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pg 1Introduction

Robert Grosseteste's On the Sphere is a more complex treatise than it might at first appear. It has been unfavourably compared to Grosseteste's later works as well as to rival astronomical texts of a similar or earlier date. Yet in quantitative terms the treatise appears as Grosseteste's greatest literary success. It survives in more copies than any other of Grosseteste's works with over fifty identified to date (Ch. 3, §1), this in comparison to the Compotus which has thirty-eight and the Commentary on Posterior Analytics with thirty-two. By contrast the other shorter scientific works survive in far fewer numbers, five for On the Liberal Arts, seven for On the Generation of Sounds, and fourteen for On Light. The Hexaemeron, the most complete and finished work by Grosseteste alongside the Commentary on Posterior Analytics, survives in only seven manuscripts. The chronological range of the surviving manuscripts, as well as its presence in five sixteenth-century printed editions, also show that On the Sphere was copied and consulted throughout the later Middle Ages and into the Early Modern period. That Grosseteste's On the Sphere was popular can, therefore, be asserted with some confidence.

What is not as clear is the purpose for which Grosseteste wrote his treatise. The popularity of the work alone might suggest an authorial intention for a broader audience rather than more specialist readers. From this position it would be a not unreasonable inference that On the Sphere was intended as a useful and perhaps introductory text. How Grosseteste's treatise is understood is also affected by the interpretation of its relationship to a near-contemporary work of the same title by John of Sacrobosco. The relationship between the two works, and in particular their respective chronologies and the use that one made of the other (Grosseteste of Sacrobosco), is discussed in more detail later (Ch. 1, §1). For the present purpose it is worth noting that Sacrobosco's pg 2treatise was certainly intended as an elementary text as its structure and pedagogical techniques, for example mnemonic verses, indicate (Ch. 5, §4.2), to say nothing of the tradition of glossing and commentary that it generated subsequently, and its place in university curricula.1 The manuscripts in which it survives are, as Lynn Thorndike put it, 'legion', and its early modern reception equally pervasive.2 The connection between the two treatises On the Sphere extended far beyond the circumstances of composition. Within the far smaller manuscript corpus for Grosseteste's text it is common to find it placed alongside that by Sacrobosco, as well the works on computus by both authors (Ch. 3, §1). These circumstances might also lead to the assumption that contemporaries understood the treatises to be similar in design, and therefore that Grosseteste's On the Sphere had the same intention as that of Sacrobosco.

Many of these assumptions about Grosseteste's treatise are to be found in two influential studies, by Thorndike, and by Sir Richard Southern. For Thorndike the two treatises, although differently executed (Grosseteste's being shorter, rougher, and unfinished, Sacrabosco's longer, polished, and complete), exhibit the same broad plan and order.3 While original elements to Grosseteste's work, such as trepidation, are noted, Thorndike placed greater emphasis on the fundamental similarities of the two works. Southern's description of the purpose of On the Sphere is unfortunate. He characterized the treatise as both a comprehensive guide to astronomy and as an elementary text.4 Although Southern highlights Grosseteste's independent thought, in this case the manner in which he approached his sources, such as the focus on Thābit's correction of Ptolemy by 'experiment', further comments reinforce an interpretation of On the Sphere as unbalanced by idiosyncrasy. It is Grosseteste's 'strong preference for the visible and the pg 3concrete' which inspires his regular appeal to visual images. The treatise also includes 'rash speculation' on the habitability of the earth, and finally, an overly long account of solar and lunar motion.5 The latter was caused, Southern suggests, by Grosseteste's particular fascination with eclipses, not for reasons of astrology but to account for the shape of the moon and the behaviour of light. The unusual structure of On the Sphere is then used by Southern as a reason for the relative lack of success for the treatise as a schools text, with comparison to the very different reception of Sacrobosco's treatise.

