Download PDF | (History of Science and Medicine Library) Eastwood, B.S. - Ordering the Heavens_ Roman Astronomy and Cosmology in the Carolingian Renaissance-BRILL (2007).
478 Pages
PREFACE
Many incarnations lie behind this book. I began studying early medieval astronomical and cosmological diagrams over twenty five years ago. More recently I became convinced that the development of astronomy and especially of astronomical diagrams from ca. 800 to ca. 1100 provided an essential basis for the European investigation and study of Greco-Arabic astronomy in the eleventh and twelfth centuries and beyond. Western familiarity with the technical concepts of the eccentric and the epicycle grew out of the Carolingian development of Roman astronomy. Roman texts were the essential sources of astronomy in Charlemagne’s Europe. This intellectual foundation paralleled the increase in mathematical precision and the instrumental developments that grew in eleventh and twelfth century Western astronomy on bases that were both Latin and Greco-Arabic.
The more I explored the three centuries from Charlemagne to Louis le Gros (or the emperor Henry IV), the more I understood the need for a book treating the Carolingian origins of the conceptual development tied to the astronomical diagrams—primarily planetary diagrams—used in the ninth-century. The past six years have been devoted primarily to writing the chapters for such a book. I have tried to describe a wide variety of Carolingian interests related to astronomy and cosmology as a context for the emergence of the study of more technical concepts. I have also tried to explain in some detail the conceptual, diagrammatic steps in the Carolingian studies of the four Roman works that were foundations of the ninth-century knowledge of astronomy.
Over the years I have had encouragements from so many friends and colleagues that I can not name them all. I mention here two who inspired me at critical moments. Marshall Clagett encouraged me early to pursue in more depth what was at first a limited investigation of circumsolar planetary diagrams in manuscripts of the early Middle Ages. John North more than once recharged my professional batteries to spark my continuing research into early medieval astronomical diagrams.
Available time to write is, of course, an ever-present need. A lengthy interval for full-time research and writing of this book, unencumbered by committee and teaching duties, was provided by a fellowship from the National Endowment for the Humanities (2001-2002) and a generous grant from the National Science Foundation (SES 0004224) for 2001-2003. I am deeply grateful for both these supports. I regret that it has taken longer than expected to complete the work and can only hope the result has been worth the wait.
Ranging widely over the holdings of so many libraries, I have found it not only useful but necessary to depend on microfilms for much of my manuscript study in this work. However, my research on the versions of the Anonymous commentary on Martianus Capella required extended study of the texts in the flesh at three libraries. I thank Marie-Francoise Damongeot, Conservateur-en-chef at the Bibliothéque nationale de France, for clearing the way for me to make direct and extended use of ms. lat. 13955. At the Bibliothéque d’Etude et de Conservation in Besancon, Marie-Claire Waille ensured that I had ready access to ms. 594 during my visits there. By far the longest of my on-site visits took place at Leiden’s University Library, where the staff of the Dousa, now reorganized under Special Collections, housing the Western manuscripts, provided friendly and efficient assistance over many weeks as I went back and forth from one manuscript to another in my studies of mss. Voss. lat. E48, BPL 36, BPL 87, and BPL 88. Investigation of the Carolingian commentaries on Martianus Capella must be founded on this group of four Leiden manuscripts, and it was a pleasure to find and return again and again to such accommodating working conditions as the Dousa provided.
It has been my good fortune to find scholars willing to take time to offer information and thoughtful advice—and also forbearance when faced with my undiplomatic disagreements. I have benefited from information and helpful suggestions given by Wesley Stevens and Faith Wallis. Stephen McCluskey’s admirable Astronomies and Cultures in Early Medieval Europe (1998) has provided me with much food for thought, and I look at my book in part as a response to questions raised by his. More especially I owe a large debt to colleagues who have read and commented on chapters in this book. John Contreni graciously found time to read and offer suggestions regarding the chapters on Macrobius, the Capellan commentaries, and diagrams. Both Paul Dutton and Richard Kremer with their distinctly different lines of expertise added important, helpful comments on the wide-ranging chapter on Pliny. Finally, an anonymous reader for the press made very many helpful suggestions and corrections. I thank these busy scholars for sharing their time and giving their insights and suggestions. Readers of the final form of the book can rest assured that many improvements came from these critiques. For the errors remaining in this book I am solely responsible.
In the process of imagining, re-conceiving, researching, writing, and rewriting such a book, there have been many times when my determination faltered and was revived by support from my wife, Sanae Asahara. She brought a sense of order into my erratic work habits and a sense of balance into my attentions to many competing interests. She listened to me talk too much about the book and never flagged in her support. Somehow she knew it would be published without needing major revisions, and she hoped very much to see the final result. I was prepared to dedicate it with gratitude and the deepest affection to my wife, but I can now only dedicate it to her memory. For me her image remains inextricably woven into the book’s fabric. Without her support I could not have written this book.
INTRODUCTION
In the lands of the Franks, roughly equivalent to France, Belgium, southern Germany, and the north of Italy today, the transition from the Merovingian to the Carolingian dynasty in the mid-eighth century has commonly been seen as a shift that ushered in a revitalization of government, religion, and culture during the next century and beyond. In modern studies of the cultural renewal, most often referred to as the Carolingian renaissance, there has been very limited attention to the natural sciences, and even this limited attention has focused almost completely on the study of computus, a discipline devoted to practical problems in the study of time, especially the calculation and projection of calendars for the feasts of the Christian year far into the future.
Throughout the first half of the eighth century no one in the Merovingian world showed interest in the classical astronomy lying dormant in ancient Roman texts. Words such as ‘epicycle’ and ‘eccentric’ did not appear in the scientific works consulted by scholars of the day, nor were there astronomical diagrams to explain any of the irregularities in the motions of the Sun or the other planets. By the middle of the ninth century Carolingian scholars were exploring and expounding upon four Roman texts that provided the knowledge needed to understand the various motions in the heavens as parts of a reasoned and transparent order. This reason and transparency was enhanced by many astronomical diagrams that gradually awakened a new perception and deeper understanding of celestial phenomena. I propose to describe and explain this fundamental transformation of astronomy by studying the reception of these four Roman works and the ways they were used by Carolingian scholars to teach the order of the heavens.
1. The Carolingian Renaissance
Christened as a renaissance by nineteenth-century historians and discussed as such well into the latter half of the twentieth century, Carolingian cultural developments have been interpreted more recently in the context of continuities from Merovingian times and of Visigothic Spanish as well as Anglo-Saxon influences. Cultural activities emerged from a long early medieval genesis and drew contributions from a wide European field.
