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The Diffusion of the Alfonsine Tables: the Case of the Tabulae Resolutae

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The Diffusion of the Alfonsine Tables: the Case of the Tabulae Resolutae The Diffusion of the Alfonsine Tables: The case of the Tabulae resolutae José Chabás University Pompeu Fabra, Barcelona, Spain Downloaded from http://direct.mit.edu/posc/article-pdf/10/2/168/1789147/106361402321147513.pdf by guest on 26 September 2021 The Alfonsine Tables were compiled during the second half of the 13th cen- tury in Toledo, Spain, and were largely diffused throughout Europe, mainly via Paris. They became the basic computing tool for European astronomers during several centuries. The Tabulae resolutae are a particular form of presenting the Alfonsine material which differs in many ways from that in the ªrst printed edition of the Alfonsine Tables (Venice, 1483). This paper focuses on the inºuence of the 15th century Viennese astronomer John of Gmunden on the genesis of the Tabulae resolutae, and analyses its contents and impact on European astronomy. 1. The Tabulae resolutae is a set of astronomical tables that circulated widely in Europe during the 15th century in manuscript form, and as printed books during the 16th century. They are strictly based in the Alfonsine Tables; moreover, they are a particular form of presenting the Alfonsine Tables which largely differs from that in the editio princeps (Venice, 1483). The most visible difference is that the Tabulae resolutae maintain the sys- tem of cyclical radices with intervals of 20 years that is explained in can- ons to the Castilian Alfonsine Tables, rather than the organization in days to be counted sexagesimally, as in the editio princeps. The history of the Alfonsine Tables is well known. Two centuries earlier King Alfonso X of Castile and León, called the Learned, gathered at his court a group of Muslim, Jewish, and Christian scholars. They translated scientiªc works from Arabic into Castilian, and wrote some original trea- tises on astronomy and related disciplines. Among them are the Alfonsine I thank Peter Barker and Bernard R. Goldstein for their for their help in writing this paper, and Beatriz Porres for her useful comments. Perspectives on Science 2002, vol. 10, no. 2 ©2003 by The Massachusetts Institute of Technology 168 Perspectives on Science 169 Tables, composed of canons and tables, and written in Toledo around 1272 by two of the king’s collaborators: Judah ben Moses ha-Cohen and Isaac ben Sid. The canons are extant in a unique manuscript in Castilian: Ma- drid, Biblioteca Nacional, MS 3306. On the other hand, the Castilian Alfonsine Tables have not been preserved in their original presentation, a fact that has given rise to all kinds of conjectures. These tables depended on the rich astronomical tradition developed in medieval Spain, mainly Downloaded from http://direct.mit.edu/posc/article-pdf/10/2/168/1789147/106361402321147513.pdf by guest on 26 September 2021 from Islamic sources, and were to become the most inºuential astronomi- cal tables in Christian Europe during more than three centuries. In the early 14th century the Alfonsine Tables reached Paris, and in the 1320s some canons were written in Latin to explain their use. The tables were also modiªed from the original model, but it is impossible to know to what extent, for the original set of tables is missing. The Latin version of the Alfonsine Tables recast in Paris then reached Oxford and Italy, and spread very largely throughout Europe, becoming the main computing tool for European astronomers (North 1977). Along with their diffusion, the tables diversiªed. They were adapted to various meridians, other than that of Toledo, which had been maintained by the ªrst Parisian astronomers. Even their presentation kept evolving. However, the underlying models, as well as the parameters they are based on, were never challenged. These tables share other common basic fea- tures, but the variety of sets of tables in the Alfonsine tradition is so vast that the term “Alfonsine Tables”, with no further speciªcation, is no longer appropriate. The scholarship devoted to this particular subject has already reached a level of precision which requires a more accurate termi- nology. 2. The diffusion of the Parisian Alfonsine Tables in Central Europe is not well known. However, a crucial role was probably played by John of Gmunden (ca. 1380–1442), the ªrst professor in mathematics and astron- omy at the University of Vienna, where he lectured since 1408 (Mundy 1942–3; Vogel 1975). He was the author of several works on arithmetic and instruments (the quadrant of Jacob ben Makhir, the astrolabe, the cylindrum, the albyon of Richard of Wallingford), and he also wrote com- mentaries to some astronomical treatises (the Theorica planetarum of Campanus, the canons of John of Murs, and the Sphaera of Sacrobosco). His original astronomical works include many calendars and ephemerides (starting from 1415), some of which were published after his death. He also composed some canons and tables, making continuous changes in them from 1422 to 1440. 