ALFA conference 2023

Alfonsine Astronomy: trends and nodal points

06.09. 2023-08.09.2023

Madrid and Toledo


Organisation: Laura Fernandez, Matthieu Husson, José Chabás, Richard Kremer


After studying the written records of Alfonsine astronomy and the mathematical/astronomical practices of Alfonsine astronomers, ALFA’s third and last phase seeks to shape the broader pictures that emerge from the specific results of the first two phases.  At this second team meeting of ALFA’s final scientific phase, we will discuss draft chapters of the future collective book on these historiographical  questions. For each presentation 15 minutes will provided to the authors to make a quick summary of their argument and 30 minutes will be devoted to a discussion, initiated by a ‘respondant’ in order to discuss ways to improve the chapter argument and its integration in the collective book.

Overall there are at least three interrelated dimensions to the historical phenomena we are trying to capture in this last phase of the project:

  1. The subtle balance of innovation and stability.  The main features of the astronomical models and computed positions remained stable over the Alfonsine era, although not entirely univocal; but practices, tables sets and the ways to think about them were constantly re-elaborated in the production of new works and the compilation of works in multiple ways in new manuscripts. Thus Alfonsine astronomy was, at the same time, doctrinally stable and intellectually dynamic.  This resulted in “internal” trends concerning numbers, the design and layout of tables, the design of canon texts, the design of instruments, and ways to articulate these elements. Creativity was also expressed in particular topics: computations of syzygies and eclipses, motion of the eight sphere, spherical astronomy, latitude computation, and specific kinds of astronomical computations (direction, aspects and planetary velocities, double-argument interpolation, etc.).
  2. The uses of Alfonsine astronomy. Astronomical activity was fostered in university and courtly contexts by scholars with differing profiles. It was put to use in various ways by astrologers, physicians, surgeons, and civil and religious authorities. The growing cultural exposition of Alfonsine astronomy to an ever wider and more diverse audience had a profound impact on its development.  This resulted in “external” trends of development for Alfonsine astronomy and had consequences expressed in various demands for “user friendliness”, accuracy, and epistemic robustness. Such studies consider, for instance, how historical actors perceived “Alfonsine astronomy” and how this image changed over time and place.
  3. Multiple astronomical traditions.  Alfonsine astronomy was not isolated as an astronomical tradition. Although for strictly computational aspects it (arguably) progressively replaced the Toledan Tables, for some Latin practitioners Alfonsine astronomy remained dependent on materials related to the Toledan Tables. In a broader historical context, Alfonsine astronomy shared essential elements with other mathematical astronomy traditions in Arabic, Hebrew or Greek that were flourishing before, at the same time and after it.


Andriani Eleonora, Cartier Clément, Anne-Laurence Caudano , Glen Van Brummelen; Chabás José,  Gessner Samuel, Hadrava Petr, Hadravova Alena, Husson Matthieu, Jacobson Nick, Laura Fernandez, Kremer Richard,  Penin Jean-Claude, Saby Marie-Madeleine, Serra Sophie, Tur Alexandre, Zieme Stefan


Wednesday  September 6, 2023

Faculty of Geography and History, Complutense University, “Sala de Grados”

Session 1:

Chair: Fernandez


Richard Kremer Circulation of the Parisian Alfonsine Tables in Latin Manuscripts

Respondant: José Chabás


José Chabás and Bernard R. Goldstein Late mediaeval star lists and the computation of precession: The case of Heinrich Selder and the Alfonsine tradition

Respondant: Richard Kremer

11h00-11h30 coffee break


Marie-Madeleine Saby The Canons for the Tables of 1322 by John of Lignères : an edition with a french translation and Introduction

Respondant: Matthieu Husson


José Chabás Computing eclipses in early Alfonsine astronomy

Respondant: Clément Cartier

13h00-14h30: Lunch

Session 2

Chair: Gessner


Alena Hadravová, Petr Hadrava Spreading of treatises on astrolabe by Cristannus of Prachatice

Respondant: Samuel Gessner


Clément Cartier Printing the “Tables of King Alfonso”

Respondant: Alexandre Tur

16h00-16h30 coffee break


Anne-Laurence Caudano A Byzantine Version of the Alfonsine Tables of Paris in an Astronomical Compilation of John Chortasmenos

Respondant: Eleonora Andriani


JeanClaude Penin, Matthieu Husson Alfonsine astronomy historiography (late 15th c. to early 20th c.)

