Planetary Diagrams — Descriptions, Models, Theories: from Carolingian Deployments to Copernican Debates Bruce Eastwood and Gerd Graßhoff Contents 1 Introduction . 1 2 The Beginnings in Carolingian Europe . 1 2.1 Astronomy and Computus before 800 . 1 2.2 Schools and Texts . 3 2.3 Diagrams and the Study of Texts . 7 2.4 Dynamics of Diagrams: Calcidius and Pliny . 7 2.5 Dynamics of Diagrams: Martianus Capella . 21 3 Qualitative Theory in the High and Later Middle Ages . 29 3.1 Dynamics of Diagrams: Construction of a Planetary The- ory............................ 29 3.2 The Capellan Tradition through the Fifteenth Century . 32 4 Merging Two Traditions: The Sixteenth Century . 37 1 INTRODUCTION Through three distinct periods from ca. 800 to ca. 1600 we find that European as- tronomers were concerned with questions about the planets that involved the dis- cussion and invention of models without quantitative expression. This qualitative tradition was first developed in the ninth century in the course of studying ancient Latin texts on cosmology and astronomy. The diagrams, used to represent different phenomena and aspects of planetary motion, continued as long as they were found useful for teaching, for exposing questions, or for proposing theoretical positions. The history of this tradition of planetary diagrams indicates a constant concern for qualitative theory and the co-existence of both qualitative and quantitative plane- tary theory after the introduction of the Greco-Arabic mathematical tradition of planetary astronomy in twelfth-century Europe. In the sixteenth century the same qualitative tradition continued as a source for approaches to new phenomena and problems. 2 THE BEGINNINGS IN CAROLINGIAN EUROPE 2.1 ASTRONOMY AND COMPUTUS BEFORE 800 From the sixth century to the twelfth century in Western Europe there was no direct influence of Greek works in the exact sciences. This was an era in which, de- spite certain Western exchanges with the Byzantine state and church, no writings in Greek on mathematics or astronomy seem to have crossed the boundaries of these two worlds. Between the Arabic-speaking and Latin worlds, with the excep- tion of an incomplete transfer of knowledge about the astrolabe in the eleventh century, the same sort of barrier appears to have existed for the exact sciences. What had been the western half of the Roman Empire in the fifth century became a mosaic of successor kingdoms in Italy, Spain, the British Isles, and the large area 2 occupied today by France, the Low Countries, Germany, and Switzerland. Within these lands, excepting Spain, which was conquered by Muslims in the early eighth century, Latin was the virtually exclusive language of scholarship through these six, early medieval centuries. The sixth century saw the decline of astronomical and especially planetary knowledge, witnessed by Cassiodorus in Italy and by Gregory, bishop of Tours, in the Kingdom of the Franks. Away from the Mediterranean, the seventh century, both on the continent and in the British Isles, was an era when the classical tra- dition of “liberal arts” was deemed of little use. The actual curriculum of studies in the only organized schools of the time, the ecclesiastical schools, focused on grammar, computus, and chant. Grammar was increasingly devoted to rules for Latin writing, with the examples being chosen much less from classical sources and much more from the Bible, stories about holy men and women, and Chris- tian poetry. Chant was a practical study, focused on the needs of Christian ritual. Computus, the sole “scientific” discipline by modern lights, attended to counting, basic arithmetical operations, and the knowledge needed to find the proper date for Easter and thereby the Sundays and all other Christian feast days throughout the year. This knowledge did not include precise astronomical observation nor any theory of the motions of the sun or the moon, but it did require calculation with lunar and solar time intervals given by definition. In the early eighth century the situation began to change with the example set by Bede (ca. 673 — 735), who in- cluded observations of the sun and moon at crucial points in their cycles, at the monastery of Jarrow-Wearmouth in northern England.1 Bede, however, did not depart from the goals of computus, nor did he integrate planetary study into the discipline. The reappearance of astronomy as a discipline, recognizably related to the as- tronomy of the fourth and fifth centuries in the Roman world, occurred about the turn of the eighth century in the kingdom of the Franks under King Charles (768 — 814), known today as Karl der Grosse or Charlemagne. As part of his search for greater stability in the kingdom, in 789 Charles sent out the Admonitio generalis, which ordered a reform of the clergy and required the establishment of schools at all monasteries and cathedrals and further prescribed that the Psalms, proper chant, writing, grammar, and computus be taught. The king also pointed out in a separate letter that the liberal arts were ill-known