Stronger emphasis has now been placed on the background of reforms in liturgy and the defense of churches and monasteries from expropriations. From Pippin (king 752-768) onward these were among the foremost royal concerns with the intent of correcting morals, establishing uniformity in religious observance (following Roman practices), and restoring order in monasteries and dioceses. Pippin’s successors Charlemagne (768-814) and Louis the Pious (814-840) vigorously pursued similar goals. The revitalization of the monarchy with the election of Pippin, the first king in the Carolingian dynasty, provided the energy and determination to give reality to what were unrealized ideals under the last Merovingians.
The Carolingian program of reform was seen primarily as religious renewal, to be carried forward by bishops and abbots under the guidance of the king. It was only after some decades of effort that the expansion of knowledge for purposes of clerical literacy and competence led to a significant expansion in the study of secular works from the Roman imperial past. In brief, what has been called the Carolingian renaissance, if we wish to focus on the revival of classical Roman texts, was very much the creature of a religious renewal and was not readily apparent before the last years of the eighth century. The reigns of Pippin and Charlemagne strengthened ecclesiastical institutions greatly, and, as the push developed for continued clerical education and broader religious and moral reform, the king and reform-minded bishops and abbots enlarged the scope of renewal and revival to include more of the Roman past.!
Models of clerical education, not necessarily in agreement with each other, stemmed from various predecessors. A well-known figure was Cassiodorus (ca. 480-ca. 575), important in the government of the Ostrogothic kingdom of Italy, who retired from public life and set up a monastery on his estate at Scyllactum in southeastern Italy (ca. 560?). Here at the monastery of Vivarium the monks were given a guide to the study of both religious and secular books. Cassiodorus’s Institutiones divided into two parts, the first recommending approaches to and interpreters of the books of the Bible as well as Christian historians and the Church Fathers. Cassiodorus opened the second book with a brief homily on the number ‘seven,’ citing Exodus, Psalms, and Proverbs to support the number of seven secular studies, or liberal arts, as foundation stones for true literacy. He named the seven arts—grammar, rhetoric, dialectic, arithmetic, music, geometry, astronomy—and proceeded to definitions, or at least lists, of their main elements and important authorities in each area.’ He praised arithmetic as the basis of the three other parts of the quadrivium (four mathematical disciplines) and proceeded to describe astronomy by listing and defining a number of its simple terms in observational and practical language. Ptolemy’s name, attached to three book titles, gave the outstanding sources for astronomy, although there is no evidence that Cassiodorus had consulted these. He also mentioned that the work of Martianus Capella, which contained a synopsis of astronomy along with the other liberal arts, had become unavailable.? In conclusion Cassiodorus wrote that this sequence of studies, ending with astronomy, should
...lead from earthly affairs minds which have been devoted to secular wisdom and have been purified by training in the sciences and place these minds in laudable fashion in the celestial realms created by God.'*
Carolingians consulted not only Cassiodorus on the seven liberal arts but other authorities as well. Isidore of Seville (ca. 570-636) dedicated the first three of the twenty books in his encyclopedic Etymologies to the same seven liberal arts as Cassiodorus but listed the quadrivium in the order arithmetic—geometry—music—astronomy, which suggested different relationships among them. Astronomy consumed by far the largest part of the space devoted to the four disciplines, and Isidore’s sources were non-mathematical Roman texts, especially Hyginus’s Astronomicon as well as parts of Macrobius’s Commentary on Scipio’s Dream and Calcidius’s Commentary on Plato’s Timaeus.° If Isidore retained, at least in his Etymologies, a largely traditional Roman sensibility in surveying the proper studies for a literate administrator of the early seventh century, his insular successors followed a different strain that could be found in his writings and elsewhere.
The seventh-century anonymous Irish text De ratione conputandi referred to the authority of Saint Augustine in prescribing the four necessary studies for clerics: the Holy Scripture, both as the account (canon dwinus) of future events and, with other Christian writings, as the record (historia) of things past, computation (numerus) in the enlarged sense of establishing the numerical order in God’s creation and its chronology, and grammar (grammatica) as the knowledge of words and their varied uses.° De ratione conputandi was one of the sources used by scholars at the Carolingian computistical conference of 809.’ And while there were clearly wide interests in the natural world among Irish writers of the later seventh century, the focus of clerical education was on grammar, Holy Writ, and computus.® The Englishman Bede (673-735) followed Irish leads, both educational and computistical.?
We can observe during the eighth century the spread of a different notion of “seven liberal arts” deriving from both continental and insular traditions. An ancient tripartition of philosophy had been adapted in Isidore of Seville’s Differentiae, in Aldhelm of Malmesbury’s De virginitate, and in an anonymous seventh-century Irish letter Ad Cuimnanum to identify three bodies of knowledge—physics, ethics, and logic—as necessary tools for the understanding of Scripture, with physics being further subdivided into seven parts. Bernhard Bischoff has identified many manuscripts with versions of this tradition and described details in the Ad Cuimnanum from an early eighth-century Anglo-Saxon codex. The text says that the arts existed already in germ, that is, innately, but undivided at the time of Adam and then unfolded thereafter. Physics is subdivided into arithmetic, geometry, music, astronomy, astrology, mechanics, and medicine; we can find these seven labeled as the seven liberal arts in manuscripts through the eighth, ninth, and tenth centuries.!°
The variety of curricula does not tell us what clerics actually studied. These lists of disciplines were to some extent no more than lists. At the same time they offered bases for potential development. Development, however, required the commitment of ecclesiastical leaders to a program, or possibly many programs, of study. And it also required texts—dependable texts in multiple copies. It was the royal directives of 789 in the Admonitio generals (General Directives, or Sermon to All) that finally laid down a foundation for clerical literacy across the Carolingian realm, but this was preceded by a great amount of pertinent activity. Charlemagne’s annexation of the Lombard kingdom of northern Italy in 774 added greatly to the image of the king as the Frankish successor to the rulers of Rome. From this point forward evidence grows of foreign poets and scholars at the royal court. We find Peter of Pisa from the Lombard court, who taught the king grammar and wrote an introduction to the subject, remaining until ca. 790. Paulinus, another grammarian, spent less than a decade at Charles’ court and returned to northern Italy as the royal appointee to the patriarchate of Aquileia. ‘Two Italian scholars at the court were awarded the bishoprics of Verdun and Pavia shortly after 780. Fardulf came to the Frankish court originally as a hostage after a failed Lombard rebellion in 776, and his subsequent loyalty to Charlemagne brought him the abbacy of Saint Denis in 793. Among the early Gospel books produced for the king was Godescalc’s (ca. 781), written primarily in Roman uncial, replete with purple and gold decoration, clearly fitting the heightened status and suggesting a Roman tradition, including a Roman text of the lectionary, for the royal patron.'! In the first decade after 774 we see a combination of royal patronage, Italian scholars, and increasingly self-conscious Roman orientation.
