Theodore of Tarsus and the Study of Computus at the Canterbury School

Abstract

The Irish Computus Einsidlensis (CE) of c. 700 contains a reference to a certain Theodore. This article makes the case that this Theodore should be identified with Theodore of Tarsus, archbishop of Canterbury from 668/9 to his death, 690, on the basis of comparison not only with other contemporary Latin versions of the same argumentum, but also Byzantine computi. The passage under discussion represents the only known computistical tract that can with confidence be ascribed to the famous Canterbury school under Theodore and Hadrian. From the evidence provided, it appears that Theodore learnt this algorithm while studying in the Byzantine Empire and introduced it through his teaching to his Canterbury audience; his Irish students brought it to Ireland, from where it got popularised on the Continent through Willibrord.

INTRODUCTION: THEODORE OF TARSUS AND THE SCHOOL OF CANTERBURY ^*

The school of Canterbury has attracted considerable attention, not least because of Bede’s praise of its curriculum and key figures, Theodore and Hadrian. Unfortunately, sources on these two scholars and the school itself are sparse and mainly limited to Bede’s account in his Historia ecclesiastica and Historia abbatum, and a passage in Aldhelm’s Letter to Heahfrith. ¹ Bede’s information can be summarised as follows: Theodore, a native of Tarsus in Cilicia, was chosen by Pope Vitalian in 667 as the new archbishop of Canterbury after the previous candidate Wighard had died in Rome before he could be consecrated. Bede relates that Theodore’s appointment happened upon suggestion by Hadrian, a native of Northern Africa, who had himself declined the position and who was then sent along to accompany Theodore, to ensure that Theodore would not spread Eastern teachings contrary to Roman doctrine. While Theodore was consecrated in 668 and arrived in England a year later, Hadrian in turn was held up in the Frankish kingdoms for another year before he could assume the abbacy of St Peter and Paul at Canterbury, allowing his predecessor Benedict Biscop to leave for the north of England.

Bischoff and Lapidge have further argued – based mainly on their analysis of the so-called Biblical Commentaries from Canterbury – that Theodore would have spent some time in Antioch and/or Edessa, coming into contact with Antioch’s exegetical traditions and possibly learning some Syriac, before fleeing the Arab conquests to Constantinople. The evidence as carefully assembled by Bischoff and Lapidge further suggests that Theodore found his way into a Greek monastery in Italy before 649, at which point he seems to have been involved in the preparation of the Lateran Council of that year. Similarly, Hadrian is thought to have fled the Arab invasion of the southern Mediterranean, entering a Greek monastery in Campania prior to the developments described above. ²

Thus, both Theodore and Hadrian have often been considered as mediators of Greek knowledge and teaching to Anglo-Saxon learning, not least because of Bede’s appraisal of their school at Canterbury: ³

Et quia litteris sacris simul et saecularibus, ut diximus, abundanter ambo erant instructi, congregata discipulorum caterua, scientiae salutaris cotidie flumina inrigandis eorum cordibus emanabant; ita ut etiam metricae artis, astronomiae, et arithmeticae ecclesiasticae disciplinam inter sacrorum apicum uolumina suis auditoribus contraderent.

This passage is usually interpreted as the key evidence for the existence of a school at Canterbury, which some scholars believe Theodore had actually founded, although Bede does refer to an earlier foundation. ⁴ So instead of founding the school, it rather seems that the new archbishop together with the abbot of SS Peter and Paul brought Canterbury teaching to new heights. ⁵ According to Bede’s description, the curriculum included not only exegesis, Latin, and possibly Greek, ⁶ but also metricae artis, astronomiae, et arithmeticae ecclesiasticae disciplinam, that is grammar (or poetry?), astronomy, and computistics. To this list can be added the discipline of liturgical music as reported by Bede as well, ⁷ and perhaps canon law as implied by Aldhelm. ⁸

