Isis Volume 80 issue 1 1989 [doi 10.2307%2F234345] Richard C. Dales -- The Computistical Works Ascribed to Robert Grosseteste.pdf

The Computistical Works Ascribed to Robert GrossetesteAuthor(s): Richard C. DalesSource: Isis, Vol. 80, No. 1 (Mar., 1989), pp. 74-79Published by: The University of Chicago Press on behalf of The History of Science SocietyStable URL: http://www.jstor.org/stable/234345 .Accessed: 07/04/2014 05:35

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NOTES & CORRESPONDENCE

THE COMPUTISTICAL WORKS ASCRIBED TO ROBERT GROSSETESTE

By Richard C. Dales*

Four computistical works-three computi and a calendar-have been ascribed to Robert Grosseteste by S. Harrison Thomson. Thomson places the Kalendarium first in order of composition, followed by the Compotus I, which he dates "before 1220." He puts the Compotus correctorius third, suggesting that it may have been written earlier than circa 1232, the date assigned by Robert Steele. Last he places the Compotus minor, which he dates 1244 on the basis of a phrase on folio 107v of the only extant manuscript: "sed a nativitate domini elapsi sunt 1200 anni et eo scilicet 44 amplius."I These works have recently attracted quite a bit of attention. Sir Richard Southern has challenged the dating and order that Thom- son assigned. Jennifer Moreton, of Trinity College, Dublin, questions Grosse- teste's authorship of two of the computi and the Kalendarium. And an edition of the computi is now being prepared by Bernard Malone of the University of Southern California. In my 1961 article on Grosseteste's scientific works, I in- tentionally omitted any consideration of the astronomical and computistical material because I felt that they presented their own peculiar problems, which I was not then in a position to solve.2 Here I will begin to fill that lacuna by investigat- ing the nature, relationship, and authenticity of the three computi.

Southern has made a notable start toward clearing up some of the misunder- standings underlying Thomson's dating. In the first place, he points out that the phrase "scilicet 44," which led Thomson to assign the composition of the Com- potus minor to 1244, was a marginal note; it does not belong in the text and in fact contradicts the computation in the text. Noting that only old-fashioned authorities (John Beleth, Dionysius Exiguus, and Gerlandus) are mentioned in the Compotus I, Southern assigns this work to about 1195 and places the Compotus minor (which Thomson had dated 1244) about ten years later. He dates the Com- potus correctorius 1215-1220.3 In changing the dating, Southern has altered the order, and hence the relationship, of the three works. But he has overlooked some remarks in the text that make his solution impossible as it stands, although much closer to the truth than Thomson's.

Jennifer Moreton has denied that Grosseteste wrote either the Compotus I or

* Department of History, University of Southern California, Los Angeles, CA 90089-0034. 1 "From the birth of the Lord, there have elapsed 1200 years, and more than that, to wit, 44":

Compotus minor, Dublin, Trinity College MS 441, fol. 107v. See also S. Harrison Thomson, The Writings of Robert Grosseteste, Bishop of Lincoln, 1235-1253 (Cambridge: Cambridge Univ. Press, 1940), pp. 94-97, 106; and Compotus correctorius, British Library MS Add. 27589, printed in Opera hactenus inedita fratris Rogeri Baconis, ed. Robert Steele, 9 vols. (Oxford: Clarendon Press, 1926), Vol. VI, pp. 212-267.

2 R. W. Southern, Robert Grosseteste: The Growth of an English Mind in Medieval Europe (Ox- ford: Clarendon Press, 1986), pp. 127-131; Jennifer Moreton, "Robert Grosseteste, John of Sacro- bosco, and the Calendar," in Proceedings of the Warburg Institute Grosseteste Symposium (May 1987), ed. John McEvoy (forthcoming); and Richard C. Dales, "Robert Grosseteste's Scientific Works," Isis, 1961, 52:381-402. I am obliged to Jennifer Moreton both for allowing me to see her paper in draft form and for her personal correspondence on the subject.

3 Southern, Robert Grosseteste, p. 131.

ISIS, 1989, 80: 74-79 74


GROSSETESTE'S COMPUTI 75

the Compotus minor (although she concedes his authorship of the Compotus correctorius). She argues instead that both are early versions of Sacrobosco's De anni ratione, into which more advanced calculations were subsequently inserted. In fact, there is much material common to Sacrobosco and the two computi attributed to Grosseteste. Moreton has raised some interesting questions, and we are obliged to consider the possibility that Grosseteste may not have written the first two computi.