At the same time, in the 770s and 780s, an Insular surge, both Irish and Anglo-Saxon, appeared at court. Notker of Saint Gall’s Gesta Karoli (ca. 884) opens with an encomium of Charles and the story of two learned Irishmen, followed by the English Alcuin, who came to the royal court to reestablish both sacred and secular wisdom in the kingdom."? We have the letter (ca. 775) of the Anglo-Saxon Cathwulf to Charlemagne on kingship and the primacy of the king over bishops as well as the arrival of Joseph the Deacon, Candidus, Dungal, and others as witnesses to Insular influence. Yet other names from other places, like Theodulf of Orleans and Angilbert, stood equally high, and it was this mixture of sources that made Charlemagne’s court famous for learning, poetry, and competitive wit. The royal patron utilized the opportunity to have some of these learned courtiers teach youths who had been selected to fill administrative posts, ensuring that these students knew proper Latin grammar, writing, and other relevant skills. The modern notion that a regular school of some sort existed at the royal court, however, lacks adequate foundation."
Just before 792, when the court settled in Aachen as its permanent location, Charles issued the Admonitio generals (789), a set of eighty-two orders together with elaborate preface and closing exhortations. The general intention of this package of major reforms was to ensure adequacy, correctness, and uniformity in clerical preaching, reading, writing, teaching, and all aspects of the liturgy in parish and monastic worship. In pursuit of these goals the king commanded (tusstmus) among other things that “schools’—formal teaching but not necessarily permanent spaces—be established for boys both in monasteries and in dioceses and that certain subjects be taught. The psalms, shorthand (tironian) notes,'* chant, computus, and grammar were to be studied and learned as were corrected copies of canonical religious works (“libros catholicos bene emendate’”). All too often, this order (section 72 of the Admonitio) continued, Christians wish to pray to God but they follow incorrect texts of the regular prayers. With this in mind, only trained adult scribes were to be allowed to copy the gospels, the Psalter, and the missal.’° The subjects for teaching at ecclesiastical schools focused on all that was needed for a good basic religious education, and the context of this training made it clear that uniformity was essential. The emendation of inaccurate texts, the correction of incorrect pronunciation, singing, and writing, and the conformity to recommended models of literary composition and calendrical computation were expected results of the reforms. Although the Admonitio went no further in prescribing subjects of clerical study, another royal document urged more extensive scholarly preparation by those clerics who were able. Charlemagne’s Epistola de litters colendis (Letter on the Study of Literature) circulated sometime in the 780s or 790s among abbots and bishops. It expressed concern about misunderstandings of the Scriptures in these words.
We all know well that, although errors of speech are dangerous, far more dangerous are errors in understanding, ... Since, moreover, images, tropes and similar figures are found in the sacred pages, no one doubts that each man in reading these will understand the spiritual sense more quickly if previously he shall have been fully instructed in the mastery of letters. Let men be chosen for this work who have the will and ability to learn and also the desire to instruct others. And may this be done with a zeal as great as the earnestness with which we command it.'°
Here we see the outspoken determination of the king to produce effective action. He specified the broad field of “letters” and left the details of choosing texts and techniques to the abbots, bishops, and their scholars. While the purpose of this letter was crystal clear, the king did not circumscribe the sorts of material to be used in advancing this educational goal. Across the land various activities contributed to its fulfillment.
2. Elaborating the Reforms
Among the participants in Charlemagne’s educational reforms Alcuin (737-804), who had been deacon, teacher, and librarian at York and came to stay with the peripatetic Frankish court by 786, is by far the best known to us.'’ While we should not try to connect him with a non-existent school at the royal court, his impact on what we might call the second generation of court scholars can hardly be overemphasized.'* He was teacher to the king for rhetoric, dialectic, and astronomy and wrote basic texts for grammar, rhetoric, dialectic, and computus. Among his works the text on grammar has special interest because of its preface, known as De vera philosopha, in which Alcuin presented the path to wisdom as a gradual approach, requiring careful attention to each step. Citing Proverbs IX, 1—‘“Wisdom has built her house; she has set up her seven pillars’—he equated the seven columns of the house of Wisdom with the seven liberal arts, each one a step upwards from grammar through rhetoric and dialectic to arithmetic, geometry, music, and astronomy. With such knowledge, he wrote, defenders of Christian orthodoxy are much better prepared to engage in public debate successfully with heresiarchs. And through these seven arts students can achieve a spiritual maturity enabling them to understand more fully the Holy Scripture.
In pursuit of these arts Alcuin drew on a wide variety of sources— patristic, classical, and post-classical. Grammars, for example, from those of Donatus (ca. 350) and his commentators along with the Insular elementary grammars that built upon and expanded Donatus were readily available in the late eighth century. To these Alcuin was instrumental in adding Priscian’s newly recovered Jnstitutiones grammaticae, whose influence one can find in Alcuin’s grammar. Cassiodorus’s Institutiones and Isidore’s Etymologies provided matter for the other disciplines along with works of Vergil (and the commentaries of Servius), Cicero, Horace, Lucan, Pliny the Elder, Censorinus, and others. For the quadrivium specifically, the works of Pliny the Elder and Macrobius were supplemented by Roman translations of Aratus’s Phaenomena as well as by Isidore of Seville’s De natura rerum and Etymologies and Bede’s De natura rerum and De temporum ratione. Needless to say, the long tradition of texts on computus, including the Irish tradition, was extensively consulted. From 796 until his death in 804 Alcuin was abbot of Saint Martin’s of Tours where he taught students at different levels; it was for the more advanced students, following the directions of Charlemagne’s Epistola de htteris colendis, that Alcuin held an ongoing seminar in the higher disciplines such as astronomy and theology.