Despite Bede’s praise of Theodore and Hadrian’s high standard of teaching, there exists no text or manuscript that could be attributed beyond doubt directly to either of the two. It rather seems that it is through their students that traces of their teaching have survived, ⁹ possibly because it has principally been conducted orally. ¹⁰ Thus, various attempts have been made by modern scholars to link material to the Canterbury school through textual and source analyses, reflecting almost the entire range of disciplines listed by Bede and Aldhelm, and beyond. ¹¹ Among the attributed texts, the so-called Biblical Commentaries and the Laterculus Malalianus are of special interest. ¹² While the Biblical Commentaries are considered notes taken by Canterbury students, ¹³ the Laterculus Malalianus, on the other hand, has been attributed to Theodore himself by its editor, Jane Stevenson. ¹⁴ Though this identification may be stretching the available evidence, ¹⁵ the text displays a negative attitude towards Irish scholars in two passages that Stevenson links to Aldhelm’s description of Irish students debating with Theodore as proof of the latter’s authorship. ¹⁶

But hardly anything that has been linked to Theodore could be classified as astronomy or ecclesiastical arithmetic (computus), two of the core disciplines ascribed to the Canterbury school by Bede. ¹⁷ It has been considered likely that Theodore introduced into Britain the paschal tract by Victor of Capua of 550 – now lost, but cited at length by Bede in his De temporum ratione c. 51 and his Epistola ad Wicthedum c. 8 ¹⁸ – but then this was more to stock the Canterbury library rather than a reflection of Theodore’s original teaching. More importantly, M. C. Welborn implies that Bede’s account of finger calculation in De temporum ratione chapters 1 and 55 may derive from Theodore’s teaching. ¹⁹ This idea is certainly strengthened by the fact that chapter 1 of Bede’s De temporum ratione and related versions enjoyed a very early separate transmission, which suggests pre-Bedan origin. ²⁰ But in no manuscript are these tracts attributed to Theodore or anybody else associated to the Canterbury school.

There is, however, an ascription to Aldhelm of a conversion table to synodic lunar ages of an A-P alphabet in the margin of calendars. Jones saw no reason to doubt the attribution, ²¹ and Borst, in his monumental study of early medieval calendars, followed his lead. ²² In his Letter to Leuthere, Aldhelm highlights how he had recently fundamentally increased his computational competence, which is usually attributed to his study at Canterbury outlined in his Letter to Hadrian. ²³ Read against this background, Lapidge is inclined to classify the synodic lunar table in question (which we may want to label the AEINB table from its first line) as a product of Aldhelm’s Canterbury class-notes. ²⁴ If this is the case, either the teaching was poor, or Aldhelm was not a very observant student, or the table suffered from careless copying. Where the table is attributed to Aldhelm, it is introduced as a device for charting the course of the moon through the zodiac (i.e. containing sidereal lunar letters), though its purpose was rather to establish the synodic lunar age of a given Julian calendar date. The system only worked in combination with a corresponding A-P column in a calendar, which according to Borst survives in only one pre-900 codex. The manuscript, Karlsruhe, Badische Landesbibliothek, Aug. perg. 167, also contains the conversion table attributed to Aldhelm (2r), and was written by an Irish hand on the Continent in the mid-ninth century. Ó Cróinín has drawn attention to the fact that another synodic lunar table is ascribed to an ‘Aldhelm, brother of Iohannes Scottus’ (Frater Iohannis Scotti Aldelmus fecit istam paginam) in Paris, Bibliothèque nationale de France, Lat. 12949, 42r. ²⁵ Given that the AEINB table enjoyed some popularity in Irish continental circles in the mid-ninth century and that there is no earlier attestation of the table or its corresponding column in calendars before that time, a ninth-century Aldelmus connected to Irish circles as suggested by the rubric in Lat. 12949 is much more likely than the seventh-century bishop of Sherborne.

Keeping in mind Bede’s special interest in the Easter controversy and computus, and the vibrancy of this monastic discipline in the Insular word in the late seventh and early eighth centuries, this is a rather meagre result. That not a single computistical idea can with any confidence be attributed to Theodore is even more surprising when considering what a crucial role computus played in Theodore’s initial appointment as archbishop of Canterbury.