The work that Thomson designates as the Compotus I exists in a single manuscript from the second quarter of the thirteenth century, Oxford, Bodleian MS 679, folios 65r-75r. It is ascribed at both the beginning and the end: "Hic incipit compotus magistri Roberti Grosseteste" across the top of folio 65r and "Explicit compotus magistri Roberti Grosseteste" on folio 75r. The manuscript contains no diagrams or tables, although the text refers to the lines and columns of tables. Its chapters are the usual ones for a computus: De duplici anno, De septimana, De mense, De anno, De concurrentibus, De regulari solari, De bissexto (i.e., leap year), De ciclo solari, De divisione anni, De anno lunari, De epactis et regular- ibus, De regulari lunari, De saltu lune, and De festis mobilibus. The authorities this computus mentions-Gerlandus, John Beleth, Dionysius Exiguus, and Theophilus of Alexandria-were already out of date by the late twelfth century, as was Isidore of Seville, whose work it uses but who is not named. It contains a number of mnemonic verses and frequently quotes Ovid's Fasti for illustrative purposes. Although there is no trace of Arabic astronomy, the author does tell us that "the Arabs begin the day at noon, saying that the sun was made at noon" (folio 65r) and that the Arabs begin the year at the summer solstice (folio 67r). The Compotus I also contains an Aristotelian dictum based on Physics 2.195a: "Nam posita causa efficiente et immediate, et ponitur eius effectus" (folio 65r).

Since there is a great deal of similarity among computi in general, and much of the computational instruction in both the Compotus I and De anni ratione appears nearly verbatim in dozens of twelfth- and thirteenth-century computi, I shall concentrate on the distinctive characteristics of the Compotus I that hint at its authorship and date of composition. It begins by distinguishing between the practice of computus, whose purpose is simply to contrive devices for determining the movable feast days of the church and which is therefore concerned only with the motions of the moon and sun, and the science of astronomy, which is concerned with the true measurement of time and with the motions of all the planets.4 But the author does not confine himself to this. He is very concerned about the errors in the calendar and in the computistic tradition that have re- sulted in the feast days coming earlier than they should. Because of such errors, he complains, we do not know the exact days of the solstices or equinoxes. The summer solstice is supposed to coincide with the birth of John the Baptist and the winter solstice with the birth of Christ. But they do not, because we make the year too long. The author calculates how much time has been lost as a result: assuming that the solstices did coincide with the births of John and Jesus, he says that "from the birth of the Lord, there have elapsed one thousand and two hundred years, and more than that. In this nunmber are ten times 120 years, and thus the winter solstice has now retrogressed by ten days."5 After a lengthy

4 "Subiectum autem huius scientie est tempus-non dico tempus secundum substantiam temporis neque inquantum est numerus primi mobilis, sed inquantum dividitur in partes suas que considerantur ab ecclesia secundum motum solis et lune. ... Compotista enim considerat tempora mensurata secundum motum istorum duorum planetarum ... Nec curat motus aliorum planetarum": Oxford, Bodl. MS 679, fol. 65r.

s "Sed a nativitate domini elapsi sunt .M. et CC. anni et eo amplius, in quo numero sunt X.es .C. et .XX. anni, et ita per .X. dies retrogressit iam solstitium hiemale": ibid., fol. 69v.


76 RICHARD C. DALES

discussion of the errors that result from the computistical rule-of-thumb methods, the last of which is the computation of the saltus lune, he concludes in some exasperation that "although the subtraction of one day rests on authorita- tive authors, nevertheless it contains many doubtful things and a good admixture of falsehood, which I shall verify at another time when the opportunity per- mits."6 Thus the author of the Compotus I explicitly promised a subsequent work that would correct the vexed problems of the tradition-that is to say, a computus correctorius.