The copying of texts, sometimes involving recovery as well, was clearly of primary importance for the advancement of such monastic schooling as Alcuin and others practiced. The king appointed as heads of monasteries court scholars like Alcuin, Angilbert at Saint Riquier, Arno at Saint Amand, Einhard at Saint Wandrille, Fardulf at Saint Denis, and Theodulf at Fleury. All of these saw to the development of regular teaching and the improvement of manuscript copying in their scriptoria. Certainly religious texts, whether liturgical or biblical or patristic, came first in order of priority, but we find the inclusion of more and more secular texts by the close of the eighth century and during the course of the ninth. Some monks found books elsewhere for their own hbraries and schools. Vadilleoz traveled from Reichenau on Lake Constance to Alcuin’s Tours and collected books which he brought back to Saint Mary’s of Reichenau. Abbot Erlebald at Reichenau commissioned copies of books from the scriptorium at Saint Denis. In the Reichenau library catalogue of 821/822 appear names of various medical and veterinary books, a numerological text for fortune-telling (Prognostica Democnti), Boethius’s arithmetic and geometry, and an Aratea. By the 840s the library there included Vitruvius’s Architectura, a copy of Hyginus’s Astronomia, and Boethius’s Musica, not to mention illustrated copies of Pliny’s astronomical excerpts, discussed in detail in our Chapter Three, and copies of the works de natura rerum of both Isidore and Bede containing many 7ofae (circular cosmological and computistical images). Our knowledge of Carolingian scriptoria, libraries, and schools is fragmentary, but studies of individual sites continue to be published, including important centers like Auxerre, Corbie, and Fleury.”!
When we look for texts and teaching of astronomy the most obvious evidence is the increase in copies and compilations of computus works. These require further consideration, but at present we are looking for works that reflect a growing awareness of classical astronomy. Although Greek theological and other religious texts came in small numbers to Carolingian Europe, no evidence at all survives for the transmission of any Greek astronomical work (in Greek). No knowledge of works by Hipparchus, Ptolemy, or ‘Theon of Alexandria, for example, appears in ninth-century Western Europe. No Greek commentaries on Plato came to the West; the only Platonic commentary was the Latin commentary with translation of Plato’s Timaeus by Calcidius. While we know of a partial translation, named Praeceptum Canonis Ptolemei, of Theon’s commentary on the Ptolemaic Handy Tables, the earliest manuscrit comes from ca. 1000, and there is no evidence of Western circulation of this text before the late tenth century.” Astronomy, aside from computus, as it was known in the Carolingian world was Roman astronomy, which included Latin translations and commentaries of a very few Greek works, such as Aratus’s Phaenomena and Plato’s Timaeus. Our studies in the chapters of this book reveal the extended and progressive body of knowledge offered by the four Roman texts of Macrobius, Pliny the Elder, Martianus Capella, and Calcidius along with other, associated works.
In our search for astronomy in Carolingian libraries and schools we shall not accept the claim, “In order to find Astronomy, as it was taught and learned in Carolingian schools, one must search for it in the computistical texts and tables extant in medieval Latin manuscripts.””* The best way to proceed beyond such confusion is to preserve the two terms ‘computus’ and ‘astronomy’ and pay attention to the texts involved and what they say. That there is overlap between the two studies, as in the use of observations of the zodiacal constellations and in determination of the solstices and equinoxes, is clear, but the separate concerns of astronomy and computus are far more numerous than the overlaps. We should remember that in the Admonitio generalis Charlemagne required the teaching of computus and not astronomy. Computus was a distinctly ecclesiastical study that used a very limited body of astronomical information about the cycles of the sun and the moon and generated elaborate tables and rules for establishing the intersections of these cycles over time in order to predict the annual date of Easter. Astronomy, on the other hand, was a very large discipline by the middle of the ninth century, including the locations of all the constellations, not just the zodiac, and both the description and the explanation of the paths of all the planets. Computus was neither interested in explaining nor capable of explaining the variations in planetary motions, including the variations in solar motion. Astronomy was implied in Charlemagne’s direction (the Epzstola de litteris colendis) to Abbot Baugulf and others to encourage those who were capable to go beyond the basics of clerical adequacy, e.g., grammar and computus, and learn the liberal arts. Cassiodorus provided a model. Alcuin and others would follow that model and its variants.
Alcuin, it is clear, taught not only computus but also astronomy. He taught it at some level to Charlemagne. He referred to the seven, not three or four, liberal arts in his analogy between the arts and the pillars of the House of Wisdom in the Book of Proverbs. He did not write on astronomy but only on computus. Still we find that his most famous student (after Charlemagne), Rabanus Maurus (780-856), identified the seven liberal arts as the central intellectual tool in the larger monastic educational program.”* When writing from Fulda around 830, Lupus of Ferriéres (ca. 805-862), referred to the quadrivium as part of the routine of studies for himself and other students there under Rabanus.” And as Mayke de Jong has remarked, by the 840s Rabanus was grumbling about the younger generation among whom there were know-it-alls (sciol) that wanted novel ideas and not just the well worn authorities.”
In Alcuin’s letters to the king there are computistical questions as well as conversations about potentially ominous events in the heavens, such as an unusually long invisibility of the planet Mars.?’ Alcuin made use of Book ‘Two of Pliny’s Natural History for discussion of celestial phenomena. Not long after his death in 804, another learned monk, Dungal, referred not only to Pliny but also to Macrobius for astronomical information regarding the planets and astronomical predictions. Astronomical excerpts were drawn from Pliny to a larger extent and from both Macrobius and Martianus Capella very briefly for important compilations of computistical, cosmological, and astronomical material during the second decade of the ninth century. By ca. 840—perhaps some years earlier—the astronomy (Book VIII) of Martianus Capella’s Marriage of Philology and Mercury was not only being studied but also submitted to an enormous effort of commentary, resulting in what we now call the Anonymous Commentary, which traveled in many versions and had tremendous influence on scholars such as John Scottus Eriugena and Remigius of Auxerre in the ninth century. And the more demanding astronomy of Calcidius’s Commentary on Plato’s Timaeus was being studied and excerpted by mid-century, and was being copied and corrected later in the century. This brief litany of the major uses of the four Roman texts to be studied in the subsequent chapters of our book bears witness to the outlines of an evolution. If computus was the bright star in the heavens of late eighth-century studies of the heavens, the astronomy of our Roman texts came gradually to the fore and outshone computus for all inquiries other than practical calendrical questions.