THE IMPORTANCE OF COMPUTUS FOR THEODORE’S APPOINTMENT

Theodore’s appointment as archbishop of Canterbury was intrinsically linked to the synod of Whitby of 664. ²⁶ In his Historia ecclesiastica, Bede narrates that differences in liturgical practices within the Northumbrian royal family had grown to a substantial conflict by the early 660s. ²⁷ Some twenty years earlier, the Bernician King Oswiu had married the Deiran princess Eanfled in an attempt to unite the northern and southern parts of Northumbria. Northern Bernicia had received Christianity in the 630s from the regiones Scottorum, particularly the monastery of Iona, while southern Deira was Christianised from Kent and Canterbury. In terms of liturgical practices, Bernicia therefore followed ‘Irish’ customs, while Deira was ‘Roman’ in outlook, or so Bede wants to make us believe. In 664 a synod, or rather council, was held at the Deiran royal monastery of Whitby, at which Oswiu renounced his ‘Irish’ heritage and accepted his wife’s ‘Roman’ practices as binding in his kingdom.

Bede is deliberately selective in the information he presents to his readers. Differences in liturgical practice were only the trigger of the conflict, not its source, which was a succession struggle between Oswiu and his son Alhfrith, omitted by Bede. ²⁸ Also, Bede is vague as to what exactly ‘Roman’ liturgical practice meant. The main issue was the date of Easter, which the Irish and Britons calculated differently from the rest of Christianity. ²⁹ But the divide was not as clear cut as ‘Irish’ versus ‘Roman’ as suggested by Bede, who wanted to place the Northumbrians at the heart of the salvation history of a unified Western Church. In order to create this illusion, Bede remained silent in his Historia ecclesiastica about the fact that Rome had only changed in the 640s or 650s from a method of calculation introduced in 457 by Victorius of Aquitaine to Alexandrian practice in guise of Dionysius Exiguus’ Latin translation. ³⁰ This meant that at the time of Whitby, Rome followed Dionysius, while the Frankish kingdoms still subscribed to Victorius’ method, as did Eanfled, in accordance with the practice of the early Deiran church. Oswiu’s challenger Alhfrith and his spokesman Wilfrid, who had only recently returned from Rome, therefore tried to play the Dionysian card against both the ‘Irish’ Oswiu and his wife steeped in Victorian tradition. ³¹

With the censored information provided by Bede and the limited details presented by Stephen of Ripon, it is not quite clear what exactly Oswiu and his retinue considered ‘Roman’. ³² Certainly, the Pope was worried that Oswiu’s recent conversion may have been misdirected. In the same year as Whitby, 664, the archbishop of Canterbury died. Oswiu, as the most powerful ruler in the Anglo-Saxon kingdoms, had an interest in influencing the next appointment to this prestigious position, and his recent conversion gave him the moral authority needed. Together with the Kentish King Ecgberht, he sent a certain Wighard to Rome, either as chief negotiator or as a candidate. ³³ Wighard died after arrival, but he or his party (or, indeed, Benedict Biscop) ³⁴ briefed Pope Vitalian on recent developments in Northumbria. Vitalian appears to have been extremely troubled by what he heard, and immediately took matters into his own hands. If Wighard was sent to be consecrated archbishop, the Pope decided that the choice of candidate should rest with him rather than with Anglo-Saxon kings and clergy.

The reasons he outlined in a letter to King Oswiu, which documents the urgency felt by the Pope about developments in the Anglo-Saxon kingdoms: the Pope could have sent any correspondence with the appointed successor to the Canterbury see, but no time was to be wasted, the letter had to be dispatched immediately. After congratulating Oswiu on his recent conversion to ‘the true and apostolic faith’ (veram et apostolicam fidem), the Pope hastens to specify what exactly this means in a passage that Bede deliberately omits because of its explicit reference to Victorius: ³⁵

Nunquam enim celebrare sanctam pascae nisi secundum apostolicam et chatholicam fidem ut in toto orbe caelebratur a Christiane blebe, id est secundum apostolicam regulam CCCXVIII sanctorum patrum ac compototum Sancti Cirilli et Dionisi. Nam in toto terrarum orbe sancti Christi una columba, hoc est ecclesia inmaculata, sanctam pascae resurrectionis diem celebrat. Nam Victoris sedis apostolica non adprobavit regulam pascae. Ideo nec sequitur dispositionem eius pro pascae.