There is a circularity in these arguments which stems from the assumptions that On the Sphere was intended as a general, and introductory, account of the astronomical system, and that it therefore serves as a poor relation to Sacrobosco's treatise.6 However, rather than operating from the basis that Grosseteste's On the Sphere is a less successful 'textbook' than Sacrobosco's, or that it was designed to be one in the first place, it is perhaps more fruitful to think about what it is that Grosseteste actually sets up in his treatise. Bruce Eastwood pointed the way in a review of Southern's treatment, remarking that:

The description of Grosseteste's De sphaera as a brief outline for beginners is incorrect. No medieval text attempting to explain trepidation can be called a primer. Nor is it helpful to say that Grosseteste found Thābit ibn Quarra to have disproved Ptolemy experimentally…Grosseteste presumably understood that Thābit had made a more sophisticated model of stellar motion to account for a supposed variation in the rate of precession, which Ptolemy considered a constant rate.7

Southern did accept that an interpretation of the intention of On the Sphere as a school textbook was mistaken, eventually instead suggesting it was meant for private study (which its reception somewhat belies); he consistently maintained that Grosseteste's treatise was 'quite unsuitable pg 4for the schools'.8 The most extensive recent discussion of the treatise, that by Cecilia Panti, also notes the introductory nature of the treatise. She calls particular attention to the elementary and superficial qualities of both Sacrobosco's and Grosseteste's work, especially with respect to the knowledge shown of Ptolemy's Almagest in comparison to that shown in Arabic summaries also available in Latin translation, notably by Alfraganus, and in Geber's critique of the Ptolemy. While this is true, however, neither work states any particular aim to provide an introduction to the Almagest.9

What On the Sphere was designed to do remains an open question and one that is explored over the course of the present volume. Grosseteste sets out his own aim succinctly: 'Our purpose in this treatise is to describe the shape of the world machine and the [relative] position and shapes of its constituent bodies, and the movements of higher bodies and the shapes of their orbits (DS §1)'. In carrying out his intentions Grosseteste concentrated on particular aspects of astronomy, from spherical geometry and various proofs for the sphericity of the world, to the measurement of night and day. While all constituent bodies of the world machine are mentioned, the fixed and wandering stars (planets), his focus is on two in particular, the sun and the moon. The movements of both are explored in some detail and the mechanics of how eclipses occur. Throughout the treatise Grosseteste discussed the whole universe without restriction, that is to say he treats the super- and sub-lunary realms together and of a piece.

This approach to the whole universe is illustrated neatly in the case of one of the most original elements of On the Sphere, the discussion of the trepidation of the eighth sphere or 'sphere of fixed stars' (Ch. 8). Grosseteste does indeed appear to be one of the first Latin authors to use this theory in detail, which he encountered, almost certainly, in a treatise On the Motion of the Eighth Sphere, translated by Gerard of Cremona, and attributed, wrongly, to the ninth-century astronomer Thābit ibn Qurra. Amongst Islamicate astronomers trepidation was used to address an apparent variation in the precession of the stars, that is, in pg 5their movement and displacement with respect to the equinoxes, that had arisen through historical observational errors. Grosseteste, however, does not merely treat trepidation as a model for explaining the observable movements of celestial bodies, but also for explaining the observable climatic effects of these celestial movements on the various regions of the earth (Ch. 8, §4).

Where Grosseteste encountered On the Motion of the Eighth Sphere is an intriguing question, and of a sort that is difficult to answer with currently available information. He was not, so far as can be ascertained, attached formally to any institution with a library, and he was a secular cleric as opposed to a monk. Presumably he acquired his own books and booklets as opportunity and circumstances allowed, perhaps in France, possibly Paris, during the interdict, perhaps elsewhere. This makes a manuscript now in the Bodleian Library, Oxford, MS Savile 21, of particular interest. S. Harrison Thomson identified Grosseteste's handwriting within the manuscript, a claim that later scholarship has accepted, albeit somewhat tentatively. The first section in Grosseteste's hand includes two horoscopes calculated for a date in 1216, which gives at least the possibility that he copied out the other works in this section at or around the same time. These works include On the Motion of the Eighth Sphere and mathematical treatises by Jordanus. All of this was reading matter well suited to the subject of On the Sphere. The case for Grosseteste's handwriting is reviewed thoroughly in what follows (Ch. 2, §1), allowing a firmer insight into the resources he had gathered by 1216, and providing additional evidence for dating On the Sphere to some point between 1216 and 1219 (Ch. 1, §1).

