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THE POWER OF DIAGRAMS: THE PLACE OF THEANONYMOUS COMMENTARY IN THE DEVELOPMENT

OF CAROLINGIAN ASTRONOMY AND COSMOLOGY

Bruce S. Eastwood

W hat might Carolingian astronomy and cosmology look like, if MartianusCapella’s Book VIII (on astronomy) had received no commentary?How much would be missing from the narrative and problematics of these Carolingian subjects in the absence of the Anonymous Commentary?

In some ways the unglossed text of Martianus’s work could have sufficed forscholars and students. But the enrichment of the text by the commentary was andis immediately obvious, and it inspired and provided content for two furtherCarolingian commentaries, those of John the Scot and Remigius of Auxerre. Twodistinctive attributes are clear. First, the Anonymous Commentary (AC) wasa work of textual analysis and interpretation, not theoretical or observationalscience. Second, AC aroused greater interest in the power of astronomical dia-grams to describe and explain celestial events. In conjunction with AC, Capella’s

work was the most authoritative astronomy of the ninth century.AC built not only upon the text of Martianus but also on scientific texts

already known and studied before De nuptiis was widely read. These includedIsidore’s Etymologies, Bede’s De temporum ratione, the works De natura rerum of Isidore and Bede, the Seven Book Computus (from the computus of 809), Pliny’s

Natural History, Macrobius’s Commentary on Scipio’s Dream, and various Latinforms and descendants of Aratus’s Phaenomena.1 AC not only drew from this

1 Sources used for astronomy by Carolingian scholars are surveyed in Bruce S. Eastwood,Ordering the Heavens: Roman Astronomy and Cosmology in the Carolingian Renaissance (Leiden:Brill, 2007), pp. 1–29 (pp. 15–29).


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Bruce S. Eastwood 194

spectrum of texts but also added to it substantially and methodologically. Sub-stantially, we can point to the most famous doctrine of Capellan astronomy, theepicyclic paths of Mercury and Venus around the Sun, which AC problematizedby offering three different forms of circumsolar orbit for the two inner planets.Methodologically, AC used dialectical arguments to sharpen the reader’s aware-ness of certain details of Capellan doctrines. And AC introduced astronomicaldiagrams in a more inventive spirit than we find in the background works men-tioned above. Let us look, then, with some care at the contributions of AC toninth-century astronomy and cosmology.2

We begin with the important manuscript witnesses to different forms of AC. There were two early, basic versions of the commentary. They appeared

before midcentury and before the Annotationes in Marcianum (c. 850) of Johnthe Scot.3 The earlier version is found in two different forms in the Vossianus(Leiden, Universiteitsbibliotheek, Vossianus Latinus Folio 48 (VLF 48)) and theBesançon, Bibliothèque municipale, MS 594 (B). The second version appearsin two identical forms in Leiden, Universiteitsbibliotheek, MS BPL 88 (Lb),and Vatican City, Biblioteca Apostolica Vaticana, MS Reg. lat. 1987 (Va). OtherCarolingian manuscripts use material from one or both of these two versions,and one notable manuscript, Paris, Bibliothèque nationale de France (BnF), lat.

13955, carries a glossed copy (s. ix) of Book VIII alone, apart from the rest of De nuptiis. The manuscripts of the first and second versions of AC include a noveladdition to the work of Martianus Capella — astronomical diagrams, which areused subsequently by other commentators on the text.

The astronomy and cosmology of De nuptiis are readily accessible for modernscholars through the well-known Teubner edition of James Willis as well as theserviceable translation by William H. Stahl. We can now add to these the lengthy summary with analysis of major parts of both the text and the commentaries in my

2 A lengthy chapter in Eastwood, Ordering , pp. 179–311, discusses De nuptiis, Book VIII, andits Carolingian commentaries with special attention to the Anonymous Commentary (AC) andits influences. Sixteen photographs of diagrams in the AC are included.

3 Iohannis Scotti Annotationes in Marcianum, ed. by Cora E. Lutz, Medieval Academy of America, 34 (Cambridge: Medieval Academy of America, 1939) (all citations of this text refer tothis edition, hereafter cited as Annotationes), based on the single manuscript Paris, Bibliothèquenationale de France (BnF), MS lat. 12960 (Pd), presents John’s commentary on Book VIII at pp.165–85. Further commentary by John on De nuptiis is preserved for Book I alone, where some

astronomical and cosmological matter appears. For this, see Édouard Jeauneau, Quatre thèmesérigéniens (Montréal: Institut d’études médiévales Albert-le-Grand, 1978), pp. 91–166, editedfrom Oxford, Bodleian Library, MS Auct. T. 2. 19, fols 1r–31 v .


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THE POWER OF DIAGRAMS 195

Ordering the Heavens. I shall not recount or summarize this large body of materialby Martianus, but we can benefit from closer attention to the kinds of focus paidto the text by AC and later commentators.

Cosmology

An adequate view of basic cosmology according to De nuptiis requires referenceto Book VI (geometry, geography) as well as the first, cosmological part of Book VIII. In the two together, AC highlighted five topics: the shape of Earth, the cen-trality of Earth, the location of the antipodes, the elements of the terrestrial and

celestial regions, and the five elemental layers of the cosmos.Even before addressing these five topics we should notice that where Martianusidentified the general arrangement of the heavens and especially the 24-degreeinclination of the zodiac, through which the planets move, as a physical aid to thestability of the cosmos, AC converted the Capellan argument from a cosmologicalinto a logical question. Martianus had said (§ 853) that this angle of the zodiac tothe equator ensured that the individual planetary motions (limited to the bandof the zodiac) from west to east would not be directly contrary to the generalmotion of all stars and planets from east to west on the axis of the equator. AC setthis up as a problem of contradictory statements and claimed that it would beillogical for the proper planetary motions to threaten the stability of the cosmos.4

4 Martianus Capella, De nuptiis Philologiae et Mercurii, ed. by James Willis (Leipzig: Teubner,1983), p. 323, § 853) (hereafter cited as De nuptiis, by book and/or section number (wheneverbook number is omitted, the citation refers to Book VIII), and/or page number from this edition): where the daily westward motion of all stars and planets is contrasted to the specific eastward

motion of each planet and the supposed danger of contrary motions is avoided by placing themat an angle to each other. When the Capellan text continues and refers to two different ways of understanding the actual motions, AC changes the argument into a syllogism thus (VLF 48, fol.79r, marginal gloss): ‘Dicunt Peripatetici quod omne quod suis partibus constat contrariam sui partem abere non potest. Mundi autem partes sunt planete, igitur contrarium cursum ei abere non possunt. Omne quod est aut totum aut pars est. Si totum est suis partibus constat mundus, autemtotum est. Planete igitur partes mundi sunt, et si nulla pars sua contraria sibi non est, planete igiturcontraria mundus motu abere non possunt, obliqui moventur’ (The Peripatetics say that anything that coheres in its parts cannot be separate from a part of itself. But planets are parts of the world,and therefore they cannot diverge on a path contrary to the world. Anything that exists is either

a whole or a part. If it is a whole, the world holds together in its parts. But the whole is the planets,therefore they are parts of the world, and if no part is contrary to itself, then the planets cannotgo against the world by a directly contrary motion. Therefore they are moved obliquely). (All


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Turning to our first terrestrial topic above, the first version of AC emphasizedthe shape of Earth by adding labelled, marginal images for a flat Earth and anegg-shaped Earth (in modum ovi). Ambiguity in these images and some apparentconfusion for students led the second version of AC to revise the vocabulary sothat all reference to ‘egg-shaped’ was replaced by the clearer and more specifically geometrical spherical ( spericam).5 Neither John the Scot nor Remigius of Auxerreadded anything beyond this clarification in their commentaries on the same pas-sage of text.