There seems then to be no good reason to doubt Grosseteste's authorship of the Compotus I. The ascriptions themselves, which certainly predate 1250, are strong evidence. Although it is true that famous names tend to attract the attri- bution of spurious works, the Compotus I is attributed not to Lord Robert Gros- seteste, Bishop of Lincoln, as one might expect of a false claim, but simply to master Robert Grosseteste, who was at the time an unbeneficed provincial master, if we can accept Southern's plausible reconstruction of Grosseteste's early life.7 Another strong bit of evidence is the author's promise to write a more satisfactory work when time permitted. The Compotus correctorius exactly fulfills such a promise, and Grosseteste's authorship of that work is too well at- tested to be questioned. I might point out an additional consideration, that of style. The sentence spanning folios 68r and 68v of the Compotus I is typically Grossetestian in its length, complexity, and coherence:

Sed quia difficile esset istas sex horas cuilibet anno continuare ita quod numquam redacte in diem alicubi poneretur, quia secundum hoc, si annus precedens incipit a mane, secundus a meridie, tertius a vespere, quartus a media nocte, et sic feria sanc- torum variantur, et ita principium Ianuarii posset ascendere quod esset circa equinoc- tium vernale et ulterius, ita quod principium anni esset in tam longis diebus sicut sit dies soisticii estivalis, ideo provisum est ut sex hore excrescentes in primo anno et sex in secundo et sex in tercio transferantur ad sex horas quarti anni, et erunt in quarto anno .XXIIII. hore, id est unus dies sic particulariter collectus, et interponitur Februario, quia mensium brevissimus est.8

The Compotus minor, which Southern rightly places second in order, exists only in Dublin, Trinity College MS 441 (ca. 1325), folios 104v-1 1 Ir. It is ascribed to Grosseteste (somewhat ambiguously) in the table of contents, written by a coeval hand, but not in the text. On close inspection, the Compotus minor turns out not to be a separate work at all, but a condensation, sometimes by para- phrase, sometimes by omission, of the Compotus I. There is no reason to believe that Grosseteste had any hand in this abridgment. It was made by someone who wanted a useful, uncomplicated computus without the alternative procedures, redundant mnemonics, illustrative material, and confusing questions that Grosse- teste had introduced into the Compotus I. It begins: "Those matters that were left out of the other treatise on the computus, or that were presented less clearly or otherwise, can be found here."9 If we assume that the "other treatise on the

6 "Sed nota quod licet hec subtractio sit ab auctoribus autentica, tamen in se multiplicem habet questionis scrupulum et falsitatis admixtionem, que alias pro loco et tempore verificabimus": ibid., fol. 73v. The saltus lune is the extra day that must be inserted in the last year of the nineteen-year solar cycle.

7 Southern, Robert Grosseteste (cit. n. 2), pp. 63-82. 8 Oxford, Bodl. MS 679, fol 68r-v. See the discussion of Grosseteste's style in Robert Grosseteste,

De cessatione legalium, ed. Richard C. Dales and Edward B. King (London: Oxford Univ. Press, 1986), pp. xv, xxix.

9 "Que vel dimissa sunt in alio tractatu compoti vel minus lucide vel aliter dicta quam ibi, hic reperiri possunt": Dublin, Trinity College MS 441, fol. 104v. See Southern, Robert Grosseteste (cit. n. 2), p. 128; and Thomson, Writings of Grosseteste (cit. n. 1), pp. 95, 97.



computus" is the Compotus I, as Southern claimed, the statement makes no sense, since the Compotus minor contains nothing, aside from the marginal nota- tion "scilicet 44," that is not in the Compotus I, and it sometimes states things less clearly (not more) but never otherwise than the Compotus I. Much less could it refer, as Thomson claimed, to the Compotus correctorius, a much more so- phisticated work than either the Compotus I or the Compotus minor. We have no way of knowing what other treatise on the computus is meant, but a likely sug- gestion is that an earlier copyist of the work than the scribe of the Dublin manuscript, having copied out some such treatise that he found unsatisfactory, added the Compotus minor as a corrective. Whether he or someone else made the condensation I can see no way of determining. There are several other places where the text says that the rules for doing a particular computation may be found in the other computus. Moreton, crediting I. S. Robinson with the sugges- tion, holds that in these cases the Dublin scribe is referring to the Compotus correctorius, which he has just copied out. This is entirely possible. But we cannot make the same assumption about the computus referred to in the opening sentence, given the character of the Compotus correctorius.