The date of the treatise also involves issues connected to Grosseteste's familiarity, or not, with other sources. The striking absence of On the Motions of the Heavens by al-Biṭrūjī (d. c.1204 ce) a work which Grosseteste clearly knew in the 1220s, and which had been translated into Latin in 1217 by Michael Scot, allows further speculation on the date of On the Sphere (Ch. 1, §1). The relationship between Grosseteste's treatise and that of the same name by Sacrobosco is also explored in some detail in what follows (Ch. 1, §1; Ch. 5, §4.2; and Chs. 6 and 7). On the Sphere shows Grosseteste's critical engagement with Ptolemy's Almagest, in whatever form it was known to him (Ch. 7, §1; pg 6Ch. 9, §1), and its legacy in Islamicate astronomy. Grosseteste makes use especially of al-Farghānī (d. 861 ce) and that independently of Sacrobosco (Ch. 7), as well as Thābit.

The two foundational thinkers for Grosseteste's On the Sphere are, however, Euclid and Aristotle. The treatise is characterized by its sustained application of Aristotelian notions of science and of Euclidean geometry. As set out in Chapters 6 and 7, Grosseteste deploys Aristotle's principles of demonstration alongside Euclid's geometrical axioms and propositions. This speaks to a longer acquaintance with Aristotle's natural philosophy, for example the Posterior Analytics, than has been emphasized by some in the scholarly tradition.10 Latin translations of the majority of these works had been available since at least the mid-twelfth century. By taking seriously Grosseteste's Aristotelian formation and command of Euclid the structure and scope of On the Sphere become clearer. These intellectual engagements speak also to Grosseteste's own intellectual development. On the Sphere sits in continuity with elements of his first treatise On the Liberal Arts, which gave pride of place to the art of astronomy.11 The continuities are important (Ch. 6, §2), and the later treatises should be read with knowledge of its predecessor in mind. Nevertheless, On the Sphere also marks a transition away from the liberal arts framework and towards natural philosophy, a transition mirrored across the thirteenth-century university curriculum.

Whether or not Grosseteste intended the treatise for a classroom is, strictly speaking, impossible to establish, though the evidence of its later transmission, and in a limited context illustration (Ch. 10), implies a work frequently consulted, which is consistent with a schools' text. The invitation Grosseteste repeats 'to imagine' the geometry set down in the treatise and the structures and movements it describes also indicates some form of student audience. This is honoured in the creation of the Virtual Celestial model which accompanies this volume in an online format and also in the sequence of diagrams to explain key aspects of the treatise (Ch. 4). What can be known or suggested of Grosseteste's pg 7whereabouts during the probable period of composition (Chs. 1, 2) certainly does not preclude a notion of the treatise as a teaching text, though for whom remains unknown. On the Sphere can, then, be placed in a broader context in terms of Grosseteste's career.

While the evidence is patchy, and this is not at all unusual, strong arguments can be made for a continued association with Hereford diocese, as advanced by Southern and Joseph W. Goering, and deepened in this volume (Ch. 1, §3). On the Sphere was written in years of political upheaval, military campaigns, and the first movement to royal recovery in England, and in the context of renewed and vigorous reform of the church led by a confident papacy. In this context it is also possible to place some of Grosseteste's other early writings, the treatises on pastoral care, and the obligation of the church to educate its clergy and laity as to their Christian responsibilities, the consequences of sin, mechanisms for restitution, and the economy of salvation. Taking these works into consideration adds a different dimension to thinking about Grosseteste's shorter scientific works and On the Sphere in particular (Ch. 2, §2). Although the treatise is counted as the third work in Grosseteste's scientific canon, he had also written, quite probably, two or three treatises on pastoral care over the same period. On the Sphere is the product of an experienced writer, in his forties, and, as far as the evidence shows, with a supportive network and patron in Hugh Foliot, archdeacon, and, by 1219, bishop of Hereford.

On the Sphere was part of a larger movement within medieval European astronomical learning and was composed in a period of considerable intellectual change. Longer inheritances from ancient Greek and medieval Islamicate thinking, made available through Latin translation, transformed the way in which astronomy was understood, taught, and practised (Ch. 5). Grosseteste's contribution to this movement was, however, independent and distinct in its structure, scope, and intentions, and to that extent the treatise is both unusual and misunderstood. Grosseteste would go on to explore the calculation of time, the elements, celestial and meteorological phenomena, the formation of the universe, and the action and activity of light and rays.12 On the pg 8Sphere establishes the physical arena in which those other interests would play out.