With regard to the centrality of Earth in the cosmos, AC simply pointed outthe location of the argument in Martianus’s text with a marginal index, Positioterre, added by the second version.6 However, in dealing with the third topic, the

antipodes, the second version of AC took a big step away from the first version.The first version reviewed the common classical doctrine that the region of theantipodes, exactly opposite us (in the southern hemisphere) on Earth, is inhabited

just as our own part of the globe.7 While pagan Latin writers, for example, Pliny and Macrobius, had no difficulty with such doctrine, Christian writers fromAugustine to Isidore and Bede opposed it vigorously, because the lands of thesouthern hemisphere were believed to be unreachable from the Christian northdue to the great heat of the equatorial realm.8 To eliminate this difficulty, the

second version of AC made a very particular interpretation of Martianus’s phrase‘our antipodes’ as ‘the antipodes close to us’, which was then considered able tomean the section of the northern hemisphere opposed to us.9 This cosmographical

translations of the gloss to Martianus in this article are mine.) See the online edition of the glossesfrom VLF 48, Carolingian Scholarship and Martianus Capella: The Oldest Commentary Tradition,ed. by Mariken Teeuwen and others, first digital edition (November 2008), [accessed September 2009], fol. 79r, gl. 67.

5 De nuptiis, § 591, p. 207; VLF 48, fol. 54r margin; Lb, fol. 109 v ; Va, fol. 82r.6 De nuptiis, §§ 599–601, p. 210; Lb, fol. 111r; Va, fol. 82 v .7 General information on this question appears in Eastwood, Ordering , pp. 55–63; De nuptiis,

VI. 602–06 (pp. 211–12); AC, in VLF 48, fol. 55r.8 Augustine, De civitate Dei, ed. by Bernardus Dombart and Alphonsus Kalb, CCSL, 48

(1955), XIV . 2 (p. 510); Augustine, The City of God against the Pagans, trans. by Robert W. Dyson(Cambridge: Cambridge University Press, 1988), XVI. 9 (pp. 710–11): ‘Whether we are to believethat there are “antipodes” on the underside of the earth, opposite our own dwelling place.’ See alsoIsidore, Etymologiarum sive originum: Libri XX , ed. by W. M. Lindsay, 2 vols (Oxford: Clarendon

Press, 1911), IX. 2. 133; Bedae Venerabilis opera, pt VI. 2: Opera didascalica: De temporum ratione,ed. by Charles W. Jones, CCSL, 123B (1977), chap. 34 (pp. 390–91).

9 Lb, fol. 112r; Va, fol. 83 v .


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sleight of hand would seem to have been intended to avoid speculation abouthuman existence in the southern hemisphere, thus quieting any enquiry aboutmen who could not be reached by the Christian Gospel message. The commen-tators of the second version must have seen the ideological utility of this new interpretation of ‘antipodes’ for teaching younger students.

The fundamental physical elements of the cosmos were five according toMartianus: earth, water, air, fire, and aether, and this is their ascending order. Hisethereal realm was the location of all planets and stars, what we would call thecelestial region as opposed to the terrestrial region of the other four elements.10

AC provided specific characteristics of certain elements. Above central Earthall the elements circled in distinct, concentric layers, contrasted to the rectilinear

motion in terrestrial nature. (It seems that terrestrial proximity rather than adistinct property of individual elements produced rectilinear as opposed tocircular motion in any element.)11 The outer ethereal element had the finest andmost refined parts, making it the most appropriate material for the enclosing fir-mament of the cosmos.12 When Martianus made Lady Astronomy allude to thegreat length of time that the stars had been circling around, AC added that theauthor was a Platonist and considered the world to be eternal.13 Here we see aCarolingian source, AC, for the opinion that Martianus was a Platonist, and

this was probably John the Scot’s source for the same opinion expressed in hiscommentary.14

The characteristics of the elements according to AC, building upon theCapellan text, were as follows. Aether was not simply most ‘tranquil’ of theelements but was most ‘subtle’ and therefore the outermost and farthest fromEarth. This subtlety ( subtilitas), characterized also as relative fluidity, existed ingraded form in each of the fluid elements below the aether, that is, in fire, air, and

water, and could be observed in the common characteristic of wavelike motion

in all three of these. These gradations are not explained, but we may imaginethem in terms of Isidore’s ranges of three elemental qualities, viz., sharp/blunt,mobile/immobile, and fine/solid. Only the element earth was immobile in

10 De nuptiis, §§ 814–15, pp. 309–10.11 VLF 48, fol. 76r (numerous interlinear glosses).12 De nuptiis, § 814, p. 309.

13 VLF 48, fol. 76r, gl. 33: ‘Platonicus iste fuit et dixit mundum aeternaliter esse’ (He was aPlatonist and said the world exists eternally).14 Annotationes, p. 22. 29.


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Isidore’s scheme. All the fluids had a similar softness (mollicies) in their flow.15 If this common attribute is unclear to moderns, it appears to have been a useful labelfor Carolingian scholars and seems to have had no meaning more precise than‘fluidity’.

Looking forward to commentators after AC, we find that the cosmology and cosmography of Martianus along with AC’s clarifications received notablemodifications. On the physical stability of the cosmos due to the angle of eclipticand equator, John the Scot followed AC and improved the presentation of thelogical argument that AC had introduced. Nothing new was said with regard tothe shape of Earth. The spherical centrality of Earth was replaced by its centrality on the plane of the ecliptic in John the Scot’s Annotationes. John seems to have

considered this a simplification of the argument, but it also excluded any dis-cussion of weight in the position of Earth. Remigius of Auxerre adopted John’s

view.16 The location of the antipodes brought more comment. In the first versionof AC this location was simply the standard position, on the diametrically op-

posed quadrant of the terrestrial globe. Between the first and second versions of AC a notion of two different meanings of ‘antipodes’ entered into the discussion.By the time of the second version, we find the idea of an inhabited antipodes that

was located in the same, northern climatic zone as the European audience but on

the opposite side of the northern hemisphere. John the Scot elaborated on this,stating the standard geometrical meaning, placing the antipodes in the quadrantopposed to us (Europeans), as well as the teaching of ‘certain scholars’ who placed‘our’ antipodes in our own northern hemisphere. John explained and recordedboth views and chose not to discredit either of them. Remigius copied John’s texton this point.17

When AC came to the five separate elements, the first and the second ver-sion of AC each followed Martianus but clarified carefully the five elements inhierarchical order from top to bottom: aether, fire, air, water, earth. AC alsotransmitted the notion that in the upper, purer realms of aether and fire there isno combustion of matter from fire, since the transient effects of fire emerge only in the lower regions — air and below.18 John, followed by Remigius, overthrew the

15 The ‘mollicies’ of the fluid elements is noted in the interlinear gloss by AC in VLF 48, fol. 76r.16 De nuptiis, VI. 599, p. 210; Annotationes, p. 141. 21–24; Remigii Autissiodorensis Com-

mentum in Martianum Capellam, ed. by Cora E. Lutz, 2 vols (Leiden: Brill, 1962–65), II (bks III–

IX), 141. 3–6; all citations refer to vol. II of this edition, hereafter cited as Remigius, Commentum.17 Annotationes, p. 143. 22–33; Remigius, Commentum, p. 144. 3–13.18 VLF 48, fol. 76r.


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Capellan view of five elements and replaced it with the classical doctrine of fourelements while preserving the idea of five elemental regions. John retained the

view that the effects of fire do not occur in the region above air. He then intro-duced the late ancient view of St Augustine and Apuleius, among others, dividing air into two regions, the upper and lower airs. He described the upper as pureand associated with the superior elements, while the lower air was denser andmoister.19 John’s sources showed him that this lower, impure air was the properhabitation for demons, fallen angels who pervaded the lower regions and inter-fered in the lives of human beings. For cosmology, in general we can see that ACtransmitted with only subtle modifications the cosmology of Martianus.