Thomson dated the Compotus minor 1244 because in the margin opposite the phrase "from the birth of the Lord there have elapsed one thousand and two hundred years and more than that," the scribe or annotator has written "scilicet 44." This marginal addition does not appear in the text at the corresponding part of the Compotus I, and it clearly does not refer to the composition date of that treatise. Moreton, arguing that the Compotus minor is a condensation of Sacro- bosco's De anni ratione, suggests that the date may have been inferred by the scribe from an anonymous line of verse, ".M. Christi bis .C. quater deno quater anno," which someone added to the quotation from Boethius's De consolatione philosophiae 3.9 that concludes both De anni ratione and the Compotus minor. This may be. It is also possible that the marginal note refers to the date when the abridgment was made. But these are only guesses. All we can say for certain is that it does not refer to the composition date of the Compotus minor. In fact, as I have suggested, the Compotus minor should be regarded merely as a condensation of the Compotus I made sometime after the composition of the latter and before circa 1325, when the Dublin manuscript was written.

We know, on the evidence of Oxford MS Bodleian, Savile 21, that by 1215-1216 Grosseteste had come into contact with a considerable amount of Ara- bic astronomy. In this manuscript Grosseteste has written out, in his own distinctive hand, several works of Thebit (Thabit ibn Qurra), some Arabic astronomical tables (including eclipse tables), and several astrological tables and diagrams. The date that Grosseteste copied this material can be determined from internal evidence as 1215-1216.10 This provides a terminus ante quem for the Compotus I, since that treatise shows no knowledge of Arabic astronomy beyond the fact that the Arabs began the day at noon and the year at the summer solstice. Grosseteste had promised in the Compotus I that he would look into some of the traditional computistical problems when he got a chance; the works copied in the Savile manuscript show that he got the chance by about 1215.

The resulting work was the Compotus correctorius. This is a much more advanced work than the Compotus I. It retains many of the mnemonic verses and some of the wording of the earlier work, but its focus is on solving the most

10 See S. Harrison Thomson, Latin Bookhands of the Later Middle Ages, 1100-1500 (Cambridge: Cambridge Univ. Press, 1969), plate 89, where a specimen leaf is reproduced. One of the diagrams is labeled: "Hec est figura coniunccionis satumi et iovis annis arabis 612 profectis mensibus 5 diebus 20," which corresponds to 1215-1216. See also the discussion of the Savile manuscript in Thomson, Writings of Grosseteste, pp. 30-33.


78 RICHARD C. DALES

serious problems of the computus rather than providing a handy elementary man- ual for provincial clergy. Its chapter headings immediately signify its more advanced purpose:

1. De causa bissexti et de modis magis verificandi kalendarium, et de ratione inven- iendi annum bissextilem. 4. De ostensione erroris kalendarii nostri in sumptione pri- mationum, et in positione cicli novadecimalis et cicli epactarum, et de modo sumendi primaciones secundum veritatem. 5. De modo extrahendi annos et menses Arabum ex annis Christi. ... 10. De ostensione erroris nostri in sumptione terminorum et lo- corum festorum mobilium, et de modo sumendi terminos et loca festorum mobilium secundum doctrinam kalendarii nostri. 11. De ratione compositionis tabularum ad invenienda festa mobilia."

This computus is firmly based on the best astronomical works, both Greek and Arabic, translated during the preceding half century. It refers to Aristotle several times without mentioning a title; probably the Metaphysica vetus is meant. It makes considerable use of Ptolemy's Almagest, with one specific citation, Alma- gest 4.2. The Arabs are also much in evidence, with citations of Thebit, "Abra- chis" (possibly a corruption of cAli ibn Abi al-Rijal), Albategni (al-Battani), Ar- zachel (al-Zarqali), the Toledan Tables, and most interestingly, Alpetragius (al-Bitrfiji). In Chapter 1 Grosseteste says that Alpetragius has recently found a way to explain "how it is possible to save the processions and stations and retro- gradations of the planets, and the reflexions and inflexions and other appear- ances in the manner of Aristotle, and without the eccentric and epicycle."12 Al- petragius's De motu celorum, written in about 1185, had been translated into Latin by Michael Scot in 1217. Thus we need only allow enough time for Grosse- teste to have read this work (or heard about it, since he does not reproduce any of the technical details), to assign a terminus post quem for the Compotus correctorius.13 Circa 1220 is about as close as we can come. Grosseteste treated his new authorities with the same critical acumen as he did the traditional ones: they were not to be accepted without reservation simply because they were the latest thing. But he recognized their general superiority to the traditional materials and used them to good effect in correcting the errors of the older computi.