Respondant: Sophie Serra


Thursday  September 7, 2023

Faculty of Geography and History, Complutense University, “Sala de Grados”

Session 3:

Chair: Kremer


Sophie Serra History, errors and corrections: Change according to Medieval Parisian Astronomers

Respondant: Nick Jacobson


Eleonora Andriani and Nick Jacobson From the Court of Alfonso to the Court of John of Bourbon: Alfonsine Astronomy as an actor’s category

Respondant: Glen Van Brummelen

11h00-11h30 coffee break


Samuel Gessner Fifteenth Century Forms of Appropriation of Alfonsine Astronomy at the Universities of Erfurt and Leipzig

Respondant: Richard Kremer


Laura Fernandez Alfonsine Astronomy, Salamanca and the Oxford Canon. Misc. 27

Respondant:José Chabás


13h00-14h30: Lunch

Session 4

Chair: Serra


Alena Hadravová  Reception of the Alfonsine astronomy by Czech humanists in the age of printing at the end of the 15th and in the 16th century

Respondant: Marie-Madeleine Saby


Alexandre Tur Reading and copying annual prognostications in the 15th century

Respondant: Laura Fernandez

16h00-16h30 coffee break


Glen Van Brummelen Bianchini’s reform of mathematical astrology

Respondant: Stefan Zieme


Stefan Zieme OnThe Equation of time in the Alfonsine tradition

Respondant: Matthieu Husson


Friday  September 8, 2023




Circulation of the Parisian Alfonsine Tables in Latin Manuscripts

Richard Kremer

ALFA’s survey of the “Alfonsine corpus” has identified about 170 manuscript copies of the Parisian Alfonsine Tables (PAT), roughly defined as containing both the Alfonsine equations and the mean motions in sexagesimal days.  The earliest known copies date from 1351 (BJ 618, Erfurt CA F384), the latest from the mid 16c.  Already in 1968 Poulle and Gingerich identified some systematic variants in the equations, caused either by column slippage (inserting or deleting an entry in a column and sliding the remaining entries up or down by one line) or random scribal errors, that appear in more than one manuscript copy.  I have found several additional systematic variants. These 7 markers (4 Mars, 2 Venus, 1 Sun), plus the radices for places added by scribes to the mean motion tables, may allow us to construct a stemma codicum of the PAT in manuscript.  All 7 markers present erroneous entries; none of the markers appear in Ratdolt’s editio princeps of 1483.

To date I have examined about one-third of the manuscripts located by the ALFA survey.  Drawing on that information plus details about provenance from the published manuscript catalogues, I will offer some preliminary conclusions about the circulation of the PAT, over two centuries, in Latin manuscript cultures.

I will also offer preliminary thoughts on the “stickiness” of Alfonsine works, again using the ALFA survey.  What other works circulated in codices that contain the PAT?  Which canons?  Which eclipse tables?  Which astrological or theoretical (e.g., theorica planetarum) texts?  Which Instrument texts?  To employ a metaphor from Alfonsine Astronomy: The Written Record (2022), can various types of computational “toolboxes” be identified within the Alfonsine corpus?


Computing eclipses in early Alfonsine astronomy

José Chabás

For mediaeval astronomers the most complex computations probably concerned eclipses, especially solar eclipses. The first generation of Alfonsine astronomers addressed these issues in a variety of texts explaining the procedures involved and providing numerical examples. The purpose of this paper is to offer a preliminary overview of these early fourteenth-century texts and the computations they display, identify the procedures they describe, and examine the innovations they contain, as well as the sources on which they depend.