Astronomy

If the Carolingian tradition of the Anonymous Commentary made notable modi-fications to the cosmology of Martianus, AC’s more strictly astronomical glossesand comments reveal a much greater variety of information, including some truly significant developments of the Capellan text. There is a wealth of substantialcomments by AC that were mostly adopted, occasionally omitted, but rarely con-tradicted by its Carolingian followers.

Examples of glosses among the common type in AC are: the concern for elab-orating the vocabulary used for the circles on the celestial sphere, a detailedexplanation of the fractions in the rising and setting times of the signs, the shapesand names of eclipse shadows, the names of lunar phases, reporting the Pliniandefinitions of absis and other terms, and, finally, correcting (with the number28) the imprecision of Capella’s statement that Saturn’s orbital period is ‘a littleless than 30 years’.20 These and other glosses by AC are an index of the care for in-structional use of Book VIII. Presumably of greater interest to mature scholars in

the Carolingian courts and schools were AC’s presentation of novel information

19 Annotationes, p. 172; Remigius, Commentum, p. 252; Augustine, De Genesi ad litteram libriduodecim, ed. by Paul Agaësse and A. Solignac, Oeuvres de Saint Augustin, 48 (Paris: de Brouwer,1972), III. 6. 8 (p. 222), III. 10. 14 (p. 232). Eastwood, Ordering , p. 207 n. 86.

20 These six examples appear as follows: the circles on the celestial sphere at De nuptiis, pp.310–15, and VLF 48, fols 76 v –77 v ; fractions in the rising and setting times at De nuptiis, pp.319–20, and VLF 48, fol 78 v ; shapes and names of eclipse shadows at De nuptiis, p. 325, and VLF

48, fol. 79 v ; names of lunar phases at De nuptiis, p. 327, and VLF 48, fol. 80r; Plinian ‘absis’ andother terms at De nuptiis, p. 335, and VLF 48, fol. 82r; adding precision to Saturn’s orbital periodat De nuptiis, p. 336, and VLF 48, fol. 82r.


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from ‘the Platonists’ about the paths of the inner planets as well as explaining anddrafting models of their epicyclic orbits. Similarly the use of an eccentric circle toexplain how the uniform motion of the Sun produces the appearance of varying solar speed and the resulting different lengths of the four seasons must haveintrigued the more capable readers of the first version of AC. Such additions andimprovements to the Capellan text, especially those introducing diagrams, deserveour careful attention.21

Order and Orbits of Inner Planets

In presenting diagrams previously absent from medieval Latin studies of the inner planets, AC opened up new ways to understand the characteristic motions of Mercury and Venus. One of the simplest and most powerful explanations camein the epicyclical diagram for either Mercury’s or Venus’s maximum elongationfrom the Sun. In the Natural History, Pliny the Elder had tried to explain thestations and retrogradations of these planets by the same general mechanismhe applied to the outer planets. He hypothesized a mysterious solar force that

variously attracted and repelled the planets, depending on their viewed anglesfrom the Sun.22 The Carolingians knew Pliny’s account. By contrast, the Capellanepicycles of Mercury and Venus were neither mysterious nor variable, and AC’sdiagrams provided persuasive force by setting a clear experience before the eyes of any student (Figure 3). That is, the circular path of each of these inner planetsaround the Sun automatically and obviously established the maximum angulardistance, as seen from Earth, of each planet from the Sun. As the Sun circledEarth, Mercury and Venus moving on their ‘epicycles’ around the Sun also pro-duced the observed progressions, stations, and retrogressions.23 Of course, neither

21 These larger topics are treated extensively below.22 Pliny the Elder, Naturalis historia, ed. by Ludwig Jan and Karl Mayhoff, 2 vols (Leipzig:

Teubner, 1906), II. 68–76 (I, 148–51).23 In a Capellan model of the orbit of an inner planet, either Mercury or Venus, around the

Sun, a student could easily identify the intervals of progression, station, and retrograde motion.Looking at the circular orbit (in Figure 3), called an ‘epicycle’, around the Sun, which in turn circlesaround Earth, we label as ‘stations’ the two points where the planet crosses the Sun’s path. We thennote the part of the planet’s motion in the same direction as the Sun’s motion, and this is the in-

terval of progression. The other part of the planet’s motion is in the direction opposite to the Sun’smotion, and this is the retrograde part of the inner planet’s motion. Furthermore, all of these partsof the inner planet’s motion are obvious as visual results of the Capellan model, or orbital pattern.


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Martianus nor AC could offer a mathematical account of the quantities of these phenomena, for example, an elongation of 22 degrees for Mercury from the

Sun, but the qualitative argument from the linear design came to have greatdemonstrative power.The evidence for planetary order from central Earth to the outermost planet

also received clarification through AC’s diagrams for the inner planetary orbits.This evidence was primarily the observed planetary brightness; the Sun and theMoon were special cases, but the five visible planets were assumed to fit thegeneral rule. According to the rule, the brighter the planet, the closer it is to Earth.This rule worked very nicely for the three planets farther than the Sun; Mars is

obviously brighter than Jupiter, which in turn is brighter than Saturn, so thesethree planets above the Sun are ordered as Mars-Jupiter-Saturn from Earth. Therule of brightness did not work so well for Mercury and Venus, because they appeared to be much brighter at some times than others, and this variation

was regular. The ancient writer Macrobius had presented the difficulty simply.Macrobius said that there are two opinions about the order of the two inner

planets, and each opinion had evidence to support it. Mercury and Venus havetheir circumterrestrial orbits either closer to us than the Sun or farther from us

than the Sun. Macrobius assigned each opinion to well-known names. Plato andthe Egyptians were credited with the supra-solar view. The infra-solar view wasthat of Cicero and the Chaldeans. Macrobius claimed that the Platonic-Egyptian

Fig. 3. Capellan epicycle for inner planet.


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view was better for two reasons. First, he called the Egyptians more astute ob-servers; the two views resulted from observations taken of different parts of the

planetary orbits, and the Egyptians understood this well. Second, the Egyptianshad a good philosophical basis, for they noted that the Sun is the closest of theluminous bodies in the heavens, the Moon being only a reflector. Since everything below the Sun reflects in order to show light, the planets Mercury and Venus mustbe above the Sun, for we know, according to Macrobius, that the five planets are

pure, luminous bodies.24 This lengthy account by Macrobius presented two fixedorders, of which only one could be correct. Yet the direct observational ex-

perience, Macrobius notwithstanding, was ambiguous. The Macrobian accountassumed the planets to be on simple circles, apparently all geocentric. Pliny theElder’s account shifted these circles to eccentrics, which still could not producethe dramatic changes in brightness of either Venus or Mercury as they movedthrough their orbits. The Capellan introduction of epicycles suddenly broughttogether the Egyptian and the Chaldean opinions as two aspects of one pattern.

With Mercury and Venus on separate circumsolar circles, or epicycles, while theSun in turn circled Earth, the two inner planets would naturally appear closer tous than the Sun at certain intervals and farther than the Sun at other intervalssimply because of their positions on the epicycles. Thus the Egyptian view pre-

sented the supra-solar part of each epicycle; the Chaldean view presented theinfra-solar part of each epicycle. And AC’s diagrams of the situation enhanced theCapellan account significantly for scholars new to the subject matter.

The Anonymous Commentary offered three separate marginal diagramsand a lengthy marginal comment where Martianus explicitly introduced the

view that Venus and Mercury do not circle Earth directly but instead makecircles around the Sun, which then carries them with it around Earth. In themargins on the two sides of this manuscript folio, alongside the relevant text, we

find images of the ‘Platonist’ circumsolar inner planets (fol. 79r), the Plinian cir-cumsolar inner planets (fol. 79 v ), and the Capellan circumsolar inner planets(fol. 79 v ). These three diagrams, for three versions of the inner planetary paths(Figure 4) appeared because of references in the marginal comment to the viewsof Plato and Pliny and the associated need to clarify precisely the text of Martianus.25

24 Macrobius, Commentarii in Ciceronem somnium Scipionis, ed. by Ludwig Jan (Quedlinburg:

Bassius, 1848), pp. 102–05. For my preferred translation with accompanying explanation seeEastwood, Ordering , pp. 36–43.

