Abstract
Anyone who has worked with medieval astronomical manuscripts will know how many parchment pages are filled with tables, and will have deduced how much of the practice of medieval astronomers was based on their production and use. Yet historians have not been so keen to edit these tables as they have other kinds of astronomical writings, such as the accompanying canons for their use. Apart from the technical challenges of typesetting and laying out tables, which often spread over multiple pages of manuscripts, there has until recently been little attempt to standardise appropriate editorial practices for tables. Thus it has been hard to produce rigorous editions, especially necessary where a tiny discrepancy of digits between two copies could reveal an important moment of astronomical practice. More fundamentally, there has not always been clarity about the purpose of editing large quantities of raw data. What conclusions can we draw from the tables by themselves?
This book stems from more than 20 years of work by its authors, effort that has demonstrated the value of a close engagement with the tables of late-medieval European astronomy. This work has yielded new understandings of their underlying mathematics, the milieux in which astronomers worked and shared information, and the ways the tables were used alongside canons.
The present publication, volume 2 in the new series Alfonsine Astronomy: Studies and Sources, 1 is a welcome addition to this body of scholarship. Chabás and Saby have edited a reasonably well-defined set of 32 tables, the first of two major sets produced by John of Lignères, a key player in the reception and popularisation of Alfonsine astronomy across Europe. The tables support a range of astronomical operations, from solar declination to the calculation of eclipses (though tables of planetary longitudes are noticeable by their absence). Alongside the tables, Chabás and Saby summarise two sets of canons, known as Cuiuslibet and Priores, that relate closely to the tables but do not precisely match their contents. They also summarise other works written by John of Lignères, plus some that they argue were mis-attributed to him.
In an article in the first volume in the Alfonsine Astronomy series, Chabás and Saby explained the basis for their edition of the tables, which uses 10 of the 46 surviving manuscripts. 2 Their descriptions of these 10 reveal some interesting details about the process of copying – including how long it took – though it might have been helpful to include more overarching analysis of the set of manuscripts, drawing out commonalities in their contents and histories, which could have informed conclusions about the use and influence of John of Lignères’ work.
The edition of tables, which forms the bulk of the book, is competently executed. Each table is briefly described with reference to any canons that mention it; if possible, its mathematical basis is explained; and there is a commentary on variant readings, which in places hints at relationships between them (though there is no attempt to produce a stemma codicum). The authors’ attention to these variants allows them to identify copying errors and estimate an overall rate – which turns out to be low, but higher than some other traditions. As for this edition, my spot-check of a dozen entries against a couple of manuscripts identified one error, which is not too bad, yet still reminds us that, like medieval copyists, none of us is infallible.
This work, alongside others by the authors, enhances our understanding of table production in general and John of Lignères’ work in particular, though we do not yet learn much about how (and how much) the tables were used. The authors’ summaries of the Cuiuslibet and Priores treatises give helpful indications about the relationship between treatises and tables, but for a fuller understanding one is left wanting a full edition (and translation) of the canons too; there are surely few historians better qualified to produce it than Chabás and Saby. 3
The authors’ conclusion that the 1322 tables are a ‘bridge’ or ‘intermediary set’ (pp. 39, 28) between the Toledan Tables and the Parisian Alfonsine Tables is stated in a few places, but not fully explained or justified. 4 This leaves the reader a little frustrated, as the potential for historical analysis remains unfulfilled. In the 20 years since the publication of Chabás and Goldstein’s groundbreaking The Alfonsine Tables of Toledo, there has been some debate about the relationship between the work of Toledan astronomers and their Parisian successors – starting with Noel Swerdlow’s review of that book in this journal. 5 Most recently, in another monumental book, Julio Samsó makes some striking claims about the Andalusi roots of Alfonsine astronomy. 6 This is, of course, highly relevant to the question of what precisely was being bridged by John of Lignères’ work, so it is disappointing that Chabás and Saby do not engage with such questions.
Nonetheless, the authors are to be thanked for their painstaking work in compiling, presenting and explicating (as they inform us) 18,264 numerical entries. This will surely provide material for subsequent scholars to analyse, and opportunities for many more interventions in the fascinating discussions about how astronomers developed and employed their mathematical tools in the later Middle Ages.