The Canons for the Tables of 1322 by John of Lignères : an edition with a french translation and Introduction

Marie-Madeleine Saby

In the early 14th c. several scholars around the Paris university worked on the Toledan tables and canons material. John of Lignères, master of art, was one of them and his name became an « authority » in the early Parisian Alfonsine Astronomy.

The two lengthy canons which can be associated to the set of Tables of 1322, just published in ALFA Project, are going to be, in turn, also edited and translated. The first set of canons, bearing the incipit Cuiuslibet arcus propositi sinum rectum is composed by 44 chapters (9,400 words). The second, beginning Priores astrologie motus corporum celesti; is structured in 46 chapters (21,000 words). Reading through such a double treatise, with the intent to provide a scientific edition and translation raises several issues dealing either with methodology or with translation itself. The purpose of the presentation should be to bring in discussion some of this points and help towards well-reasoned choices.


Late mediaeval star lists and the computation of precession: The case of Heinrich Selder and the Alfonsine tradition

José Chabás and Bernard R. Goldstein

Mediaeval astronomers compiled star lists based on Ptolemy’s star catalogue and adapted it to their times by adding a constant due to precession to all stellar longitudes in it. In this paper we focus on one such list, composed by the Swabian astronomer Heinrich Selder (mid-fourteenth century). We also propose a classification of the many star lists found in Latin astronomical manuscripts and we compute the values for precession according to the algorithm described by John of Saxony in his canons to the Parisian Alfonsine Tables.


Spreading of treatises on astrolabe by Cristannus of Prachatice

Alena Hadravová, Petr Hadrava

For Alfonsine astronomy as a whole, it is characteristic the dissemination of its works (tables and canons for their use, texts on instruments and theoretical works) between the centres of learning throughout Europe, where they were further copied, elaborated, commented, and became a study material for students of mediaeval universities. Some of the works have survived in dozens of copies (e.g. Parisian Alfonsine Tables, Tempus est mensura motus), which testifies the particular attention with which these works were regarded as the basis for relevant type of work because of their quality. Among the works on instruments, the treatises on Composition of the Astrolabe (inc. ‘Quamvis de astrolabii composicione’) and on its Use (inc. ‘Quia plurimi ob nimiam quandoque accurtacionem’) by Cristannus of Prachatice from 1407 were outstanding, both widely copied and published in print as the first works on this instrument ever, although sometimes mistakenly attributed to other authors (e.g. Robertus Anglicus, Prosdocimo de Beldomandi). In our contribution we will mention both the great spreading of Cristannus´ work itself and its influence on the founder of the Vienna astronomical school, Johannes von Gmunden.


Printing the “Tables of King Alfonso”

Clement Cartier

This paper aims to understand how the printing worlds from the 15th to the 17th adopted and transmitted the “tables of King Alfonso”: what is the textual, astronomical and mathematical contents that was put under this name? how was these contents presented in printed editions? and what could have been the motives of early printers to produce editions of these tables? A lot of materials that would fall under what we now call the “Alfonsine tradition” circulated during that period. Many of them were almanacs, ephemera or calendars. Some others claimed a relation with the Tabulae resolutae, were derivatives of the Tabulae directionum, or had other titles indicating their link with traditions we consider as alternative versions of the “Parisian Alfonsine Tables”. But only six printers during this period proposed an edition of the “tables of King Alfonso”, explicitly invoking the figure of Alfonso the Wise. I focus my attention on these editions, and try to understand the implications for editors of choosing this name. It appears that the “tables of King Alfonso” don’t seem to designate one well-defined object: it is rather a practical heritage of a “christian” culture, which the (humanist) mathematicians who inherit it can take advantage of, adapt, and use to further their own interests.