25 See below, n. 28.


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It was AC and AC alone that set down for subsequent generations of students the

interesting problem of interpreting the text in Capellan Book VIII for the patternof the planets Mercury and Venus. The three diagrams posed by AC were repeatedin some later commentaries but without the explanatory comment; in other, latercommentaries that preserved the explanatory comment, the three diagramsdid not appear. In other words, all later commentaries chose to economize and

present partial results without sufficient comment, words and diagrams together,to explain the three choices precisely. It was only in Carolingian centres whereAC, or at least its textual sources, existed that scholars could puzzle out the

proposed paths of the inner planets according to Martianus, Plato, and Pliny. The post-Carolingian manuscripts of Martianus preserved only a truncated account. When we look at the three patterns proposed by AC for the inner planets, weare seeing the diagrammatic interpretations of three different texts, and wesee implicitly the correct option according to AC, that is, the design labelled‘Martianus’. The Platonist image seems to have come from Calcidius’s commentary on the Timaeus. Our earliest surviving evidence of the use of Calcidius for astron-omy in the Carolingian world appears in a text I have called the ‘Paris Compend’.26

Fig. 4. Three versions of circumsolar orbits.

26 The Paris Compend is located in BnF, MS lat. 13955, fols 56r–60r. For details of thecontents see Eastwood, Ordering , pp. 314–24.


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This set of excerpts from Macrobius, Pliny, and Calcidius appeared in the secondquarter of the ninth century and may have been a product of Corbie, where it existedat that time. Although lacking Calcidius’s diagrams, excerpts from his commen-tary were used in the Paris Compend to explain both the dispute over the orderof the inner planets and the way that uniform circular motions, specifically epi-cycles and eccentrics, produce the supposedly erratic phenomena of individual

planets. In explaining the positions of the inner planets the Compend refers tothe order of Plato and the Egyptians in contrast to the order of Pliny, Cicero,Archimedes, and the Chaldeans (fol. 56 v ). No preference for one order over theother is stated, and the various appearances of the two planets are attributed toepicycles at a later point (fol. 58r) in the same chapter of the Compend. The use

of epicycles to explain the inner planetary order as well as the identification of Pliny with the Chaldean view are found here in the Paris Compend. Both of thesefacts were used by the author of AC’s marginal comment on Martianus’s text,leading to the three diagrams for circumsolar planets. AC wrote as follows:

Si secundum platonem ordinem planetarum voluit ostendere in hac sententia terris poteststare. Si vero pytagoricos pliniumque secundum ordinem planetarum velimus assumere,nunquam intelligere poterimus nisi ablatum fuerit terris ut sic sententia scribatur, sed cumsupra solem sunt, propinquior mercurius, et subaudiatur soli.27

(If one wished to show the order of the planets according to Plato, the word ‘terris’ (‘toEarth’) can stay in this sentence. If, in fact, we prefer to assume the order of the planetsaccording to the Pythagoreans and Pliny, we can never understand this sentence unless the‘terris’ is removed so that the sentence is written thus: ‘when they are above the Sun,Mercury is closer’, so that ‘[closer] to the Sun’ is understood.)

This marginal comment referred to a sentence of Martianus that said, ‘Sed cumsupra solem sunt, propinquior est terris Mercurius, cum intra solem, Venus,utpote quae orbe castiore diffusioreque curvetur’28 (When they [the inner planets]are above the Sun, Mercury is closer to Earth, when inside the Sun, Venus, in-asmuch as the orbit is both limited and wider). What we have here, when taking into account the Capellan text and the comment of AC on it, is a complex butdefinite situation. The original text of Martianus (§ 857, emended in the modernedition) appears to have said that when the two planets are above the Sun,Mercury is closer to Earth, and when they are below the Sun, Venus is closer to

27 Lb, fol. 162 v . For details about manuscript variants see Eastwood, Ordering , pp. 246–47 nn.

173–74.28 De nuptiis, § 857, p. 324; VLF 48, fol. 79 v . Willis’s reading of the manuscripts for line 17 in

his edition shows that all manuscripts have either ‘castiore’ or ‘castioque’.


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Earth, inasmuch as Venus has a larger orbital circle. However, by the time Capella’s work had passed through the sixth and seventh centuries it had suffered woefully;the part of the text we are studying here had seen the Latin word castior (tighter,narrower) replace the word vastior (larger) in describing the orbit of Venus, andall medieval readers accepted this corruption, making it necessary to interpretanother part of the text differently. The result was the reading we have seen inthe marginal comment about the designs of Plato, Pliny, and others. That is, for‘Earth’ the commentator substituted ‘the Sun’ so that the Capellan text woulddescribe Mercury being closer than Venus to the Sun when above the Sun andthen describe Venus being closer to the Sun when below the Sun. Hence theintersecting circles of Mercury and Venus around the Sun according to the

Carolingian text of Martianus Capella.All this commentary and diagramming was clearly the result of textual re-

search, not any other sort of research. It shows the bias of study for the purposeof explicating the text according to the spatial logic of the text rather thanaccording to physical-astronomical awareness. Because of the new meaning causedby the word castior , the path of Venus should be closer to the Sun when passing below the Sun, and so another part of the passage had to be reinterpreted tomake the Sun the reference point for distance instead of the Earth. Thus we have

intersecting circles of Mercury and Venus, and the text of Capella makes spatialsense but not astronomical sense. But the purpose was to teach students to readthe text carefully, not to teach students how to evaluate an astronomical hypoth-esis. AC was, after all, the product of literary scholars, not astronomers or physicalscientists. And all this led to a much heightened awareness of all texts dealing withthe paths of Mercury and Venus and to comparisons of these texts with an eyeto discovering the most persuasive interpretation. This also involved appeals toauthority and the emergence of recognized authorities with regard to specificastronomical questions. The authority of Martianus Capella became virtually unchallenged in the Carolingian era and beyond when discussing the paths of Mercury and Venus with respect to the Sun.29 AC was responsible for this result.

About the interaction of text and commentary at this point, we shouldnotice an external effect as well. The reference in AC’s comment to a Platonist

view of circumsolar planets can be identified as the likely source of John the Scot’s

29 See Bruce Eastwood and Gerd Grasshoff, ‘Planetary Diagrams — Descriptions, Models,Theories from Carolingian Deployments to Copernican Debates’, inThe Power of Images in Early Modern Science, ed. by Wolfgang Lefèvre, Jürgen Renn, and Urs Schoepflin (Basel: Birkhäuser,2003), pp. 197–226 (pp. 212–17).


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notorious reference to a Platonic heliocentrism in his commentary on MartianusCapella, where John, only in one version of his commentary, described a confus-ing pattern of planets at one point.30 It is only in the marginal comments of theVossianus manuscript that we can find a direct reference to ‘Platonists’ and animage of the planets attributed to Platonists. In Lb we can find the marginalcomment mentioning Plato along with an unattributed image of the Platonist

pattern for Mercury and Venus. The appendix of diagrams at the end of theCapellan text in these manuscripts gives no attributions to the three circumsolardesigns. In later Carolingian manuscripts of Capella with these diagrams of cir-cumsolar planets, the pattern initially assigned to the Platonists by AC receivedeither no attribution or was assigned to Bede; no hint of Plato or Platonists re-

mained.31 (Indeed, the name of Bede was associated with this design all the way to the Jesuit astronomer Riccioli in the seventeenth century!)32 So we know where

John the Scot probably got his idea of a ‘Platonist’ circumsolar planetary pattern,but his description is sufficiently divergent to suggest that he was going by hearsay rather than direct inspection of a manuscript with the diagram.33 Or he may have seen a manuscript of Capella containing the written comment without anaccompanying diagram. In either case, AC was the ultimate source for Johnthe Scot, and we know that this reference and any heliocentrism disappeared in

another version of his commentary on Capella.34

In that version John seems tohave consulted more manuscript copies of Capella and changed his mind on this point.

