars and ecclesiastical administrators, such as Nicole Oresme (d. 1382), Pierre d’Ailly (d. 1420), and Nicholas Cusanus (d. 1464) correlated these iterative and approximating methods of calculation with practical modes of knowing, which they associated with a distinct realm of human experience and political action. Drawing on Aristotelian natural philosophy, these scholars often questioned the reliability of the data established in the tables for being based on conjecture and the particularities of sense perception rather than the exact, invariable principles necessary to establish universally accurate predictions. In this paper, I argue that the early Parisian astronomers who shaped the Alfonsine Tables in the 1320s may have already been aware of these epistemological judgments, and sought to mitigate such criticisms in their canons with recourse to Aristotelian definitions themselves. We see this particularly in the first two propositions of John of Saxony’s 1327 canons, which provided instructions for converting epochs of different nations contained in the tables. In these propositions, John of Saxony cited Aristotle’s treatment of the commensurability of time and physical motion, the infinite divisibility of continua, and the importance of observational experience in order to establish the certainty and convertibility of different epochal radices.

Samuel Gessner (Postdoc ERC project ALFA)

Embedding New Theory in Brass: Alfonsine Trepidation Spheres

The slow changing position of the fixed stars with respect to the vernal point, directly observable through the stars’ changing ortive amplitude, were accounted for by diverging models during the Middle Ages. Ptolemy assumed a linear increase of stellar longitude over time. A text on the movement of the Eighth Sphere (the sphere of the fixed stars), sometimes attributed to Thābit ibn Qurra, circulated in the West and described a back-and-forth movement. In the Latin world this movement of “access and recess” was termed trepidation. The Toledan tables (11th c.) included this same movement of trepidation. In the Castilian Alfonsine tables (ca. 1270) trepidation of the Eighth Sphere is also considered. In Parisian Alfonsine astronomy those secular changes are described by combining a linear change (one revolution in 49000 years) with a trepidation movement. Very few spatial, material representations of these aspects of astronomical theories are known: today only about a dozen surviving armillary spheres are modelling the phenomenon of trepidation. Some such trepidation spheres from the 16th century are signed by the famous G. Arsenius. A systematic description and comparison of these spheres is still lacking. An outline of such a comparative study will here be proposed. It will have to tackle the relationship between competing theories, astronomical tables and canons on the one hand and visual representations, including diagrams and material models, like armillary spheres, on the other.