We should recognize here one Roman text, the Phaenomena of Aratus, translated from the Greek by different Romans, that does not receive discussion in this book. The various Latin versions, sometimes with commentary, were treated primarily as literary sources in the Carolingian world. Lupus of Ferriéres wrote to Ansbaldus in 847 to obtain a copy of Cicero’s translation of Aratus. Aratea were commonly illustrated, indicating their luxury quality, and an outstanding example is the Leiden manuscript Vossianus lat. Q.79, probably produced in the royal scriptorium, possibly in 816.** The images of the celestial mythological figures that accompanied Aratea manuscripts did not usually attempt to reproduce the individual stars in the proper points of each constellation and very often failed even to reproduce the correct number of stars in each constellation according to the text. Produced primarily for nontechnical general interest, the various versions of Aratea might best be called catalogues of constellation names and stories;” the descriptions of star positions in each constellation could only be discerned by looking directly at the night sky with the assistance of an instructor who had already learned when and where to find the constellations.
The works of Macrobius and Pliny were much in evidence early in the century, especially, let us say, over the first quarter of the ninth century. Capella seems to have rocketed onto the scene with the huge anonymous commentary we have mentioned and was clearly the most prestigious source for astronomy by the 840s and thereafter, although Pliny continued to hold ground as an important ancillary through the ninth century and beyond. Calcidius became an astronomical source for Carolingians by the 840s as well, but his text apparently posed certain difficulties for full comprehension so that it was appropriated into the astronomical curriculum slowly and at a limited number of centers before the eleventh century.
The sorts of issues presented to Carolingian scholars by these Roman sources make clear how far beyond the limits of computus they pushed the boundaries of cosmological and astronomical understanding. From Macrobius came natural reasoning for accepting the earth as the center of the universe and arguments from symmetry for the human habitation of all four quadrants of the globe. Pliny offered such a variety of perceptions that the choices are legion; two of special interest were the physical cause of the bounded elongation of the inner planets from the Sun and the physical cause of the retrograde motions of five planets. The Capellan astronomy was a representative survey of major topics, and among the more important were these three: (a) the precise forms of the epicycles of Mercury and Venus around the Sun, (b) the precise nature of the changes in the lengths of daylight through the year, and (c) the cause, not simply the description, of the different lengths of the four seasons. As for Calcidius, if more difficult at times, his qualitative geometry of celestial phenomena promised to Carolingian students fully rational explanations of the four seasons (by eccentric circles), retrograde motions (by epicycles), and the bounded elongation of Mercury and Venus from the Sun (by epicycles). It need hardly be said that these questions were beyond the scope of computus and that some monastic teachers and students came to engage in these novel explorations with delight as the four Roman sources came to be better known and more available.
By the end of the ninth century two of the most fundamental techniques of classical Greek astronomy, the eccentric and the epicycle, were being investigated not only in theory but in application. Their full comprehension depended on a perspective that returned to astronomy— it had been lost—only with the recognition that observation of a body’s (a planet’s) motion against a separate background 1s a relative change in position that can vary in more than one way, depending on the relationship of the point of observation with the centers of motion and background framework. Such recognition depended on the ability to represent this sort of situation adequately in diagrams. Students of Calcidian astronomy in the late ninth and tenth centuries were wrestling with and solving the problems in producing such diagrams. Students of computus showed no such capability and may well have considered it auseless exercise. Astronomical diagrams and computistical images had different goals and developed quite differently over the ninth century. They reflect the growing differences between those clerical scholars who pursued the continuing elaboration of knowledge in all of the seven liberal arts and those who held to the more restrictive interpretation of the goal of religious renewal as stated explicitly in Charlemagne’s commands in Section 72 of the Admonitio generalis.
3. Materials for the Carolingian Renaissance in Astronomy
The collection, correction, copying, and dissemination of manuscripts was the foundation both for Charlemagne’s conception of a literate, correctly trained, and conforming clergy and for the more intellectually ambitious and narrowly focused project of learning the quadrivium, especially astronomy. At a general level we can say that the royal court and royal monasteries, that is, monasteries founded or at least funded by the king, were the primary locations for manuscript books. ‘The king had an interest in supporting these institutions. The abbots and scholars at such monasteries reciprocated with a strong desire to obtain books. Gospels, psalters, and liturgical manuscript books were the major part of this literary traffic, but we shall now turn our focus to books that facilitated the study of astronomy and related areas like astrology.*” Astronomy and astrology occurred, we should remember, as a pair of recognized disciplines in the alternate division of the seven liberal arts, defined in the eighth-century Ad Cuimnanum as arithmetic, geometry, music, astronomy, astrology, mechanics, and medicine, and this division was used and taught in Carolingian schools.*! Saint Augustine had already warned Christians firmly against astrology and its practicioners, the mathematic.” Isidore had attempted to make a clear distinction between astronomy and astrology in his Htymologies, where he defined each as follows.
Now astronomy considers the turning, rising, setting, and motion of the heavenly bodies (“siderum”), or why they are named as they are. Astrology in turn is partly natural and partly superstitious. ‘Natural,’ insofar as it investigates the courses of the Sun and the Moon or the defined stations of planetary orbits; ‘superstitious’ fits the part followed by the mathemati, who augur by the stars and who assign the twelve signs of the zodiac individually to parts of the soul or body and who attempt to foretell the nativities and characters of men by the course of the stars (“siderum”).*8
While astrology was a suspect science according to some, it was more than tolerated. It was sought after, although not in the sense of individual horoscopes, by Charlemagne and Louis the Pious to name only the most famous examples. These rulers wanted at different times to know the significance of observed phenomena like eclipses or comets or other notable celestial events, always potentially ominous, that seemed to correspond with momentous earthly events.** Over the course of the ninth century not only rulers but many others came to consult the order of the heavens, as witnessed by the elaborate development of lunaria, or calendars with the days of the lunar cycle marked as good, bad, or appropriate only for certain activities.*? David Juste has studied a number of Carolingian manuscripts of a short text that begins, “In quo signo versetur Mars” IQSVM hereafter), which describes a way to compute the longitude for any planet—Mars, Jupiter, Saturn, Venus, Mercury—at any time. The procedure simply requires the arithmetical manipulation of the zodiacal periods of the planets, the time interval since Creation, and the reported positions of the planets at Creation. IQSVM was included in three of the major astronomical-computistical collections of the ninth century. Its most obvious use was astrological, and in, for example, Heiric of Auxerre’s copy of this text (Melk 412, p. 29) from ca. 840 we discover both the method for finding planetary longitude and the means to find the rising sign, or astrological ascendant.*° Astrology in the Carolingian world was an expanding concern with techniques to interpret and prognosticate from all sorts of phenomena in the heavens, including the sublunar heavens. Although we have no personal Carolingian horoscopes surviving, we have just seen that the text IOSVM provided the critical element in the construction of a horoscope, the ascendant at the time of birth. As we shall see in subsequent chapters, the desire to predict the future from the heavens was neither absent nor severely restrained at the literate level. Only the practices of the unlettered, common people were seen as dangerous and to be prohibited. Given the books available to them, Carolingians resorted to many learned paths to know what is to come.’