The following two sentences that Bede does transmit become intelligible in context, but only through this missing passage: ³⁶

Hominem denique docibilem et in omnibus ornatum antistitem, secundum vestrorum scriptorum tenorem, minime valuimus nuc repperire pro longinquitate itineris. Profecto enim dum huiusmodi apta reppertaque persona fuerit, eum instructum ad vestram dirigemus patriam, ut ipse et viva voce, er per divina oracula omnem inimici zizaniam ex omni vestra insula cum divino nutu eradicet.

Thus, the Pope struggled with finding a person suitable to ‘eradicate the weeds of the enemy’, i.e. Victorius of Aquitaine, mentioned in the immediately preceding passage omitted by Bede. Competence in computus, a full understanding of the Alexandrian/Dionysiac system that was to replace Victorius in the Anglo-Saxon kingdoms, was an – if not the – essential criterion in Vitalian’s job profile for the Canterbury see.

This specialism Vitalian thought could best be found outside of Rome, which had converted to Dionysius only some ten to thirty years earlier. He conducted his search in the Byzantine contact zone south of Rome. His first choice was Hadrian, whom Bede describes as ‘vir natione Afir, sacris litteris diligenter inbutus, monasterialibus simul et ecclesiasticis disciplinis institutus, Grecae pariter et Latinae linguae peritissimus’. ³⁷ When read in connection with Vitalian’s letter, the ‘monastic and ecclesiastical disciplines’ certainly included, first and foremost, computus. The language specification is also very interesting in this context. Fluency in Greek was certainly not needed for communication in the target country, the Anglo-Saxon kingdoms. The insistence on Greek, as a book language, is rather an acknowledgement that a full understanding of Alexandrian computus could not be achieved through Dionysius’ Latin translation alone. More information could be found in Greek texts, and first-hand oral teaching.

Hadrian declined, arguing that he lacked seniority and erudition. This may be dismissed as a common expression of humility, but it could also indicate genuine concern by Hadrian about his own ability, as this job required a highly specialist skill-set. Hadrian helped in finding a suitable candidate, and eventually suggested Theodore, ‘natus Tarso Ciliciae, vir et saeculari et divina litteratura, et Grece instructus et Latinus’. ³⁸ Here, Bede more specifically refers to Greek literature rather than more broadly to learning, confirming the point made above. Unknown to Bede, there may have been more arguments for choosing Theodore as a specialist in Alexandrian computus, as his personal network may well have included key Eastern scientists. The reign of Emperor Heraclius (610–641) saw a peak of computistical activity: ³⁹ in 623, the Emperor himself composed a short computistical manual that was added to Stephanos of Alexandria’s Ptolemaei tabulas manuales of 617–619, ⁴⁰ and under the patronage of the patriarch of Constantinople, Sergius, the anonymous Chronicon paschale of 630 incorporated computistical material; ⁴¹ more importantly, the two most substantial Eastern works on computus were written towards the end of Heraclius’ life within three years of each other, by Georgios Presbyter – the spokesman for the Byzantine era – in 638/9 and Maximus Confessor – once secretary to Heraclius – in 640/1. ⁴² Theodore will have had access to this circle of intellectuals in Constantinople in the 630s, and he must have been in close contact with Maximus Confessor in Rome in the lead-up to the Lateran Council of 649. ⁴³

