ALFA Conference 2022

Alfonsine Astronomy: trends and nodal points

11.10. 2022-13.10.2022

Observatoire de Paris, Salle du Conseil


Organisation: 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 first team meeting of ALFA’s final scientific phase, we will discuss potential topics of research.  We do not expect, at this point, to review completed research in written contributions, but rather to shape together our individual and collective research programs.

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 could, for instance, also consider 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.


Under these broad dimensions, we  will have during the conference three different themes explored. A first group of contributions, assembled under the title Trends in the transmission of Alfonsine works,  explore how the tradition and reception  of different central, or more peripheric works in alfonsine astronomy reveals important facts about the development of this tradition. A second series of contributions, assembled under the heading  Specific milieus view on Alfonsine astronomy, adopt a less diachronic view and analyze how Alfonsine astronomy takes a different shape in different contexts. The third series of contributions, assembled under the title  Alfonsine astronomers views on their practices, study different facets of the astronomical practices as described by astronomers themselves.


Albouy Ségolène, Andriani Eleonora, Bui Camille, Caudanau Anne-Laurence, Glen Van Brummelen; Chabás José,  Gessner Samuel, Hadrava Petr, Hadravova Alena, Husson Matthieu, Jacobson Nick, Kremer Richard,  Penin Jean-Claude, Saby Marie-Madeleine, Serra Sophie, Tur Alexandre, Zieme Stefan


Tuesday  October 11, 2022 

Trends in the transmission of Alfonsine works

Chair: Husson

9h30-10h15 Introduction

10h15-11h30 Kremer Circulation of the Parisian Alfonsine Tables in Latin Manuscripts

11h30-11h45 coffee break

11h45-13h00 Saby and Chabás  Titles and incipits of canons in relevant texts in early Alfonsine astronomy

13h00-14h15 lunch

Chair: Gessner

14h15-15h30 Zieme OnThe Equation of time in the Alfonsine tradition

15h30-16h45 Hadrava Layout of Tabule resolute

16h45-17h00 coffee break

17h00-18h15 Andriani & HussonDiscussion on the book JoL Tabule magne and related texts


Wednesday October 12  2022

Historical actors views on their astronomical practices

Chair: Trigg

9h-10h15 Serra, Historical Changes and the Notion of Change in Medieval Parisian Astronomy

10h15-11h30 Jacobson, Observations, precision and the use of instruments in canons texts

11h30-11h45 coffee break

11h45-13h00 Chabás,  Computing eclipses in early Alfonsine astronomy

13h00-14h15 lunch break

Chair: Serra

14h15-15h30 Husson, Probatio operationis,  Alfonsine astronomers views on accuracy and the epistemological values of computation

15h30-16h45 Fernandez Alfonsine Astronomy, Salamanca and the Oxford Canon. Misc. 27

16h45-17h00 coffee break

17h00-18h15 Jacobson, Discussion on his book on Alfonsine canons


Thursday October 13, 2022 

Specific milieu views on alfonsine astronomy and their historiographical importance

Chair: Jacobson

9h-10h15 Hadravova, Reception of the Alfonsine astronomy by Czech humanists in the age of printing at the break of the 15th and 16th century (Augustinus Moravus Olomucensis, Bohuslaus Hassensteinius a Lobkowicz)

10h15-11h30 Andriani & Jacobson, From the Court of Alfonso to the Court of John of Bourbon: Alfonsine Astronomy as an actor’s category

11h30-11h45  coffee break

11h45-13h00 Gessner, Fifteenth Century Forms of Appropriation of Alfonsine Astronomy at the Universities of Erfurt and Leipzig

13h00-14h15 lunch break

Chair: Andriani

14h15-15h30  Brummelen, Bianchini’s reform of mathematical astrology

15h30-16h45 Caudano, A Byzantine Version of the Alfonsine Tables of Paris in an Astronomical Compilation of John Chortasmenos

16h45-17h00   coffee break

17h00-18h15 General discussions



Titles and incipits of canons in relevant texts in early Alfonsine astronomy

Marie-Madeleine Saby and José Chabás

Thorndike and Kibre’s list of incipits of medieval scientific writings (1963) has proven to be an extremely useful tool for research in the history of medieval science. In a much shorter, but more detailed scale, we present here a specific research tool for the history of Alfonsine astronomy, consisting of the titles and incipits of the canons in major texts written by the first generation of Alfonsine astronomers. This tool should allow researchers to identify such canons, even when they appear separately in miscellaneous manuscripts.