For both astronomy and astrology the manuscript sources are often anonymous. The surviving Carolingian manuscripts of our four Roman authors are frequently untraceable; that is, we do not know precisely when or where they were copied. The positions of those we can locate, that is, the cathedral or monastic libraries, appear on the map (Figure 1.1). Our earliest extant copy of the complete text of Macrobius’s Commentary on the Dream of Scipio appears in Paris 6370, copied ca. 820 at Tours and subsequently used and corrected by Lupus at the monastery of Ferriéres.** We know that an earlier copy existed at Saint Denis in Paris in 810-811 because of Dungal’s extensive quotations in his letter of 811 to Charlemagne, yet no direct record survives of a copy at that monastery. Later in the century copies were made at Corbie and Fleury as well as the region of Ferriéres. Other copies appeared in France and we find a German copy by the end of the century.*? The currency of Macrobius in the ninth century would seem to have been limited to major French centers from the Loire north with the exception of copies of Dungal’s letter, which traveled to Verona and elsewhere.
Both Macrobius and Pliny were seen as sources for astronomical excerpts that could be used in schools, and we do not find their texts heavily glossed. The earlier books of Pliny’s Natural History were known and excerpted for specific astronomical doctrines by both Isidore and Bede in their respective works with the title De natura rerum. In Carolingian times copies were held at the royal court, as letters of 798 and 799 by Alcuin to Charlemagne indicate. The king’s librarian, Gerward, built the royal library for Charlemagne and rebuilt it for Louis the Pious, both times including Pliny’s encyclopedia.*” Books 2 and 18 of Pliny, the sources for excerpts in the Seven Book Computus ca. 812, may have come from the Corbie library, where Paris 6796, a now mutilated and incomplete manuscript, had been copied. The earliest surviving copy of the Seven Book Computus, Madrid 3307, was made at the monastery of Murbach, along the headwaters of the Moselle River, ca. 820,*' and a very similar copy ca. 869 at Lobbes in southern Belgium.” A copy of Books 1-17 (now incomplete) of Pliny was produced at the royal monastery of Lorsch on the Rhine River.** An inventory of the books owned by Saint Riquier in 831 indicates a copy that can no longer be traced. Pliny was excerpted along with Macrobius and Calcidius for the Corbie compendium of astronomical and other sciences in the midcentury Paris 13955, which we discuss below in Chapter Five under the title “Paris Compend.”*” And at Reichenau at mid-century a copy was made of a long set of excerpts from the first six books of Pliny that had first been produced ca. 800 at the Sankt Gallen monastery. A complete copy of the Natural History (Leiden Lipsius 7) was made in the first half of the century by two scribes whose handwriting shows one to have been trained at Murbach, the other at Luxeuil. At the same time, two centers with important teaching masters in the second half of the ninth century, Auxerre and Laon, seem not to have possessed copies of either Macrobius or Pliny.*® This fact does not indicate a lack of interest in natural science or astronomy but rather the unpredictable distribution of books in the Carolingian world—unpredictable not in the sense of a thoroughly random distribution but rather because of the varying conditions at individual scriptoria. The presence of a copy of a work at a particular monastery depended not simply on having a library but also on contacts with other centers, the knowledge of the holdings of other libraries, the presence of a competent scribe trained either locally or elsewhere, and many other factors.”
The fifth-century work of Martianus Capella was recovered and spread rapidly during and after the second quarter of the ninth century as a set of ready-made handbooks on the liberal arts, although the trivium, especially grammar, continued to be taught by using many other texts. Capella’s work had been mentioned by Cassiodorus, whose lists of books were one of many guides used by Carolingians to select the contents of their own libraries. Gregory of ‘Tours (d. 594) spoke of studying Martianus, but this was rather surely a reference to the books of the trivium, and Gregory’s brief text on stellar time-keeping does not depend on Capella. The Capellan books on the quadrivium, especially astronomy, were seized upon as rare gifts for teaching these arts.** Of our four Roman sources for astronomy only Capella—indeed all nine books of his Marnage of Philology and Mercury—received extensive interlinear and marginal glossing and commentary in the ninth century, intended both for school use and individual study. ‘Twenty copies of Capella survive from the ninth century, and two of these are separate copies of Book 8 (the astronomy), indicating the early interest in having copies of this part of Capella’s De nuptus (Marriage of Philology of Mercury) alone. We can locate eleven of the twenty during the century, giving us some sense of the distribution of the work. In Germany (and Switzerland) copies existed at Cologne, Constance, Freising, and Lorsch;*’ in France (and Belgium) there were copies at Auxerre (2), Corbie (2), Reims, Saint Oyan, and Soissons.*° Four more of the twenty manuscripts can be designated as French in origin.’ With one-fifth of the manuscripts at major centers in southern and southwestern Germany and over half at French, primarily north French, cathedrals or monasteries, the preponderance of French scriptoria, libraries, and schools is obvious in the case of Capella’s work. And as Chapter Four below emphasizes, the major commentaries on Capella’s astronomy in its first decades of Carolingian school use are French, those of the Anonymous and John the Scot. These facts suggest the special importance of Martianus Capella’s work for teaching astronomy and the greatest attention being given to this work from the Loire valley northwards.