The first few years of Theodore’s incumbency agree with these assumptions, and demonstrate that Theodore certainly took the brief he had received from Pope Vitalian very seriously. After arrival in Britain in 669, he immediately toured the Anglo-Saxon kingdoms, with one main purpose, to teach ‘rectum vivendi ordinem, ritum celebrandi paschae canonicum’. ⁴⁴ In the same passage, Bede specifies four disciplines taught by both Theodore and Hadrian to students attracted by their erudition: exegesis, grammar, astronomy, and computus (‘ita ut etiam metricae artis, astronomiae, et arithimeticae ecclesiasticae disciplinam inter sanctorum apicum volumina suis auditoribus contraderent’). This laid the intellectual ground on which true Roman Easter customs could grow and spread, but more than anything this liturgical reform needed institutional backing throughout the Anglo-Saxon kingdoms. Theodore made sure that bishops already in place were in line with Rome, and filled vacant posts with appropriate candidates. This work came to a close at the Council of Hertford in September 672. It laid out ten decrees, which may be considered the foundational charter of an English Church. Tellingly, the very first decree stipulated ‘that we all observe the Holy Day of Easter universally on Sunday after the fourteenth moon of the first month’ (‘Primum capitulum: “Ut sanctum diem paschae in commune omnes seruemus dominica post XIIII^am lunam mensis primi.”’) ⁴⁵ Dionysius was finally accepted by all church officials of the Anglo-Saxon kingdoms. Three years into his office, Theodore had accomplished the principal task given to him by Pope Vitalian: the ‘weeds of the enemy’ Victorius had been eradicated. ⁴⁶

LINKS BETWEEN IRELAND, THE ANGLO-SAXON KINGDOMS AND THE SCHOOL OF CANTERBURY

Theodore’s appointment to the Canterbury see, therefore, came with a clear doctrinal mandate – the universal acceptance of Alexandrian Easter practice – that had to be underscored by proper education in liturgical practices, especially ‘ecclesiastical arithmetics’ – computus. An existing Canterbury school was upgraded, one might say, into an academy. ⁴⁷ This may have changed, to a degree, the educational dynamics of Britain and Ireland. Certainly in northern Northumbria, with its strong Irish links, the first generation of monastic students went to the regiones Scottorum for their studies. ⁴⁸ This was probably out of necessity, since monastic libraries and educational structures had to be set up first in Northumbria, while they were fully functioning in neighbouring Ireland with its already existing, two-century old Christian tradition. With Oswiu’s decision at Whitby, those not renouncing their Irish heritage went to the regiones Scottorum for religious exile, both Irish and Angli clerics.

These movements created substantial networks of scholars in the Insular world, of which only glimpses are transmitted to us through the most well-known figures and institutions mentioned by Bede, like Ecgberht and Rath Melsigi or Colmán and Mayo. Rath Melsigi deserves special mention here, as it became a key player in the Easter controversy: The debates at and following Whitby doubtlessly reached the Northumbrian intellectuals in this monastery, which became one of the earliest Irish communities to embrace the Alexandrian/Dionysiac reckoning. Rath Melsigi may have been instrumental in Armagh’s conversion to this method of calculating Easter, ⁴⁹ and when the last stronghold of traditional practice, Iona, contemplated change, it invited Ecgberht himself as a specialist advisor, completing the switch to Dionysius in 716. ⁵⁰ Further afield, Rath Melsigi’s doctrinal views travelled with Willibrord to Francia and especially his monastic foundation of Echternach in Austrasia, which became a powerhouse in the introduction of Dionysius on the Continent. ⁵¹

Arguably the most prominent product of these networks was the Northumbrian King Aldfrith, who received a monastic education in the regiones Scottorum and when king invested in monastic education in his realm. ⁵² A continuous influx of Irish texts into their libraries in the first two or three generations after the adoption of Christianity meant that Northumbrian students could study Irish learning at home and became less dependent on travel. Bede is a good example of this generation, managing to have a prosperous scholarly career without leaving his monastery of Wearmouth and Jarrow.