As with the first volume in this series more complex mathematical discussion is presented throughout in the form of inset boxes as well as tables and figures. This is an instantiation of the interdisciplinary approach adopted for the elucidation of Grosseteste's scientific works, which flows from the collaborative reading symposia which constituted the primary forum for encountering and understanding the text. All authors of Mapping the Universe have brought their particular disciplinary expertise to the task of collaborative writing as well as the experience of translating and sharing their insights in the reading sessions. Writing together is a different exercise to reading, and a very different one over the compass of a monograph-length study. It is, however, a methodology that the Ordered Universe Research Project has championed as a means to draw out the richness in breadth and depth of Grosseteste's thought, the wider culture and networks in which this is to be understood, and the implications of medieval exploration of the world around them for modern questions of the same phenomena.

The current volume, unlike that which it succeeds and those that will follow, is dedicated to a single treatise. Since this is a jointly-written study, in its parts, and, more distinctively, as a whole, the individual chapters are listed as for a conventional monograph study. Most chapters are the product of collaborative writing and the contributions of individual authors are indicated in the front matter. Internal references to On the Sphere are made in-text in what follows and indicated by paragraph number for both Latin edition and modern English translation. Cross-references to pertinent discussion in other parts of the volume are used throughout, these are again in-text, and are indicated by chapter and section numbers. A cross-reference within a chapter is indicated by section number alone. Names of ancient and medieval authors have been retained in their conventional English-language forms. With respect to Arabic-language authors these are named by a simplified transliteration from Arabic, or where appropriate, most commonly in discussion of their reception by medieval Latin authors, in their conventional Latinate forms (Albumasar, Alfraganus).

pg 9What follows is an elucidation of a remarkable treatise, from the edition and translation, to the explanation of astronomical terms, analysis of its striking features, for example trepidation, and its larger structures and arguments. To this are added consideration of the diagrammatic tradition, the longer conceptual frameworks which Grosseteste inherited, directly and indirectly, and the historical context in which he and his writing can be placed. The dialogue between now and then finds sharper focus in the dialogue between the authors of the volume, from their individual perspectives, and a wider collaboration between natural sciences and humanities. It is in this spirit that the volume was conceived and produced, and it is in the same spirit that it is offered to wider readership.

Notes

1 Thorndike, On the Sphere, 18–41, 42–6.

2 Thorndike, On the Sphere, 74. Matteo Valleriani (ed.), De sphaera of Johannes de Sacrobosco in the Early Modern Period (Cham: Springer, 2020); Kathleen Crowther, Ashley Nicole McCray, Leila McNeill, Amy Rodgers, and Blair Stein. 'The Book Everybody Read: Vernacular Translations of Sacrobosco's Sphere in the Sixteenth Century', Journal of the History of Astronomy, 46 (2015), 4–28; Corinna Ludwig, 'Die Karriere eines Bestsellers. Untersuchungen zur Entstehung und Rezeption der Sphaera des Johannes de Sacrobosco', Concilium medii aevi, 13 (2010), 153–85; Jürgen Hamel, Studien zur 'Sphaera' des Johannes de Sacrobosco (Leipzig: AVA, Akademische Verlagsanstalt, 2014).

3 Thorndike, On the Sphere, 10–13.

4 Southern, Grosseteste, 142.

5 Southern, Grosseteste, 145–6.

6 Southern, Grosseteste, 145–6.

7 'Robert Grosseteste: The Growth of an English Mind in Medieval Europe by R. W. Southern', review by Bruce Eastwood, Speculum, 63 (1988), 233–7.

8 Southern, Grosseteste, lix, n. 47, and 146.

9 Panti, Moti, virtù e motori celesti, 45, 67–132 at 88.

10 James McEvoy, 'The Chronology of Robert Grosseteste's Writings on Nature and Natural Philosophy', Speculum, 58 (1983), 614–55; at 617 McEvoy presents Grosseteste in On the Sphere as 'still far from being the complete Aristotelian scholar'.

11 Grosseteste, De artibus liberalibus, §§11–13.

12 See McEvoy, 'The Chronology', 617.

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