Textual research and scholarly comparison produced the design that ACattributed to Pliny. In a manner analogous to the thinking that led to the modelattributed to Martianus, we can discern the construction of a picture to representPliny’s text — again a case of literary textual research for an astronomical diagram.The truncated and pendant circumsolar paths for the inner planets with respectto the Sun raised no problem for AC. This design fits Pliny’s text and was thereby

30 Annotationes, pp. 22–23; see also Bruce S. Eastwood, ‘Johannes Scottus Eriugena, Sun-Centred Planets, and Carolingian Astronomy’, Journal for the History of Astronomy, 32 (2001),281–324 (p. 286).

31 Eastwood, Ordering , pp. 258–59.32 Giovanni Battista Riccioli, Almagestum novum (Bologna: Benatius, 1651), II. 283a.33 John’s view of Plato does not fit any source we know — certainly not Plato, nor Calcidius,

nor AC.34 The text of a straightforward Capellan planetary order can be seen in John’s commentary

on Book I of Martianus Capella in Jeauneau, Quatre thèmes, p. 114.


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necessarily correct!35 Of course, it also suggests why the Plinian pattern of circum-solarity was not nearly as successful with Carolingian scholars as was the Plinianorder of the planets.

The question of the paths of Mercury and Venus in relation to the Sun is anexcellent example of scholarly definition and research in order to clarify andsolve a problem. The process produced a well-defined set of models as possiblealternatives, which were then open for individual selection or rejection, depending on the further questions raised in study of the text and study of the astronomicalsituation. We should consider the question of the epicycles of Mercury and Venusaccording to Martianus Capella, taken in conjunction with AC’s commentary, asa classic case of scholarly and early scholastic question-and-answer procedure.

The Different Lengths of the Four Seasons of the Year

When we turn to the question that best exemplifies the fruitful application of eccentric circles by AC, we encounter a more complicated situation — morecomplicated both textually and historically. This is the question of the differentlengths of the four seasons of the year. Stated in another way, it is the question of the changing speed of the Sun as it travels through the twelve signs of the zodiacin a year. Writers of computus texts, concerned to set down a continuous, Chris-tian luni-solar calendar, tended to minimize or even eradicate the differences inseasonal lengths.36 It was the astronomical texts that paid attention to this phe-nomenon. Martianus Capella approached the question but actually dealt only

with the different lengths of time taken for the Sun to travel through two halvesof the zodiac.37 AC commented on this text and presented a diagram that clearly divided the zodiac into four equal quadrants (three zodiacal signs in each) to becontrasted to the unequal segments of time for the Sun to pass through these four

quadrants. The explanation, or answer to the question, was the eccentricity of Earth with respect to the circle of the Sun’s path (Figure 5). That is, Earth is at the centre of the circle of the zodiac, but Earth is not at the centre of the Sun’s circle around Earth.

35 Pliny, Naturalis historia, II. 72–73 (I, 149–50).36 Bede, De temporum ratione, chap. 35 (pp. 391–95). Bede assigns the four seasonal turning

points to the twelfth of the calends of January, April, July, and October. Rabanus Maurus, Martyr-

ologium; De computo, ed. by John McCulloh and Wesley Stevens, CCCM, 44 (1979), p. 244.Rabanus defined the four seasons as exactly equal lengths of time.

37 De nuptiis, § 873, pp. 330–31; see Eastwood, Ordering , p. 277, for a translation.


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The result is the appearance of slower and faster speeds of the Sun as it is respec-tively farther from and closer to Earth at different points in its annual path

around us. When farther from us, the Sun looks slower against the circle of thezodiac; when closer to us, the Sun seems faster against the circle of the zodiac. Butthe Sun actually keeps the same speed and produces the appearance of change only because of the eccentric circle of its motion around us.

Hellenistic astronomers knew and described the geometrical-eccentric pattern.On the other hand, the Roman authors available to Carolingian scholars eitherdid not know it, for example, Macrobius, or did not describe it well, for example,Pliny.38 It became available to the Carolingians with a full explanation, including

Fig. 5. Explanation of the four seasons according to Calcidius.

38 See Eastwood, Ordering , p. 335 n. 50, for various sources used by Pliny on the seasons.Macrobius described Earth as central, not eccentric, in the Sun’s orbit.


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diagrams, only in the commentary of Calcidius on Plato’s Timaeus.39 This text was not widely studied for astronomy until late in the ninth century and beyond.In Martianus Capella the account was brief and needed explication.40 AC pro-

vided the explication, but AC’s diagram was wrong. However, there were scholars who knew and used the Capellan account in summary form and did not attempta diagram. One of these was Martin of Laon, who, during the third quarter of thecentury, taught Bede’s De temporum ratione to his students at Laon and addeda notable comment on Chapter 30, regarding the intervals between the solsticesand equinoxes. Martin used Martianus’s explanation and emphasized the eccen-tricity of Earth as the natural cause of the Sun’s travel through the zodiac at

varying speed.41 In this way Martin improved on Bede by stating the cause for the phenomenon.

39 Calcidius, Timaeus a Calcidio translatus commentarioque instructus, ed. by Jan H. Waszink,Plato Latinus, 4 (London: Warburg Institute, 1975), pp. 125–30 (§§ 78–80); this account describesonly the explanation by an eccentric, which is the only pattern mentioned by Martianus Capella.Calcidius gave an epicyclical account as well in the following section.

40

De nuptiis, pp. 330–31: ‘Illud etiam non tacendum quod cum sint duo hemisphaeria, unumab aequinoctiali circulo in septentrionem, aliud in austrum ab eodem aequinoctiali, tamen soldiversa utrumque ratione transcurrat, cum, ut dixi, paria sint signa partis utriusque. Verum id, quodad solstitialem consurgit, clxxxv diebus et triente diei noctisque, id autem, quod ad brumalemdeprimitur, clxxx diebus peragitur; quod utique illa res facit, quod eccentron solis circulo dixiesse tellurem et in superiore hemisphaerio altius tolli, in inferiore ad terrae confinia propinquare.Dubium autem non est citius transcurrere breviorem sinum tardiusque diffusum.’ Translation in Martianus Capella and the Seven Liberal Arts, II: The Marriage of Philology and Mercury, trans.by William H. Stahl, with E. L. Burge (New York: Columbia University Press, 1977), p. 339: ‘Wemust not overlook the fact that although the two hemispheres are of equal dimensions—one fromthe equator to the north pole, the other from the equator to the south pole—and although, as Ihave mentioned, the signs on either side are equal, the sun nevertheless courses through them inunequal periods. It completes its ascending course to the summer tropic in 185¼ days, and itsdescending course to the winter tropic in 180 days. The obvious cause of the discrepancy is that,as I have said, the earth is eccentric to the sun’s orbit, which is more elevated in the upperhemisphere and draws closer to the earth in the lower. There is no doubt that the sun courses overits shorter curve more swiftly and over its more extended curve more slowly.’

41 Martin of Laon’s gloss to Bede’s De temporum ratione, chap. 30, is published in Bedae opera, pt VI. 2, p. 372, marginal gloss to line 15 of Bede’s text. Martin wrote that Martianus showed the

cause of the phenomenon: ‘SPATIO] Et secundum Martianum non aequaliter in omnibus signissol moratur. In illis enim ubi altius a terra extollitur longius moratur; in illis uero ubi inferiusinclinatur ibi citius transire dicitur. Sic et luna facit.’