This means that much of the nascent Anglian but also Saxon churches were stocked with Irish books. Outside of Northumbria, Irish presence – and with this learning and books – was substantial, particularly in East Anglia and Wessex as represented by the known figures of the brothers Fursa, Foillán, and Ultán, ⁵³ but also the Frank Agilbert, who studied in Ireland before becoming bishop of Wessex. ⁵⁴ In consequence, educational travel from Ireland to the Anglo-Saxon kingdoms did not make that much sense, as not much new could be learned there by a mobile Irish cleric with a thirst for knowledge. The main exception was, of course, Canterbury. How welcoming to students from the West Canterbury may have been in the early decades since its foundation in 597 must remain speculative. Certainly, the earliest archbishops of Canterbury pursued a rather antagonistic policy against its western neighbours, with an uncompromising stance against differences in liturgical practices. The hostility between Canterbury and Briton clergy soon became institutional. ⁵⁵ At least the southern Irish turn towards a more Roman outlook in the 630s could have provided for a more amiable relationship with Canterbury, but Cummian’s Letter suggests that, for guidance and knowledge acquisition, the Irish went to Rome directly rather than relying on a second-generation intermediary in the south-eastern corner of Britain. ⁵⁶

The arrival of Theodore changed these dynamics. The Canterbury see had been held by the first generation of missionaries sent to England in 596/601 until 655, when this generation was followed by the incumbency of one native archbishop, Deusdedit. This means that, in terms of personnel, there was no direct appointment from Rome from the foundation of the Canterbury church to the arrival of Theodore. This fact alone will have made it attractive to study under Theodore, who brought first-hand knowledge from the centre of Western Christianity. The circumstances of his appointment added to this: the recent change of liturgical practices by the Roman curia (from Victorius to Dionysius) made it desirable to learn about the details, and being able to do this closer to home than Rome will have been most welcome, especially if the teacher sent was an evident expert. Theodore’s Greek background, which opened up an entirely new universe, both theologically and linguistically, will only have been the icing on the cake of this fresh learning opportunity in neighbouring Britain.

That the Canterbury school of Theodore and Hadrian attracted Irish students is evidenced by Aldhelm’s Letter to a certain Heahfrith. ⁵⁷ In this curious document, Aldhelm welcomes Heahfrith’s return to Britain to take up his ‘vocation as teacher’ (praeceptoris vocamine) after a six-year study stay in north-western Ireland (Mayo?). He hopes that Theodore’s and Hadrian’s school will remove the decade-old necessity to study in Ireland because of a lack of suitable alternatives in Britain. In fact, Aldhelm drives the point that the Canterbury school has fully turned the tide. This he illustrates by one example, Theodore’s superiority in debating the ‘obscure and acute syllogisms of chronography’ (chronographiae opacis acutisque syllogismis) with his Irish students, which may well be a reference to the Easter question. ⁵⁸

Aldhelm’s language could suggest an aversion on the part of Theodore to this group of Irish critics, which would be further accentuated if the Laterculus Malalianus is, in fact, from Theodore’s pen. ⁵⁹ If so, it seems not to have impacted the Irish desire to study at Canterbury, as travel dictionaries may provide additional evidence: the codex St Gall, Stiftsbibliothek, 913 is directly connected to the Canterbury School through its Leviticus glosses, which refer by name to Hadrian (p. 143). ⁶⁰ These are followed by the famous Vocabularius Sancti Galli, a glossary in three parts: ⁶¹ thematic, alphabetic, and glosses to Aldhelm’s De laudibus virginum. The alphabetic part is rooted in the Anglo-Saxon glossing tradition, and the glosses to Aldhelm point in the same direction (and provide another link to Canterbury where Aldhelm studied). ⁶² The thematic Latin–German glossary, which makes up more than three quarters of the Vocabularius, is more complex. It is extremely practically oriented, including architecture, social rank, weather, animals, etc. Wolfgang Heil has proven that it was the work of an English author, who turned an existing Latin–Old English glossary into a Latin-German one by translating the Old English terms into a mix of Franconian and Upper German dialect. ⁶³ This obviously raises the question of who composed the Latin–Old English original that formed the basis for the Vocabularius. ⁶⁴ Since much of the manuscript context points to the Canterbury school, it may not be too far-fetched to imagine that the original was used by one of its students (if not by one of its teachers, like Hadrian?). The one major group of foreign students who would be in need of a Latin–Old English glossary known to have attended the Canterbury School is the Irish contingent. The potential Willibrord/Echternach connection of the glossary may further corroborate this theory (given that Willibrord came to the continent from Rath Melsigi in Ireland), ⁶⁵ as does the fact that the same codex contains some computistica of evidently Irish influence. ⁶⁶