Calcidius’s Commentary on Plato’s Timaeus was known already by the end of the eighth century, apparently at the royal court, as is witnessed by its use among Alcuin’s students, especially by Candidus. For astronomy the work of Calcidius seems to have emerged suddenly in the 840s in a Corbie manuscript, Paris 13955, containing a group of upper level school texts. Certain references of John Scottus Eriugena to Platonist views in his Annotationes to Martianus Capella (composed in the 850s) suggest a second-hand, erroneous grasp of what may have been astronomical doctrines inspired originally by Calcidius’s Commentary, and we do not know where John discovered the supposedly Platonist notions reported for him in Paris 12960. Cicero’s incomplete translation of the Yimaeus circulated in conjunction with his De natura deorum, De dwinatione, and De fato, but Cicero’s version did not provide the views that John the Scot invoked in his commentary on Capella.*? While there are other references to Platonist astronomical views, specifically in the Anonymous commentary on Capella’s astronomia, the only extant ninth-century manuscripts of Calcidius are two, Lyon Bibliothéque municipale 324 and Valenciennes Bibliothéque municipale 293. The Valenciennes copy was rather surely made at Reims in the late ninth century, and it was taken by Hucbald of Saint Amand (d. 930) when he left Reims for Saint Amand where the manuscript remained until the French Revolution.** This copy in turn testifies to a copy at Reims that served as exemplar, although we have no further information about that exemplar.” As the chapters below on Martianus Capella and Calcidius show, there were many Carolingian references to astronomical doctrines of Plato (or Platonists). Some of these derived from Macrobius’s Commentary, but Cicero’s translation of the Timaeus as well as Calcidius’s translation and commentary must have been far more widely known than surviving manuscripts indicate. For astronomy, which depends much more on the commentary of Calcidius than on the text of Plato, our evidence is strong for direct knowledge, with the extended quotations in the Paris Compend (in Paris 13955) of the 840s, but weak for widespread use, with only two surviving copies of the commentary earlier than the tenth century.*®
In general there were five ways in which Roman scientific works entered Carolingian culture and had their effects. First there was, of course, the simple recovery of classical books. After that we find imitation and the multiplication of copies. Further, some users preferred to select parts of Roman works, and we find many longer excerpts as well as florilegia, or collections of little snippets. Next, with the appearance of extensive glossing and commentaries we encounter creative teaching, such as the Carolingian Anonymous commentary on Capella used in expanding the number of geographical latitudes when reporting the amount of daylight through the year and thereby making the nature of the change more evident. Finally, beyond creative teaching we can find innovative theorizing as with the comparison in the Anonymous commentary of models of circumsolar planetary motion derived from three different ancient sources. By the middle of the ninth century we can find all of these forms of Roman scientific impact and stages of Carolingian interaction in the study of astronomy.
4. Roman Astronomy in the Carolingian Renaissance
In 1927 Charles Homer Haskins declared the scientific vista of the early Middle Ages to be largely a wasteland. He was most emphatic in his view of the mathematical sciences and focused especially on astronomy, claiming that nothing of significant value was done. As for computus, he noted, its achievements were trivial. ‘Thus astronomy had to wait for the twelfth-century importation of Greco-Arabic sciences to begin its medieval European development. In 1975 Olaf Pedersen argued against Haskins’ blanket dismissal of early medieval astronomy, proposing that computus was precisely the area where astronomical achievements were made, calling it “a purely scientific effort to elucidate the only astronomical problem of immediate importance for early medieval society.” Finally, in 1994 Brigitte Englisch elaborated carefully and extensively upon Pedersen’s points and further claimed that computus was the sole area where real scientific thinking and work emerged in early medieval astronomy. It was Bede who did this most clearly, and Englisch blamed Rabanus Maurus and others in the ninth century for abandoning this model of how to do good science.”
Some scholars have pointed out to me that observation was the most important element of early medieval astronomy and that this came often in connection with computistical work. Wesley Stevens has described the elaborate efforts of Bede to determine with some precision the date of equinox, and Stevens’ detailed account provides us with much food for thought regarding Bede’s observational apparatus.”® First we learn that Bede accepted the so-called Alexandrian date of 21 March for spring equinox in preference to the Roman date of 25 March; both of these dates were established by authorities in the past, and Bede followed his own schoolmaster, abbot Ceolfrith, in preferring the decision of the Egyptians. Stevens then presents us with Bede’s large gnomon and zodiacal circle laid out on the ground; it was designed to show “anyone who did not learn in school as a child” how to understand and observe the movement of the sun through the year. We might properly say that this large pedagogical demonstration was Bede’s way of moving the dustboard of the abacus out of doors, enlarging it sufficiently to produce the acknowledged facts of annual solar motion and to allow easy presentation of the different divisions of the signs of the zodiac. Following Bede through his operations with this large horologium, Stevens argues that it is extremely difficult to observe precisely the equinox and that Bede’s difficulties and failure are quite understandable—even forgivable. However, it seems much more likely that Bede did not fail in his intent. Bede’s intention was to show the date of equinox “horologia inspectione.” In fact, his intent was to show “horologia inspectione” (“by observing with the gnomon”) that the date of equinox was 21 March rather than 25 March. In the Ecclestastical History Bede wrote that the Alexandrian date of 21 March could be approved by such a device (“horologica inspectione probamus”).** The issue here was approval of a preferred authority, not independent experimentation. Taking Bede’s observational work in this sense, a sense that had a long tradition through Antiquity, we see it as a nice example of disproof of the opposition, not as an example of experimental investigation.” It is all too evident that Bede did not say that he would have liked a better dating than 21 March but could not achieve it. That is the view of the modern historian.
Among the Carolingians Bede’s work On Time Reckoning (De temporum ratione) appears to have been the preferred guide for computistical study, even though it did not gain the status of sole authority. On the contrary, Bede’s work simply competed successfully with a variety of others, including extracts from Isidore, Irish compositions, and Carolingian works.®! In the ninth century computus was in an expansive mode, encyclopedizing, as it were, rather than solving new problems. Large compilations characterize this era in the history of computus, including the two collections discussed below in Chapter Three, the Seven Book Computus and the Three Book Computus. Keeping in mind the traditional computistical concern to establish a regular cycle of Christian feasts, not to establish a cycle of astronomical periods, we may see Carolingian computists as following both the lead of Cassiodorus and Alcuin in enlarging their understanding of the motions of the luminaries used to define the calendar and also the lead of Bede in his careful precision in defining all the elements of the calendrical cycle. ‘Thus the apsidal and latitudinal motions of the sun and moon in the contexts of planetary apsides and latitudes according to Pliny enlarged Carolingian computus beyond its very specific needs. At the same time Carolingians continued to debate the correct length of calendrical time since the beginning of the world.” In the Carolingian world computus was a precise science but not an experimental science.” It thus remained a science of numerical calculation and cycles.