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 catalogs, 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?


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

Anne-Laurence Caudano

Codex Vaticanus Grecus 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.


Computing eclipses in early Alfonsine astronomy

José Chabás

For medieval 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.


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.


Layout of Tabule resolute

 Petr Hadrava

Tabule resolute (TR) were derived from Parisian Alfonsine tables (PAT), however, their layout differs significantly and it evolved in the course of the spreading of TR to different European centers of education. The abandoning of the systematic usage of the sexagesimal system and the usage of cyclic radices in tables of mean motion are the most conspicuous but not the only features in which TR differs from PAT. A review of them will be presented in the contribution.


Reception of the Alfonsine astronomy by Czech humanists in the age of printing at the break of the 15th and 16th century (Augustinus Moravus Olomucensis, Bohuslaus Hassensteinius a Lobkowicz)

Alena Hadravová

On the case of the two foremost Czech humanists, Augustinus Olomucensis in Moravia and Bohuslaus Hassensteinius a Lobkowicz in Bohemia, I would like to show how the Alfonsine astronomy was still living, vivid and flourishing at the break of the 15th and 16th century in the Czech countries. Augustinus Moravus (1467–1513), a provost in Brno and Olomouc, studied in Cracow and Padua and a stimulating environment of both universities influenced his interests in astronomy and in publishing of its important contemporary works (cf. his edition of Bianchini´s Tables in 1495, his inspiration of Santritter´s edition of PAT in 1492), while the nobleman Bohuslaus Hassensteinius (1461–1510) is known as the owner of the rich library, containing best contemporary titles (both incunabula and early modern prints), including astronomical production. He owned a collection of astronomical instruments, too, and tried to observe and work with them in his castle Hasištejn. There existed also some direct contacts between both these prominent persons of the Latin phase of humanism in the Czech lands since the end of the government of the King Georg of Poděbrady up to the end of the reign of Jagellonians (1471–1526).

Historical Changes and the Notion of Change in Medieval Parisian Astronomy

Sophie Serra

One of the main areas of investigation left open for Phase 3 of the ALFA project is the analysis of the acknowledged innovative and creative aspects related to Alfonsine Astronomy. To take up this subject, one approach could be to select several crucial and innovative traits (ways of displaying tables, trends in organizing tables, values selected…), but another one could be to look at innovation in itself and how it was conceived by astronomical actors, thus giving us, ultimately, an entry point and help us perceive from the historical changes in astronomy through the scope of the notion of change. Indeed, any innovation presupposes to leave aside what was previously accepted. Therefore, to reflect upon how correction, adaptation, gradual approximation, incorporation of minor regional changes were thought of and put into use by astronomers at the turning point of the 13 th and the 14 th 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 delicate tipping point of the beginning of the 14 th 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).

This paper will then aim at contributing to a better knowledge of a precise aspect of the history of Alfonsine Astronomy (change and error management), while at the same time being an historiographical and epistemological study on the categories of change and error.


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 were the primary purpose of 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 Court to which he put his skills at the service of, 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 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 for him. 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 emphasizes the content of the material and how it fits within a curriculum, and in the Court context he emphasizes rather the status of Alfonso as a patron.


Probatio operationis  Alfonsine astronomers views on accuracy and the epistemological values of computation

Matthieu Husson

In a student manuscript left by John of Saxony (Erfurt, 2° 377) we find a series of autograph notes providing some kind of mathematical rationale (demonstratio) of shadows and sun altitude computations as described by John of Lignères canons Cujuslibet arcus. Later John of Saxony made an extensive commentary on the canons of his master John of Lignères consisting of long, slightly commented, computed examples following the Cujuslibet instructions.  This commentary mention an intriguing probatio operationis of the same procedures for shadows and altitude.  Relying on the manuscripts and the edition made by Marie-Madeleine Saby, I propose to analyze this small corpus and reflect on what a probabtio operationis could be for John of Saxony and his milieu.

I will then explore the historiographical potential of the lessons learned from this initial case study in a broader way as a means to think about historical actors’ views on accuracy and the form of reasoning they develop through computations cautiously expanding beyond the Parisian milieu where to my knowledge this expression is first attested.


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 visualize the complex sequences of computation and make evident the relationship of quantities that astronomers routinely manipulated. 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 examine the profiles 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 analyze the images from a formal and iconographic point of view.


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.