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AC’s diagram for the solar speed (Figure 6) assembled all the elements of theCapellan account but did not arrange them with the proper spatial relationships.The inner circle is the circle of zodiacal signs, although actually drawn in AC asa circle of eleven constellations rather than twelve signs. The zodiacal circle isdivided in two halves, with Aries and Libra identifying the spring and fall equi-noxes at the ends of the horizontal diameter. The vertical diameter is the lineconnecting the summer and winter solstices. Earth, always at the centre of thezodiacal circle, is eccentric to the outer circle, which is the Sun’s annual circle

around us. The commentary here includes no added description for the diagram;the diagram is the commentary. Around the outer, solar circle we find two wordsthat complete the diagram and are drawn from the Capellan text (§ 873). As bothCapella and AC wrote, the Sun traverses one arc faster (citius) and the remaining arc slower (tardius). However, the arcs in Capella are reversed in AC! Throughthe shorter of two solar arcs, which Capella said the Sun traverses quicker simply because of its constant speed, AC said the Sun travels slower — at a differentspeed. What AC wished to preserve was the reported experience of changing solar

speed, and the diagrams in the Vossianus and the Besançon manuscript of ACreveal this intention nicely. The Besançon example shows it better, for there thesolar and zodiacal circles are concentric, so the two arcs of the annual solar path

Fig. 6. Explanation of the four seasons according to Anonymous Commentary.


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are equal, while the Sun is said to traverse one arc faster than the other! Martianus pointed out that Earth’s eccentricity causes the appearance of change, and thismeans that the Sun’s orbit is closer to Earth during the winter (lower) semicircle,

where the Sun appears to move faster, that is, to pass through in fewer days, fromthe autumn to the spring equinox.

From a non-causal point of view, AC gives a satisfactory account of the sit-uation. He properly labels the interval from fall to spring as the time of faster solartravel. He makes the inner, zodiacal circle, in which Earth is central, eccentric tothe outer, solar circle. He fails only in the small item of placing Earth closer to thesolar circle in the winter. From an experiential and fundamentally descriptiveoutlook, this failure is only one element among many correct facts. But, as we

moderns know, this is exactly the critical point, since the correct representationof the eccentric is the basis for a causal account, an explanatory rather than asimply descriptive account. The causality locked into the geometry of eccentricshas escaped the commentator. The commentary shows here what I call a compu-tistical sensibility regarding astronomical events. Reportage is everything; causality is beyond the responsibility and possibly the comprehension of the reporter. Weneed to recognize that all our Western computi of the seventh to ninth centuries

pay no attention to geometrical necessity or causality with regard to planetary phenomena. Only in accounts of the Moon’s appearances, the phases and espe-cially eclipses, do we find computists using very simple geometrical relationshipsto explain why certain lunar phenomena must occur. AC was following thecommon outlook and sensibility of the time in his mistaken commentary — thediagram — on the Capellan explanation of the lengths of the seasons. To be more

precise, we should say that AC shows an intermediate stage between the mostly non-geometrical astronomy of the early ninth century and the eleventh-century ability to construct epicyclical and eccentric models for causal accounts of plane-tary observations.42

What the Anonymous Commentary represents in the development of Westernastronomy is the recognition that diagrams can provide more of the astronomicaltruth than words alone. Previously, in the early medieval Western tradition of astronomy, diagrams were used to present in clearer form certain information.

42 An eleventh-century capability is displayed in diagrams in Vienna, Österreichische Na-tionalbibliothek, cod. lat. 443, fols 174 v , 175 v , 183r–v . See Bruce S. Eastwood, ‘Calcidius’s Com-mentary on Plato’s Timaeus in Latin Astronomy of the Ninth to Eleventh Centuries’, in Between Demonstration and Imagination: Essays in the History of Science and Philosophy Presented to John D. North, ed. by Lodi Nauta and Arjo Vanderjagt (Leiden: Brill, 1999), pp. 171–209 (pp. 204,207, 208–09).


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The computistical literature used schemata — a schema is more than a diagram —to make information more memorable. Diagrams included in the works of Isidoreand Macrobius, and diagrams added to Pliny, reiterated or completed the descrip-tions of spatial relationships found verbally in the texts.43 In the Plinian circulardiagrams for planetary latitudes we can see the first Carolingian perception of arelationship between space, or distance, and time in astronomical diagrams, andthese Plinian diagrams were quickly abandoned and replaced by the simpler, rec-tangular type of latitude diagram, which set forth only positions and distances.44

Similarly the Plinian diagrams for planetary apsides showed positions, and some-times distances, but not temporal relationships.45 It was the attempt of AC toinvent a diagram for the Capellan account of the apparent change in solar speed

through the year that began a new kind of astronomical diagram in the West. What AC should have liked was the pair of diagrams originally provided by Calcidius in his Timaeus commentary to explicate very nicely the phenomena of seasonal lengths.46 But these diagrams of Calcidius, based directly on classicalGreek astronomy, were beyond the ken of the scholars of AC’s generation. Andthe Carolingian manuscripts of Calcidius offered inadequate or corrupt forms of his explanatory diagram. Nonetheless, AC had begun a new tradition of astro-nomical diagrams.

The Anonymous offered a set of ten astronomical diagrams (Figure 7) at theend of the text of De nuptiis.47 Among these we find one diagram, deceptively simple to moderns, that shows the level at which Carolingian students (and mostteachers) of astronomy operated. It is a circle with sixteen equally spaced radii.

43 On Isidore’s diagrams see Michael M. Gorman, ‘The Diagrams in the Oldest Manuscriptsof Isidore’s De natura rerum’,Studi medievali, ser. 3, 42 (2001), 529–34. On Macrobius’s diagramssee Bruce Eastwood and Gerd Grasshoff, Planetary Diagrams for Roman Astronomy in Medieval

Europe, ca. 800–1500 , Transactions of the American Philosophical Society, 94. 3 (Philadelphia:American Philological Society, 2004), pp. 50–55. For Plinian diagrams see Bruce Eastwood, ‘Plin-ian Astronomical Diagrams in the Early Middle Ages’, in Mathematics and its Applications to Science and Natural Philosophy in the Middle Ages: Essays in Honour of Marshall Clagett , ed. by EdwardGrant and John E. Murdoch (Cambridge: Cambridge University Press, 1987), pp. 141–72.

44 Eastwood, ‘Plinian Astronomical Diagrams’, pp. 157–61.45 Eastwood, ‘Plinian Astronomical Diagrams’, pp. 154–57.46 The diagrams for Calcidius’s account in the early manuscripts are confusing and/or in-

correct. For a modern reconstruction of the correct diagrams, see Eastwood, Ordering , pp. 321,

323.47 Eastwood, Ordering , p. 258 (Figure 4.10) and p. 392 (Figure 6.9), shows the original and

a later, improved copy of the appendix.


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Fig. 7. A set of astronomical diagrams found in Paris, Bibliothèquenationale de France, MS lat. 8671 ( De nuptiis), fol. 84r (s. ix2).


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The words around the periphery of the diagram refer to the fact that the circum-ferential arcs between fixed radii will become smaller and smaller as we shortenthe radii. Given that cartwheels were readily seen in ninth-century Europe, wemay wonder why such a diagram was needed. I believe that what we are seeing insuch a diagram is the development of a consciously abstract awareness of quan-titative dependent variability in the arcs, angles, and radii in the diagram. Theeffect of larger cartwheels was obvious to the Carolingian traveller. The abstraction,and especially the vocabulary, of the relationship of radius, angle, and circum-ferential arc was perhaps not so obvious. We know that the challenge of explain-ing the lengths of the seasons by a diagram with an eccentric, which uses the same

vocabulary, appears to have been beyond the imagination of the AC scholars.48

The Changing Lengths of Daylight through the Year

Martianus Capella devoted a great deal more space to the Sun and to the Moonthan to any of the planets, including circumsolar planets. The De nuptiis affordedcomputists an astronomy of these two central bodies to complement the standardinformation in computistical tracts. With AC, Capella’s Book VIII described theSun’s regular succession of daily rising and setting points on the horizon throughthe year and the changing lengths of daylight through the year in addition to thedifference in the lengths of the two intervals from spring equinox to fall equinoxand from fall equinox to spring equinox.49 AC provided diagrams for each of these. We have discussed the last in much detail. The first two deserve some atten-tion as well. The diagram for the successive rising and setting points is labelled‘Libra — Aries’ and appears in the appendix of ten diagrams which I call ‘TheAppendix’ (see Figure 7). ‘Libra — Aries’ appears at the bottom of the sheet onthe left. It shows by the use of numerals from one to four the identity of four

successive intersections made by the Sun at the rising and setting points withthe horizon, which occur at diametrically opposite points on the horizon.50 The

48 The full text and translation, with medieval diagrams, of Calcidius’s account of the seasonsappears in Eastwood and Grasshoff, Planetary Diagrams, pp. 73–82.