by the religious and should be 1General history of education in this era appears in Pierre Riché, Education et culture dans l’occident barbare, VIe - VIIIe siècles, Paris, 1962; translated as Education and Culture in the Barbarian West, Columbia, S.C., 1976. An excellent background to the early medieval computus up to the seventh century appears in D.J. O’Connell, “Easter Cycles in the Early Irish Church,” Journal of the Royal Society of Antiquaries of Ireland, 66 (1936), 67 - 106. For description of the seventh-century study of computus see Wesley Stevens, “Scientific Instruction in Early Insular Schools,” Cycles of Time and Scientific Learning in Medieval Europe, Aldershot, 1995, ch. 4. The same author’s “Bede’s Scientific Achievement,” ibid., ch. 2, depicts the reappearance of limited astronomical observation within the framework of computus in the work of the most remarkable scholar of the early eighth century, the Englishman Bede. 3 cultivated by those who were able.2 His close advisor, Alcuin (ca. 730 — 804), in a letter sent from the abbey of Saint Martin of Tours in 797, mentioned that studies there followed the pattern of the royal court, which included not only the Bible but also the arts, especially grammar and astronomy. Elsewhere Alcuin wrote as part of his own grammar text a preface, commonly referred to as “De vera philosophia”, in which he quoted from the biblical book of Proverbs the statement that Wisdom built her house with seven pillars, and he proceeded to connect the seven gifts of the Holy Spirit with the seven liberal arts, which, Alcuin said, would lead up the steps to perfect knowledge (perfecta scientia). These steps he identified explicitly as the arts, ending with astronomy (astrologia), and emphasized that they were needed for the enlightenment of the soul as well as for the defense of the faith against heresiarchs.3 Along with Alcuin, the king not only supported study of the arts but also had a personal interest in both computus and astronomy.4 2.2 SCHOOLS AND TEXTS The study of astronomy in the schools and outside the schools from the time of King Charles onwards required the recovery and dissemination of texts that seem to have lain relatively unknown during the preceding two hundred years. Beyond the works of Cassiodorus, Isidore, and Bede, none of which gave ade- quate guidance for a coherent understanding of planetary astronomy and none of which presented a useful picture of the celestial sphere without supplementary oral instruction, there were six Roman Latin texts that provided essential knowledge. The descriptions of the celestial sphere and the constellations appeared in Aratus’ Phaenomena, as translated by Germanicus (and Cicero and Avienus), and in Hyginus’ Astronomia. The foundations of planetary astronomy came to Carolingian scholars in Pliny’s Historia naturalis, Macrobius’ Commentarii in somnium Scipionis, Martianus Capella’s De nuptiis Philologiae et Mercurii (Book VIII), and Calcidius’ In Timaeum com- mentarius. This second group of four works is where we must turn for planetary diagrams. The study of these Roman works and the development from them of a note- worthy foundation for planetary astronomy occupied more than half a century, beginning in the late 700’s. For none of the four is there a continuous prior his- tory of a manuscript tradition. Between Boethius in the early sixth century and Isidore in the first third of the seventh century we find the last references to these astronomical sources until the time of Bede or later. Even with Bede only limited 2Monumenta Germaniae Historica. Legum Sectio II: Capitularia, I, ed. A. Boretius (Hannover: Hahn, 1883), 59-60, 79-80. 3Monumenta Germaniae Historica. Epistolae, IV: Karolini aevi, II. ed. E. Duemmler (Berlin: Weid- mann, 1895), pp. 176-177. Migne, Patrologia latina, 101, coll. 849-854. 4In addition to Charles’ convening of the computistical conference that led to the Calendar of 809, various letters in his correspondence with Alcuin show the king’s active interest. See the examples in Monumenta Germaniae Historica. Epistolae, IV: Karolini aevi, II, pp. 185-187 (nr. 126), 228- 235 (nrs.144-145), 237-245 (nrs. 148-149), 278-283 (nrs. 170-171). 4 acquaintance with Pliny’s Historia naturalis is certain. He made use of one work by Macrobius but made no mention of the commentary on Cicero’s Somnium. The earliest surviving manuscripts of the four Roman works are from the ninth century, a testimony both to their earlier disuse and to their revival in Carolingian times. For the availability of Pliny’s work we have as witnesses not only Alcuin’s letters to the king but also the survival of three manuscripts from the beginning of the ninth century containing major portions of the complete work.5 Macrobius’ commentary on the Somnium Scipionis was known and being used for its astron- omy during Charles the Great’s lifetime, as a letter in 811 to the king from the monk Dungal at Saint-Denis makes clear.6 The text of Calcidius’ commentary on Plato’s Timaeus was apparently in the royal library by ca.