In the exploration of Roman astronomy and cosmology in the Carolingian world I have tried to set out the ways that four Roman texts were used to bring order into the picture of the heavens in the late eighth and ninth centuries. ‘The books themselves derived from the first to the fifth centuries. Limited use of one or more of them can be discovered in the works of Isidore of Seville and Bede, but the fuller use of all four of these books, aimed at a comprehensive view of the world above us in the skies, emerged in the age of Charlemagne and his successors. It was this revival, or renaissance, of Roman knowledge that enabled those scholars who were competent to reach the fullest understanding of the art of astronomy. This was the study of God’s “laws,” as Isidore said, made visible in the heavens. What was seen in the heavens could, in turn, be made visible in a different and more elaborated way by the use of astronomical diagrams.
This renaissance of Roman astronomy made possible later in the ninth century a line of study that opened up to Carolingian scholars a coherent view of two fundamental techniques of Greek geometrical astronomy, the epicycle and the eccentric. The epicycle was seen at first, through the astronomy of Martianus Capella, as a peculiarity of the motions of Mercury and Venus, useful in explaining their limited elongations from the Sun. This peculiarity was opened up by excerpts from Calcidius’s commentary on the Timaeus to reveal the applicability of epicycles to all the planets. Similarly, the abbreviated explanation by Capella of the different lengths of the four seasons became in Calcidius’s account a clear, qualitative geometrical explanation, using eccentrics, of the variation in seasonal lengths. ‘These specific astronomical understandings were completely enmeshed in the larger Carolingian search for knowledge of the heavens and could only emerge as individual realizations after many decades. In fact, only in the early eleventh century do we find evidence of scholars showing clearly a full understanding of the epicycle and the eccentric as astronomical techniques. But it was this long development, from the Carolingian deployment of Roman astronomy to the eleventh-century engagement fully with all the questions and techniques of Capella and Calcidius, that laid a conceptual basis for the twelfth-century inquiry into Greco-Arabic astronomy.
My focus in this book is the Carolingian framework—the rebirth of the quadrivial art of astronomy—with all its associated learning. With Macrobius’s Commentary on the Dream of Scipio we find an orderly overview of the cosmos. It is sufficiently general to serve as a cosmology for computists and not to stimulate questions about the astronomical limits of computus. The cosmos as a sphere with the spherical earth at the center is the basis. The parallels between the terrestrial and celestial zones are highlighted. We are shown the symmetry of the earth, its parts, and its inhabitants. If Macrobius can be used to suggest order and interrelatedness, Pliny is used to display the diversity of the world. From Pliny Carolingians learned details of the planets, comets, eclipses, winds and storms, as well as portents associated with all of these. Pliny also provided rationales for planetary phenomena, eclipses, and winds of different kinds. Explanations, not simply descriptions, emerged as important contributions of Plinian astronomy at those points where it used the configurations of eccentric apsides to account for changing speeds and brightness of planets. Extensive detail and remarkable diversity were found in Pliny’s accounts of what happens in the skies.
Explanations increased with the use of Martianus Capella, whose handbook offered the appearance of a comprehensive overview. Carolingians seized on his astronomy text as an ordered guide to the subject. In it they found improved understanding of the change in the amount of daylight through the year. Students were also given an explanation of the different lengths of the four seasons. If it was not as good a geometrical guide as Geminus had been for ancient students and Sacrobosco would be for thirteenth-century students, Capella’s astronomy managed to present topics in a coherent sequence and preserved at least some portions of the mathematical picture of solar, lunar, and planetary motions in Greek astronomy. A number of these points became subjects for elaboration and investigation in Carolingian commentaries on Capellan astronomy.
Calcidius offered Carolingians for the first ttme a coherent philosophical and qualitative geometrical account of the cosmos. This account was, at least geometrically, a challenge that clearly was beyond the aptitude of most early readers, and only a modest number of students were likely to have benefited from a work such as the Paris Compend, which extracted Calcidius’s explanations of solar motion using both an eccentric and an epicycle and showed their equivalence. Yet this set of excerpts was meant as a textbook, or study guide, and its inclusion in the same codex with a roughly contemporary commentary on the astronomia of Capella is further evidence of the fact.
To repeat in quick chronological summary, approximately 800-820 saw the introduction of Macrobius with his big picture of the cosmos aided by Pliny’s expansive coverage of many more topics in detail. Adding to this foundation in the 830s and beyond were the copies of Martianus Capella’s astronomical textbook, often with elaborate commentaries. And as the Capellan superstructure solidified by extended copying of both the text and the commentaries, from the 840s onwards Calcidius’s Commentary offered a larger philosophical framework and the opportunity to focus on new and unfamiliar geometrical techniques.
Throughout these four Roman works diagrams were used by Carolingian scholars to illuminate the meanings of the texts; they gave not only descriptions but also, in many cases, explanations. Macrobius had provided a set of diagrams, and ninth-century readers not only used but also modified them. Pliny made no mention of diagrams for his text, but a set of four, subsequently modified (or improved), was invented to accompany four lengthy astronomical excerpts from Pliny. Martianus Capella likewise made no mention of diagrams, but more than one commentator at or before mid-century devoted much time to the invention of diagrams for Capella’s text and for parts of the commentary. These diagrams were usually illustrative, at times exploratory and theoretical, and occasionally revealing of unexpected barriers to understanding. Finally, for Calcidius’s text there were geometrical diagrams to which the text referred and fully depended on. Because many of these diagrams did not survive uncorrupted into the Carolingian world, ninth-century scholars had a double difficulty, first the challenge of incorrect diagrams, second the challenge of a geometrical perspective sufficiently unfamiliar so as to make it hard to determine which diagrams were incorrect and in what ways they were incorrect.
In the diagrams produced by Carolingians for each of the four Roman sources we learn much about the abilities and limitations of the scholars involved. It is especially from the Carolingian diagrams, copied or invented for one or another of these works, that we discover much more deeply what and how the ninth-century teachers and students were able to understand. It has been said that a picture is worth a thousand words, and, for investigating Carolingian astronomy, a coherent diagram and an incoherent diagram are each worth a thousand words.
Unraveling an incoherence can be at least as instructive as following an orderly, coherent diagram. Expanding our survey of each of the four Roman works to incorporate relevant material from literary, religious, and other scientific sources gives us a far more complete awareness of Carolingian astronomy and cosmology and its integration within the literate culture. At the same time, a highly detailed analysis of diagrams, such as the (coherent) three versions of circumsolar planetary motion in the Anonymous commentary on Capella or the (incoherent) diagram assembling the elements of Capella’s explanation of the different lengths of the seasons, can reveal buried assumptions and understandings that we are unlikely to discover in any other way. Both expansion of our vista across the culture and penetration into the hidden geometry of Carolingian mindsets are goals of the following chapters.
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