49 The sun’s rising and setting points on the horizon through the year are described in Denuptiis, p. 330; AC, in VLF 48, fols 79 v –81r. The changes in lengths of daylight during the year

are described by De nuptiis, §§ 875–78, pp. 331–33; AC in VLF 48, fol. 81 r–v . We have dealtabove with Martianus’s and AC’s treatments of the different lengths of the four seasons.

50 Eastwood and Grasshoff, Planetary Diagrams, pp. 117–19. Eastwood, Ordering , pp. 403–05.


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diagram for changing lengths of daylight, labelled ‘Equinoctium’, also appears inthe appendix and was the solar phenomenon receiving the most Carolingian com-mentary. As part of his discussion Martianus identified eight climates (climata),and AC pointed out, first, that Pliny had identified twelve ( Naturalis historia,VI. 219–20) and, second, that it was ‘the moderns’, according to Pliny, who hadadded four.51 As its distance from the equator increased, each ‘climate’, or lati-tudinal band, would show increased difference in the lengths of day and nightthrough the year.

While AC’s attention to Pliny as a source beyond Martianus is notable, it isAC’s diagramming, which calls attention to a geometrically based increase anddecrease in the amount of daylight, that is most striking. Many Carolingian

writers adhered to an older, arithmetical account that reported a fixed change of two hours per month from one solstice to the next throughout the year at a farnorthern latitude where the minimum and maximum lengths of daylight were sixand eighteen hours. AC followed the Capellan text and emphasized the following geometrical sequence of monthly hours of daylight, to be added and then sub-tracted as each six months passed from winter solstice to summer, at the samenorthern latitude in a regular rhythm: 1 hour, 2 hours, 3 hours, 3 hours, 2 hours,1 hour. AC’s diagram here was not self-evident, and its nature rather clearly

required explication by an experienced teacher. So we find here one more exampleof a likely use in schools, although certainly not all schools, for the AC com-mentary on Capellan astronomy.

Another evidence of pedagogy occurs in connection with the topic of thechanging lengths of daylight. Martianus dealt with the topic twice, and the de-tailed attention to climata and precise lengths of daylight appeared later (§§ 876–78), where we find extensive commentary by AC. The previous, initial mentionof the phenomenon (§ 846) drew less comment, as Martianus was there assessing the logic of the claim that night and day should always be the same length. The

primary concern of AC at that point was to follow the logical analysis of thestatements about the lengths of daylight and night and to make the nature of thearguments as clear as possible. Regarding one sentence, the marginal commentary noted, ‘vera propositio sed falsa conclusio’ (true proposition but false conclusion),and subsequently, ‘Rhetorici sunt isti silogismi quia non habunt igitur’ (These

51 A climate is a latitudinal band on Earth’s globe. For details see Bruce S. Eastwood, ‘Climate’,in Trade, Travel, and Exploration in the Middle Ages, ed. by John B. Friedman and Karen M. Figg

(New York: Garland, 2000), pp. 112–15. For the ‘Equinoctium’ diagram see Eastwood and Grass-hoff, Planetary Diagrams, pp. 124–25; Eastwood, Ordering , pp. 282–84. Pliny, Naturalis historia,VI. 211–20 (I, 517–22).


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syllogisms are rhetorical [and not demonstrative], since they do not use a ‘there-fore’.)52 These were useful notes for students.

Solar Radial Forces

In the last section of Book VIII, surveying the phenomena of each of the five planets, Martianus made clear his close attachment to the same solar dynamics wecan find in Pliny. Both of these authors presented the anomalies — the stationsand retrogradations — of each planet as effects of the power of solar rays. Theeffects were stronger on planets closer to the Sun. With the outer planets we ob-serve that the greatest variation in planetary motion appears with Mars, and Marsis much closer to the Sun than Jupiter or Saturn. Furthermore we can see thatthe effects of solar rays on Jupiter’s motions are greater than on Saturn’s, againbecause of the relative distances of these two planets from the Sun. When weconsider the situation of the inner planets, Mercury and Venus, we find that bothPliny and Martianus, following a Hellenistic, Stoic line of thought, conceived the

planetary phenomena to result from the forces of solar rays. For Pliny, the forces were sometimes attractive (centripetal?), sometimes repulsive (centrifugal?), andsometimes simply motive (continuously circular), producing the reported retro-

grade, stationary, and forward motions; he conceived them as arcs of motion withstationary terminal points. Pliny imagined the same situation for inner and outer

planets.53

Martianus reformed the Plinian heliodynamic by differentiating its effects onthe inner planets from its effects on the outer planets. According to the Capellanreform, solar radial forces held the two closest planets, Mercury and Venus, sotightly that these two could no longer circle around Earth like the three outer

planets, but instead moved on small circles around the Sun, and Martianus gave

the name ‘epicycle’ to each of these two circumsolar orbits. He used this nameonly once in the whole of Book VIII, and it was simply his descriptive term for the path resulting from solar radial forces acting on Mercury and Venus.54 There wasno question of using epicyclic patterns for the outer planets. Thus epicycles found

52 De nuptiis, p. 320; VLF 48, fol. 78 v . In addition to sources cited in the previous note, seeEastwood, Ordering , pp. 284–88, especially n. 239.

53 For background on Pliny’s idea of solar radial force, see Pliny, Histoire naturelle, ed. by Jean

Beaujeu (Paris: Les Belles Lettres, 1950), II. 158 (n. 1); Pliny, Naturalis historia, II. 68–76 (I, 148–51). Eastwood, Ordering , pp. 112–14.

54 For his use of the term epicyclus, see De nuptiis, § 879, p. 333; Eastwood, Ordering , pp. 291–92.


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only the most special and limited use in Capellan astronomy. An epicycle was nota general geometrical tool for Martianus. Nor did AC see the larger possibilitiesfor epicycles, but it was the elaborate commentary by AC on the epicyclical pathsof Mercury and Venus that first brought such a planetary pattern clearly to theattention of Carolingian scholars. And to a lesser extent we may say the samething about AC’s attempt to diagram an eccentric to explain the apparent changesin solar speed through the seasons of the year.

Martianus Capella’s astronomy together with the Anonymous Commentary made geometrical descriptions much more suggestive and influential for Caroling-ian scholars than either Macrobius or Pliny had done. In all cases it was diagramsthat highlighted this development. Macrobius used only geocentric images, which

explained few of the astronomical phenomena. Pliny introduced eccentrics, butonly for a few phenomena. Martianus added epicycles, again for a limited numberof phenomena. AC provided diagrams for many phenomena and aroused moreawareness of the utility of eccentrics and epicycles. AC represents the awakening of Carolingian teachers and scholars to the persuasive power of certain diagramsto convey astronomical knowledge. And teachers like Martin of Laon saw thedistinctly explanatory, not simply descriptive, value of these geometrical tools.The next step would be the recognition that geometrical patterns should befound for all the motions of celestial bodies, and this came with the wider study of Calcidius’s Timaeus commentary in the tenth and eleventh centuries.