Alfonsine astronomy historiography (late 15th c. to early 20th c.)

Jean-Claude Penin, Matthieu Husson

How Alfonsine astronomy progressively became an object of historical inquiry?  This is the central question considered in this chapter.  While, as demonstrated by other contributions,  this question can be approached differently and through different sources, we chose a longue durée approach to it extending from the second half of the 15th century, when we can perceives the first clues of an historiographical sensibility to Alfonsine astronomy, to the first half of the 20th century (before world war II), when the shaping of the question of the ‘origin’ of the Alfonsine tables was settled. In this long period exhaustivity can not be achieved and thus we selected in each century a few references allowing us to point to the main articulations of this historiography. Astronomers and bibliographers, which can often be one and the same persons (e.g. Simon de  Phares or  Lalande), are the two fundamental types of authors we are considering in this study. They are mostly holding the grounds until the 17th century. During the following two centuries astronomers and bibliographers continue to be central but new types of concerns brought by different authors  become more and more present.   In the 18th century more philosophical approaches to history in general and to history of astronomy in particular, emerged with the enlightenment, while from the second half of the 19th century a progressive institutionalisation of historical research within state universities was accompanied by the development of national approaches. Along these different moments we will follow the types of primary and secondary sources which are used, the treatments and analyses they apply on them, the type of question they address and the form of discourse they produce.


A Byzantine Version of the Alfonsine Tables of Paris in an Astronomical Compilation of John Chortasmenos

Anne-Laurence Caudano

Codex Vaticanus Graecus 1059 is an early 15th century astronomical miscellany with many texts and tables, as well as a variety of astronomical exercises all copied or done by the Patriarchal notary John Chortasmenos (ca. 1370-before June 1439). Within this material is the only Byzantine version of the Alfonsine Tables of Paris and accompanying methods ascribed to the statesman and anti-Latin theologian Demetrios Chrysoloras (ca. 1360-after April/May 1416). Tables of radices for Paris and Cyprus (dated 1379), likely point to Cyprus as the origin of the text and tables. All the examples are dated 1377-1379, as may be expected, but intriguingly, the examples all seem to use a different set of radices (for Constantinople?). That the tables belong to the tradition of the Parisian Alfonsine tables, as published by Ratdolt in 1483, is clear from their overall layout and the data they reproduce, but the order of the tables is different as the Greek tables are sorted by planets.  Furthermore, Chrysoloras’s accompanying canon differs from that of John of Saxony in two ways. First, the language seems to be borrowed from Theon of Alexandria’s Short Commentary to the Handy Tables, sometimes word for word. Second, the text is decidedly shorter than the Latin canon and Theon’s commentary. No theoretical explanations or definitions are provided, only the necessary means to use the tables reproduced afterwards. Finally, there are no methods or tables related to the calculation of eclipses, a puzzling observation considering Byzantine astronomers’ interest in the subject at the time.


History, errors and corrections: Change according to Medieval Parisian Astronomers

Sophie Serra

Innovative and creative aspects related to Alfonsine Astronomy have been many times highlighted all along the duration of the ALFA project. To take up this subject, one approach is to select several crucial and innovative traits (ways of displaying tables, trends in organising tables, values selected…), but another is to look at innovation in itself and how it was conceived by astronomers, thus giving us, ultimately, an entry point and help us perceive the historical changes in astronomy through the scope of the historical actors notion of change. Indeed, any innovation presupposes to leave aside at least some elements of what had been previously accepted, taught and copied faithfully. Therefore, to reflect upon how correction, adaptation, incorporation of minor regional changes were thought of and put into use by astronomers at the turning point of the 13th and the 14th can give us material to build a narrative about how Alfonsine Astronomy imposed itself from the 1320s, using for that both the practices and declarations about changes in astronomy by the historical actors themselves. In order for this narrative to deal with the still too little-known tipping point of the beginning of the 14th c., this paper will examine four cases of change and error management: two “pre-Alfonsine” astronomers (John of Sicily and William of Saint-Cloud) and two “Alfonsine” astronomers (John of Lignières and John of Murs), with a special focus on prologues and theoretical declarations and comments on the more practical aspects of their works. This paper will then aim at contributing to a better knowledge of a precise aspect of the history of Alfonsine Astronomy (the definition, identification and management of error), while at the same time being an historiographical and epistemological study on the categories of change and error that can be used by the historian of science to reflect on the very moving nature of its objects.