BISSEXTUS ALGORITHM

It would therefore not be surprising to encounter Canterbury learning of the late 670s and 680s in Irish educational, especially computistical texts of the late seventh and early eighth centuries. Three Irish computistical textbooks of this period survive: the Computus Einsidlensis (CE), ⁶⁷ the Munich Computus (MC), ⁶⁸ and De ratione conputandi (DRC). ⁶⁹ Of these, only the Munich Computus is securely datable, to 718/9. ⁷⁰ Comparison to this text combined with its early Frankish reception suggests a date between 719 and 727 for De ratione conputandi. ⁷¹ The same textual analysis also indicates that the Computus Einsidlensis predates MC, but postdates one of MC’s main sources, the Victorian Computus of 689. ⁷² A prologue of 699 to an updated Victorian Easter table further suggests that the southern Irish still followed Victorius as late as the end of the seventh century, which would narrow the date of the Dionysiac CE to 699 × 718. ⁷³ Especially because of their familiarity with Victorius, who was followed in the seventh century in southern but not northern Ireland, all three textbooks have been located in Ireland’s south. ⁷⁴

All three Irish texts, and for that matter also Bede’s De temporibus and De temporum ratione, are structured in a very similar way, with the first major section focussing on solar theory and the mechanics of the Julian calendar. ⁷⁵ The bissextus, the additional leap-day every four years, was one of the key mechanisms of the Julian calendar, and there was considerable discussion about its origin and appropriate placement within the calendar year (24 February according to Macrobius, 2 March as suggested by Isidore, or 21 March linked to Creation), especially among societies that had just been introduced to this calendar through Christianity. The reason for the additional day obviously was that the period from one vernal equinox to the next was calculated as 365 ¼ days, which made the addition of an extra day every four years necessary. But this phenomenon attracted numerous other explanations and allegories. ⁷⁶

The only reference to a certain Theodore in early medieval computistica can be found in a discussion of the bissextus in the oldest of these Irish textbooks, CE. ⁷⁷ Here, the chapter proper on the intercalated calendar day is followed by an additional subchapter with a peculiar argumentum: ⁷⁸

De bissexto quem secundum Theodorum formamus hoc modo: ut in numero horarum diei per totum annum septenum ponamus numerum et quodcumque superfuerit septenum numerum, hoc fiat materia bissexti.

Cuius probatio hęc est: Annus diebus CCCLXV conputatur. C uero dies horas habent I̅CC. Ita et CCC dies habent horas I̅I̅I̅DC. LX uero dies habent horas DCCXX. V autem dies horas LX habent, que simul faciunt horas I̅I̅I̅I̅CCCLXXX. Ita et nox eundem numerum horarum per totum annum habet. Hinc conpotus est horarum totius anni V̅I̅I̅I̅DCCLX. Hoc septeno numero diuide, VII milia et DCC, remanent I̅ et LX. Remitte itidem DCC, remanent CCCLX. Partire iterum hunc numerum in quinquaginta, hoc est septies quinquaginta, remanent X. Deduc VII ex hoc numero, remanent III horę, quę septenum numerum supersunt et quę per quadriennium diem bissexti licet abusiuum faciunt et non diem proprium.