Saving the Text, not the Phenomena — Mercury’s Limits

The importance of Martianus’s astronomy together with AC is undeniable, and we should not forget the characteristics of the commentary. Along with the usualglossing of single words, it was, as we have said, very much a product of textual

analysis and interpretation. It was not a work of either theoretical or observationalscience. Whatever physical science was involved came, at best, third-hand viaMartianus, who drew on the work of others. The method of textual study andanalysis shows up clearly in a remarkable conflict between the Carolingian textand ordinary, reasoned understanding of the phenomenon of the bounded elonga-tion of the planet Mercury. The accepted elongation of Mercury from the Sun was22 degrees. This value was reported by Pliny and Bede and even by AC at pointsin the gloss to Book I of De nuptiis.55 It seems obvious to moderns that Martianus

55 Pliny, Naturalis historia, II. 38–39 (I, 138–39); Bede, De natura rerum, chap. 13, in BedaeVenerabilis opera, pt I: Opera didascalica ed. by Charles W. Jones, CCSL, 123A (1975), p. 205; for


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knew and therefore would report this value for Mercury’s elongation. How-ever, the text of Book VIII suffered many corruptions, and one was the reading for Mercury’s limited distance from the Sun. The Carolingian text in almost allmanuscripts gave this value as 32 degrees.56 Unwilling to declare the text corruptat this point, AC adopted a strategy of special interpretation and proposed thatthis value of 32 degrees was only under special conditions. The gloss argued thatthis angular distance was sub sole (under the Sun), whatever that means. Elaboratehedging and a strange diagram appear here in the commentary. AC nowhereactively rejected the value of 22 degrees, but the intent of the commentary appearsto have been to agree with a 22-degree limit along the path of the Sun, that is, onthe ecliptic, but then to claim that Mercury’s orbit somehow hangs below the

plane of the ecliptic to make a 32-degree elongation from the Sun.57 It would benice if we could assume that AC imagined this to be simply the angle of Mercury’scircumsolar orbit to the ecliptic plane, but we have no textual evidence in either

De nuptiis or AC to support it. All this reasoning is designed to save the text, notthe known phenomena. The fact that bounded elongation from the Sun is nec-essarily a viewed angular measurement and so the 32 degrees can not stand, if 22degrees is the accepted elongation along the ecliptic, seems not to have been con-sidered. It certainly was not discussed. AC was concerned to preserve and justify

the text, even when this required a most unusual spatial interpretation.

AC’s awareness see the marginal gloss on VLF 48, fol. 2 v , gl. 104: PLIADUM] ‘Pliades septemfuerunt quarum ista sunt nomina Terope, Meropias, Cilleno, Maia, Alcione, Tagete, Electra.Dictae sunt autem “apo tu plistos” id est “a pluralitate” vel “a Matre,” ut sint filiae Adlantis. EtPliadis vel a pluvia. Et sunt in genu Tauri. Et tunc quasi Mercurius Matrem salutat quando cumSole in Tauro moratur, quia secundum vera astrologia nunc quam ( sic , lege numquam) longius

a sole nisi viginti duabus partibus distat.’56 De nuptiis, p. 333; see the editorial note for line 16 of the text, where Willis found 33

degrees in the manuscripts; in fact, many manuscripts report 32 degrees, e.g., VLF 48, fol. 81 v .57 VLF 48, fol. 81 v . The marginal diagram shows Mercury on a circle subtending the Sun

with the following text filling Mercury’s circle below the Sun: ‘hoc sciendum quod quantum inlatitudinem potest Mercurius a Sole fieri xxxii partibus, quantum vero ad lineam solarem itaangustatur circa ipsum ut non possit plus xx et duabus partibus ab eo separari’ (It is recognizedthat with respect to latitude Mercury can be 32 degrees from the Sun, but with respect to theSun’s actual path the planet is restricted near to it so that Mercury cannot be separated more than

22 degrees from the Sun). Compare De nuptiis, § 879, p. 333, where the latitudo of Mercury isdefined as 8 degrees. See also Eastwood and Grasshoff, Planetary Diagrams, pp. 125–26, andEastwood, Ordering , pp. 292–97.


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The Importance of Diagrams

Here we should understand an important characteristic of AC’s diagrams. The

diagrams, especially when set apart in an appendix to De nuptiis, came to functionas a distinctive part of the work with an eventual authority of their own over thesucceeding decades. What does this mean? Among other things it means that thediagrams came to be independent evidence for the astronomical arrangements andmotions identified and described in the text. The diagrams were complementary to the text, and they gave precision to the text. When the text was in any way unclear, the relevant diagram would offer more clarity, thereby introducing oreven creating additional evidence. We have already encountered examples of this.

The diagram for the position of Mercury, 32 degrees ‘sub sole’, certainly creatednew evidence not suggested by Martianus. Likewise the three alternative diagrams

proposed for the circumsolar orbits of the inner planets, resulting in the identi-fication of the pattern of intersecting circles as the correct design for the text of Martianus, created (in compressed fashion) a large body of evidence beyond

what could be found in the text. A survey of subsequent references to or uses of Capellan astronomy will show the remarkable familiarity with the intersecting-circles model of circumsolar Mercury and Venus over the next four centuries and

its continued attribution to Martianus Capella.58

AC in conjunction with the Capellan text was the most important astro-nomical source in the Carolingian world. Only with Book VIII of De nuptiis didthe ninth century have a relatively complete textbook of astronomy. In many Capellan manuscripts the astronomy received as extensive commentary as any other of the seven liberal arts. Book VIII was also singled out for separate copy and

presentation at least twice in the ninth century, including an elaborate com-mentary probably made at Corbie.59 The works of Macrobius and Pliny receivedno such treatment, although they were mined for useful ideas and informationby AC. Macrobius had offered a simplified, ordered cosmos — a geometricalmetaphor. Pliny had collected a mass of data on celestial phenomena. Martianusdid both of these things and gave greater sophistication to the geometry andgreater order to the data. AC saw this virtue and elaborated on it.

58 Eastwood and Grasshoff, ‘Planetary Diagrams — Descriptions, Models’, pp. 212–17.59 The commentary on Book VIII of Capella, made probably at Corbie late in the ninth

century, appears in BnF, MS lat. 13955, fols 46 v –53 v . David Ganz, Corbie in the Carolingian Renaissance, Beihefte der Francia, 20 (Sigmaringen: Thorbecke, 1990), pp. 152–53, includes thismanuscript in his list of books in the Corbie library.


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The circulation of AC with its diagrams indicates a successful identificationof astronomical ‘questions of the day’ and led to imitations. Both John the Scotand Remigius of Auxerre wrote commentaries on Martianus, and both madeextensive use of AC. Remigius, for example, went to AC more than to any otherexisting commentary, although Remigius occasionally appreciated John’s morelucid account of some items. Other anonymous commentaries, such as the onein the Leiden manuscript (Universiteitsbibliotheek, BPL 87 (Lc)), used AC and

were in turn used by Remigius. And we may even notice the impact of AC in aninnovative, though little circulated, text like the Paris Compend. In the Compendthe explanation by excerpts from Calcidius of epicyclic motion and the motionof a solar eccentric would seem to be understood as improvements on the expla-

nations in Book VIII of De nuptiis and in AC. (The Compend does not cite orexcerpt Capella, but it does excerpt from Pliny and Macrobius to set the stage formore sophisticated geometrical accounts of celestial phenomena.) Thus the ParisCompend shows us a midcentury replacement of the very well known accounts

provided by Martianus and AC for the circumsolar planets and the lengths of thefour seasons. And so, whether in affirmation or in contradiction, scholars of theninth century testify that AC provided the fundamental elucidation of Book VIIIof De nuptiis, and we see that this text combined with AC stood as the most

authoritative astronomy of the Carolingian world.

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