Astronomical tables abounded in late medieval Europe. They survive in hundreds of manuscripts, testifying to their theoretical interest for scholars and, especially, to their practical utility. Their proliferation stemmed from tremendous consolidation efforts undertaken for Alfonso X of Castile (1221–1284), but they depended for their underlying theory and observational data on centuries-old work, most notably that of Ptolemy. This ‘Greek’ tradition was filtered through centuries of Arabic-language scholarship, whose most significant contributor was al-Battānī (d. 929); alongside it ran a parallel and eventually cross-fertilizing ‘Indian’ tradition, represented by al-Khwārizmī (fl. 830) and his successors. In addition, a flourishing strain of astronomy in Hebrew, exemplified by Levi ben Gerson (d. 1344), should be mentioned. In the early fourteenth century the work of the Alfonsine astronomers underwent considerable study and modification in Paris; this led to the dissemination of Alfonsine tables, largely in Latin, across western Christendom.

This dissemination of astronomical knowledge is a fascinating story, which is still in the early stages of reconstruction; the tables themselves provide essential evidence in mapping the transit of knowledge. However, so far they have largely been studied as individual manuscripts or, at best, as strands within the wider tradition. Exceptional in this regard are the articles by E.S. Kennedy – ‘A survey of Islamic astronomical tables’, Transactions of the American Philosophical Society 46 (1956), pp. 123–177 – and by David A. King and Julio Samsó, with Bernard R. Goldstein – ‘Astronomical handbooks and tables from the Islamic World (750–1900): an interim report, Suhayl 2 (2001), pp. 9–105. But such work has not hitherto been undertaken on Western manuscripts.

In their earlier study of The Alfonsine Tables of Toledo (2003), Chabás and Goldstein wrote that

It is this deficiency which the authors are working to rectify in the current book. They describe their efforts as

As such, this is more than a survey: it is also a guide or handbook, and to some extent a manifesto for further work in this field.

Before proceeding to praise the depth of focused scholarship represented by this work, it is perhaps desirable to note what it is not. It is not, as the authors acknowledge, a history of astronomical tables. Nor, despite the publishers’ claim that the potential readership includes ‘all those interested in the history of science in the Middle Ages’, is it particularly accessible to those unversed in the principles and terminology underpinning ancient and medieval astronomy. The authors have explained a number of complex issues as thoroughly as can be expected in a slim volume. They include twenty-six diagrams, which are conducive to theoretical understanding, though in a few places, such as the section on spherical astronomy, the three dimensions could perhaps have been represented with more clarity. On some topics, such as eclipses, the authors have done a marvellous job of summarizing the theory clearly enough to necessitate no further reading. In other areas (notably precession and planetary latitudes), their explanation is unlikely to be sufficient for those not previously familiar with the material, but their watertight referencing makes it easy for readers to consult more detailed explanations of each concept. Readers seeking an introduction to late medieval astronomy will want to work up to the present volume, but might be advised first to seek a more gentle initiation into the basic concepts and terminology, perhaps with James Evans's primer, The History and Practice of Ancient Astronomy (1998).

But this volume is first and foremost a survey, not a primer, and as such it presents an unprecedented picture of the variety of tabular material produced in this period, drawn through years of painstaking research (whose finely balanced frustrations and rewards are hinted at in the Preface). It is arranged according to nineteen categories of tables: trigonometry and spherical astronomy, precession and apogees, mean motions and radices, and so on. Within these category chapters, explanations of the theories and their significance are given alongside almost 160 tables, which present material from eighty manuscripts. Most are substantially redacted,

Some – perhaps the most useful for a general reader – collate historical values for a particular parameter from a wide range of sources. This presentation may exaggerate the heterogeneity of the material, but that is perhaps the inevitable price for such comprehensive coverage.

The authors make no concluding remarks, modestly leaving the wealth of material they have compiled to speak for itself, and to stand as a resource for the analyses and conclusions of other scholars. And it is a tremendous resource. It will perhaps be most useful for scholars studying the work of individual astronomers, who will find invaluable comparative, contextualizing, and explicatory material here. But it is also of interest to anyone seeking to understand the tremendous productivity, mathematical creativity and competence of medieval astronomers. The authors are to be thanked for this considerable contribution to scholarship in this field.