This leaves only the Kalendarium to be considered, and it may be disposed of briefly. Thomson assigned the work to Grosseteste on the basis of several late thirteenth-century manuscript ascriptions and because, he says, Grosseteste explicitly referred to his own Kalendarium in the Compotus correctorius and the Compotus minor.14 But there are many more unascribed than ascribed manu- scripts of the Kalendarium, and the ascriptions we do have are too late to be trustworthy. Moreover, it is simply not true that Grosseteste referred to his Ka- lendarium in his computi. The phrase "our calendar" often appears in these works, but always in the sense of "the ecclesiastical calendar in common use." Finally, Moreton has pointed out that this Kalendarium is nearly identical with that of Roger of Hereford.

This study, I hope, has clarified some problems concerning Robert Grosse- teste's computistical works. The most important question is his authorship of the Compotus I and its date. I think we may be reasonably sure that Grosseteste was

Opera ... Rogeri Baconis, ed. Steele (cit. n. 1), pp. 212-213. 12 Ibid., pp. 235 (Almagest citation), 217 (quotation). 13 For the Latin version see al-Bitrfiji, De motibus celorum, ed. Francis J. Carmody (Berkeley/Los

Angeles: Univ. California Press, 1952). For the Hebrew and Arabic versions and English translation see al-Bitrtiji, On the Principles of Astronomy, ed. Bernard R. Goldstein, 2 vols. (New Haven, Conn.: Yale Univ. Press, 1971). See also Southern, Robert Grosseteste (cit. n. 2), pp. 130-131.

14 Thomson, Writings of Grosseteste (cit. n. 1), p. 106.



the author. The similarities between this computus and Sacrobosco's De anni ratione can more easily be explained by assuming that Sacrobosco used the Compotus I than the other way around; it is also possible that both men simply appropriated common computistic lore. There is nothing innovative in the Com- potus I except the author's more than usual concern about the errors in the calendar. Even his computation of the time lag as one day in 120 years is not original. The treatment of errors in the calendar was part of the computistic tradition. It is not the fact that such concerns arise, but the manner in which they are expressed, that points to Grosseteste as the author of the Compotus I. The date of this treatise, on the basis of the date given in the calculations on folio 69v, should, it seems to me, be placed shortly after 1200.

The Compotus minor is an abridgment, not of De anni ratione, but of the Compotus I. It omits the redundant, illustrative, and confusing material and ap- peals to the contents of another computus to supply rules for various complicated calculations, thus saving the scnrbe the trouble of copying them. In no way does it augment or correct either the Compotus I or the Compotus correctorius.

The Compotus correctorius fulfills the promise of the Compotus I that the author will return to the difficult problems of the traditional computus at a later date. The Savile manuscript and the use in the Compotus correctorius of Alpe- tragius's De motu celorum indicate that Grosseteste had already begun the study of Arabic astronomy by 1215-1216 and probably composed the Compotus correctorius around 1220.

This study should provide a firmer basis for the study of Grosseteste's other astronomical works: De impressionibus aeris, De motu supercaelestium, and De sphaera.


Article Contentsp. 74p. 75p. 76p. 77p. 78p. 79

Issue Table of ContentsIsis, Vol. 80, No. 1 (Mar., 1989), pp. 1-200Front Matter [pp. 1-5]Editorial: Farewells and Introductions [pp. 6-10]A Noble Spectacle: Phosphorus and the Public Cultures of Science in the Early Royal Society [pp. 11-39]European Malaria Policy in the 1920s and 1930s: The Epidemiology of Minutiae [pp. 40-59]Critiques & ContentionsAlfred Marshall, W. Stanley Jevons, and the Mathematization of Economics [pp. 60-73]

Notes & CorrespondenceThe Computistical Works Ascribed to Robert Grosseteste [pp. 74-79]