170 The Diffusion of the Alfonsine Tables These canons are being edited by Beatriz Porres (2003), and have al- ready been the object of a ªrst survey. It turns out that John of Gmunden’s canons to his tables depend heavily on those written for the Alfonsine Ta- bles by the Parisian astronomers of the early 14th century: John of Sax- ony’s (1327), on the one hand, but especially the canons by John of Lignères written in 1322 and beginning with “Cuiuslibet arcus propositi” and “Priores astrologi”. Downloaded from http://direct.mit.edu/posc/article-pdf/10/2/168/1789147/106361402321147513.pdf by guest on 26 September 2021 The tables appended to his canons form a voluminous and coherent set. John of Gmunden uses “physical” signs of 60°, as in the version of his ta- bles in Vienna, Nationalbibliothek, MS 5151, but some time later switches to “zodiacal” signs of 30°, as in another manuscript, also in Vi- enna, MS 5268. In Gmunden’s tables, the mean motions of the luminaries and the ªve planets are displayed for groups of 20 years, which is the standard period that was used in the original Castilian Alfonsine Tables, a fact explicitly mentioned in the Castilian canons. We note that this was not the period used by John of Lignères (25 years). Then follow the equations for access and recess, the 8th sphere, the Sun and the Moon, and the ªve planets. The tables for the solar declination and the lunar latitude use parameters well attested in medieval Spain: 23;33,30° for the obliquity of the ecliptic and 5;0,0° for the maximum latitude of the Moon. The tables for the planetary latitudes and for planetary visibility and retrogradation are identical to those found among John of Lignères’s ta- bles, but also identical to those in such pre-Alfonsine sets as the Toledan Tables. It should be noted that John of Gmunden knew directly, with no intermediary sources, the Toledan Tables, for in his will, in which he leaves his books and instruments to the faculty of arts of the University of Vienna, one of the items is a “white book in parchment containing tabulas toletanas” (Mundy 1942–3, p. 198). Among the trigonometrical tables compiled by John of Gmunden there is one entitled “Tabula differentie ascensionum”. This table is not at all a common feature in the standard literature, but there is a very similar one in another pre-Alfonsine material, the twelfth-century Almanac of Azarquiel (Millás 1943–50, p. 225). The same table is found in the Ta- bulae resolutae for Salamanca, compiled by Nicholaus Polonius ca. 1460 (Chabás 1998, p. 171). Most of the other trigonometrical tables of John of Gmunden are computed for a latitude of 47;46° which corresponds to Vi- enna. The same applies to the only table for parallax in Gmunden’s tables. These are some of the tables related to John of Gmunden’s canons, but they are by no means the only ones he computed or copied in his working papers. There are many others, but two of them are of special interest. Perspectives on Science 171 First, there is a double-entry table to determine the time between mean and true syzygies, a table depending on John of Murs (Porres and Chabás 2001). Then there are also double-entry tables for the planetary latitudes that complement the tables “bipertiales” and “quadripertiales” of Toledan origin mentioned above. It is also noteworthy that the heading of these double-entry tables for the planets indicate that they were compiled in Oxford, thus pointing to the tables of Oxford for 1348. Downloaded from http://direct.mit.edu/posc/article-pdf/10/2/168/1789147/106361402321147513.pdf by guest on 26 September 2021 To sum up, it is clear after examination of his tables that John of Gmunden had at hand a vast quantity of astronomical material, including the best material one could possibly have at the beginning of the 15th century. It is, so to speak, a “Christian” material, which at that time means “Alfonsine”, and no direct inºuence of Arabic or Jewish astronomy is found in his tabular work. It is also clear that John of Gmunden did not make any substantial innovation in his tables; rather, all his tabular work follows the previous tradition, the Alfonsine tradition. Many of Gmunden’s tables are not among those traditionally attributed to John of Lignères, but it is indeed difªcult to be more precise on that point because no edition of these tables has been done yet. On the other hand, some of Gmunden’s tables seem related to a tradition more directly connected to the pre-Alfonsine work. This is the case, very particularly, with the tables for the colors of eclipses and for the unequal motion of the planets, both of them described in the Castilian canons to the Alfonsine Tables, but very rarely found in other sets of tables of the Alfonsine corpus (Goldstein, Chabás, and Mancha 1994).
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