From the Court of Alfonso to the Court of John of Bourbon: Alfonsine Astronomy as an actor’s category

Elonora Andriani & Nick Jacobson

In the Middle Ages and the Renaissance, astrological practices ranked among the most prominent reasons for making astronomical calculations, and were considered an essential component of medical practice and political decision-making. A historical figure who perfectly embodies the crucial link between astrology, astronomy and politics in the second half of the 15th century is certainly the Zurich astrologer and physician Conrad Heingarter. Heingarter offers a unique window into the context of two milieus, the Bourbon Court in which he was active, and the University of Paris with which he maintained intellectual links even after his studies. The manuscripts he collected as part of his service to Duke John II of Bourbon, most of which are preserved at the BnF, came to shape what texts constituted Alfonsine Astronomy as defined by modern historians. In our contribution we aim to define what Alfonsine Astronomy meant for Conrad Heingarter, and how it served as a category framed within a broader history of astronomy. By investigating his library and new documents that have not yet been considered, we will address this research question in two different respects. In the first case we will look at the Parisian University context in which Heingarter was educated and in which he developed a curriculum for the study of astronomy that he meant to pass on for future generations. In the second case we will examine his career as a court astrologer and how he fashioned his role at the Bourbon Court after the manner of those astronomers who first compiled the Alfonsine Tables. Depending on which context Heingarter was serving, he references this tradition in different ways: in the University context he emphasises the content of the material and how it fits within a curriculum, and in the Court context he emphasises rather the status of Alfonso as a patron.


Fifteenth Century Forms of Appropriation of Alfonsine Astronomy at the Universities of Erfurt and Leipzig

Samuel Gessner

This study concerns the reception of the works of the Parisian Alfonsine astronomers at German universities. It focuses on the emergence of an original type of planetary instrument: the Theorice Novelle. This development was based on the understanding of the Alfonsine tables and on full mastery of astronomical computation. The instruments are a simple way to visualise the complex sequences of computation and make evident the relationship of quantities astronomers routinely manipulate. The instruments were probably conceived in Erfurt, one of the largest universities in German lands, in the third quarter of the fifteenth century.

It has long been known that the Theorice Novelle were connected to Erfurt and Leipzig (Zinner 1956, Pedersen 1958, Poulle 1980). The collegium Porta Coeli in Erfurt, founded by Amplonius Ratinck de Berka in 1412, probably served as the intellectual context of this invention. In recent years, a few more copies of these instruments have been newly located (e.g. Kremer 2011). Some of these come with the necessary mean motion tables and radices. Among them are instruments that present hitherto unknown variant developments of the initial principle. Based on this, the present study inquires on the context of development of the instruments and their spread. To do so it will look at the profile of some of the authors and owners of works related to Theorice Novelle.


Alfonsine Astronomy, Salamanca and the Oxford Canon. Misc. 27

Laura Fernandez

Ms. Canon Misc. 27 preserved in the Bodleian Library, Oxford, is a miscellaneous manuscript of Hispanic origin, datable to the 15th century. It includes two texts on astronomical tables, one by Jacobus Bone Diei and the other by Nicolas Polonius, both according to the meridian of Salamanca. Thanks to the indication that we find in one of the tables by Polonius, on folio 118r, we can know not only where they were made, but also in what year, 1460, which has led us to consider that Nicolas Polonius himself was the author of the compilation. In addition, the book has a set of beautiful representations of the zodiacal constellations (ff. 152r-157v), with their stars highlighted in red and descriptive legends written in Castilian that can be related to Alphonsine materials. To which Alphonsine sources do these data refer? Where could Polonius have learned about them, in Salamanca or before arriving in the city? In a first approach to the manuscript I will try to locate the possible textual source of the legends as well as to analyse the images from a formal and iconographic point of view.