News of the ProfessionFifth International Conference on the History of Science in China [pp. 80-81]International Summer Institute in the German Democratic Republic [pp. 81-82]Eloge: Eric Gray Forbes, (1933-1984) [pp. 82-83]

Special Section on History of MedicineReview: Desperate Disease [pp. 84-86]General WorksReview: untitled [pp. 87-88]Review: untitled [pp. 88-89]Review: untitled [pp. 89-90]Review: untitled [pp. 90-91]Review: untitled [pp. 91-92]

InstitutionsReview: untitled [pp. 92-93]Review: untitled [pp. 93-94]Review: untitled [pp. 94-95]Review: untitled [p. 95]

Humanistic Relations of MedicineReview: untitled [pp. 95-96]Review: untitled [pp. 96-97]Review: untitled [pp. 97-99]

Seventeenth & Eighteenth CenturiesReview: untitled [pp. 99-101]Review: untitled [pp. 101-102]

Nineteenth CenturyReview: untitled [pp. 102-103]Review: untitled [pp. 103-104]Review: untitled [pp. 104-105]Review: untitled [pp. 105-106]Review: untitled [pp. 106-107]Review: untitled [pp. 107-108]Review: untitled [pp. 108-109]

Twentieth CenturyReview: untitled [pp. 109-110]Review: untitled [pp. 111-112]Review: untitled [pp. 112-113]Review: untitled [pp. 113-114]Review: untitled [pp. 114-115]

Essay ReviewsReview: Probability and Statistics in Historical Perspective [pp. 116-124]Review: Getting Respect [pp. 124-128]Review: Just the Facts [pp. 129-135]

Book ReviewsHistoriographyReview: untitled [p. 136]Review: untitled [pp. 136-137]

General WorksReview: untitled [pp. 137-138]Review: untitled [pp. 138-139]Review: untitled [pp. 139-141]

Reference ToolsReview: untitled [pp. 141-142]Review: untitled [pp. 142-143]Review: untitled [p. 143]

Philosophy of ScienceReview: untitled [pp. 143-144]Review: untitled [pp. 144-145]Review: untitled [pp. 146-147]

Scientific EducationReview: untitled [pp. 147-148]

Social Relations of ScienceReview: untitled [pp. 148-149]Review: untitled [pp. 149-150]Review: untitled [pp. 150-151]

Humanistic Relations of ScienceReview: untitled [pp. 151-152]Review: untitled [pp. 153-154]

MathematicsReview: untitled [pp. 154-155]Review: untitled [pp. 155-156]Review: untitled [pp. 156-157]

Physical SciencesReview: untitled [pp. 157-158]Review: untitled [pp. 158-159]Review: untitled [p. 159]Review: untitled [pp. 159-161]

Biological SciencesReview: untitled [pp. 161-162]Review: untitled [pp. 162-163]Review: untitled [pp. 163-164]Review: untitled [pp. 164-165]Review: untitled [pp. 165-167]

Social SciencesReview: untitled [pp. 167-169]

TechnologyReview: untitled [pp. 169-170]Review: untitled [pp. 170-171]Review: untitled [pp. 171-172]Review: untitled [pp. 172-173]Review: untitled [pp. 173-174]Review: untitled [pp. 174-175]

Classical AntiquityReview: untitled [pp. 175-176]Review: untitled [pp. 176-177]Review: untitled [pp. 177-178]Review: untitled [pp. 178-179]

Middle Ages & RenaissanceReview: untitled [pp. 179-181]Review: untitled [pp. 181-182]

Seventeenth & Eighteenth CenturiesReview: untitled [pp. 182-183]Review: untitled [pp. 183-184]Review: untitled [pp. 184-185]Review: untitled [pp. 185-186]

Nineteenth CenturyReview: untitled [p. 186]Review: untitled [pp. 186-187]Review: untitled [pp. 187-188]Review: untitled [pp. 188-189]

Twentieth CenturyReview: untitled [pp. 189-190]Review: untitled [pp. 190-191]Review: untitled [pp. 191-193]Review: untitled [p. 193]Review: untitled [pp. 193-194]

Back Matter [pp. 195-200]

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Isis Volume 80 issue 1 1989 [doi 10.2307%2F234345] Richard C. Dales -- The Computistical Works Ascribed to Robert Grosseteste.pdf