Reception of the Alfonsine astronomy by Czech humanists in the age of printing at the end of the 15th and in the 16th century

Alena Hadravová

In the second half of the 15th century, the Middle Ages declined in the Bohemian lands and humanism began to emerge. Among astronomers who at the break of the 15th and 16th century cultivated Alfonsine astronomy more or less in the traditional spirit, was Wenceslas Faber of Budweis (1455/60–1518), whose works were mostly published abroad (Leipzig). At this time, however, the works of Alfonsine astronomy also began to attract the attention of the leading early Czech humanists. They were able to impact public opinion and support education and scholarship thanks to their influential position in the state or church administration. Among them, Augustinus Moravus Olomucensis (1467–1513) and Bohuslaus Hassensteinius a Lobkowicz (1461–1510) occupied a prominent position. They helped bring works of the Alphonsine tradition into the 16th century. The Alfonsine tradition was then practically followed and partly cultivated by a mathematician, astronomer and astrologer Cyprianus Leovicius a Leonicia (Cyprián Karásek Lvovický ze Lvovic, 1524–1574), who lived and worked in Lauingen, Bavaria.


Reading and copying annual prognostications in the 15th century

Alexandre Tur

Anecdotic before the 15th century, annual prognostications seem to peak in the wake of the development of Alfonsine astronomy. Based on key astronomical events (equinoxes, solstices, eclipses…), they detailed their potential impact on weather patterns, agricultural yields, wars and epidemics, and other important aspects of daily life. Unlike the more traditional astrological predictions (nativities, interrogations, elections), dedicated to one patron and generally kept secret, annual prognostications were aimed at a wider audience and made publicly available in universities, but also in courts and towns, and progressively through manuscript and printed booklets. They were particularly eagerly collected and copied in regions in which they were less common. Could they be considered the result (or the mean) of a “cultural exposure” to Alfonsine astronomy?

This paper seeks to provide a broad overview of the dissemination and reception of annual astrological predictions in fifteenth-century Europe, before and after the invention of printing, and questions their relationship with the networks of Alfonsine astronomy.


Bianchini’s reform of mathematical astrology

Glen Van Brummelen

The two versions of Giovanni Bianchini’s Tabulae primi mobilis are quite different from each other with respect to their mathematical methods and tables, but their purposes were the same: to introduce planetary latitudes into the practice of astrology. While he was not the first European astronomer to use latitudes, he may have been the first to be systematic about it, and to operate according to mathematical standards at the level of Ptolemy. Bianchini made three contributions: firstly, he demonstrated that incorporation of latitudes can shift the astrological house into which a planet falls, thereby changing the forecast substantially. Secondly, he invented a new model for projecting the rays that uses latitudes. Thirdly, in the Tabulae primi mobilis B he used his new theory of coordinate conversion to reform the traditional practice of primary directions. His influence endured; indeed, some of this work is still used (and still named after Bianchini) by professional astrologers today.


OnThe Equation of time in the Alfonsine tradition

Stefan Zieme

The table of the equation of time is one of the few tables in tabular astronomy that was recalculated time and again. Since the equation of time is determined for a specific apogee of the sun, the need for recalculation is linked to the advance of the solar apogee. Within the corpus of Alfonsine Astronomy there are about ten different tables for the equation of time. In this talk I will present a survey of these tables, including their pre-Alfonsine precursors and their Copernican successor. I will discuss how different users, compilers, and editors of sets of astronomical tables copied, corrected, recalculated, or modified tables for the equation of time.