The argument here is that a non-bissextile year of 365 days (i.e. without the excess of 6 hours actually necessitating the intercalation every four years) has 8760 hours; if these are divided by 7 (clearly a reference to the seven-day week), 3 hours remain, which make up a quarter of the 12 hours of daytime, and therefore accumulate to a 12-hour day in four years. ⁷⁹

The same curious algorithm can also be found in a parallel passage in MC, but with distinctly different wording. ⁸⁰ The concept is so counterintuitive, but also complex, that it is difficult to perceive that two authors would have developed the same idea independently of each other or of a common source. Bearing this in mind, the attribution is noteworthy: CE ascribes this algorithm to a certain Theodore, MC to ‘the Greeks’. The rarity of the name Theodore in the context of seventh- and early eighth-century Insular computistics has already been pointed out and an identification with Theodore of Tarsus proposed. ⁸¹ This is supported by MC’s reference to the Greeks. Apparently, the author of MC considered this argumentum to be of Greek origin, either because he knew which Theodore was meant if he was working from CE, or he had learned the algorithm from a source he clearly thought to be of eastern origin. The latter option seems to be the more likely one, given the fact that the two passages in CE and MC have only the concept in common, but display no interdependency in wording (see Table 1 below). While in both CE and MC, the calculation of the hours of a year is comprised of the same intermediate steps, the division by seven is not carried out in detail in MC. This textual and structural difference may in fact be an indicator of an oral source, for otherwise there would be clear textual parallels between these two closely related texts. Either way, MC’s awareness of the Greek origin of the argumentum supports the identification of Theodore.

Table 1: The three oldest extant witnesses of the bissextus algorithm paralleled

CE of c.700 and MC of 718/9, however, are not the only texts transmitting this argumentum. Its earliest occurrence, to our present knowledge, is attested in the Computus Digbaeanus of 675, a computistical formulary of sixteen items initially published as Dionysius Exiguus’ argumenta of 525, ⁸² but subsequently proven to be a revised and elaborated version of Dionysius’ original corpus updated in 675. ⁸³ Our algorithm is part of the final item, and is therefore commonly known as pseudo-Dionysius Argumentum XVI (§2). Though slightly disconnected from the preceding 15 argumenta in the codex unicus of the Computus Digbaeanus (Oxford, Bodleian Library, Digby 63, 78v–79r), it appears that Argumentum XVI was added to the Dionysiac canon in 675. ⁸⁴ This date for the first occurrence of this algorithm in Latin computus certainly fits very well with the theory that it was introduced by Theodore of Tarsus. It is noteworthy that, again, the argumentum in the Computus Digbaeanus represents the same concept as in CE and MC, yet disclosing no textual relation. This is another indicator that this argumentum was originally transmitted in oral form.

Another copy of this argumentum – closely related to the Computus Digbaeanus – was included in the Computus Cottonianus of 689, which has been argued to have been composed in Rath Melsigi in Ireland for Willibrord’s Frisian mission, ⁸⁵ preserved in a codex from mid-eighth-century north-eastern France (London, British Library, Cotton Caligula A XV, 79r). The version of the argumentum in these two texts is almost identical with the one in the codex of 823 that transmits MC (Munich, Bayerische Staatsbibliothek, Clm 14456, 65v–66r), and also very close to the version in the computistical compilation of c. 874 containing CE (Einsiedeln, Stiftsbibliothek, 321 (647), p. 146). It seems, therefore, that by way of Willibrord’s mission this initially orally transmitted argumentum started a new life in a fixed written form once it had crossed the Channel, being disseminated widely across the Carolingian kingdoms, often alongside other Insular computistica. ⁸⁶

Thus, there are several observations to be summarised here: the argumentum appears not only in the related Irish textbooks CE of c. 700 and MC of 718/9, but also in the (probably Anglo-Saxon) Computus Digbaeanus of 675, from where it was probably copied into the Computus Cottonianus of 689 linked to Willibrord and Rath Melsigi. The distinct differences in wording suggest that the argumentum was taught orally and then noted down by different authors in their respective computi. It would not be inconceivable to assume an Irish origin of the argumentum that was then taught to Anglo-Saxon computists e.g. in Rath Melsigi. ⁸⁷ However, all of the texts just discussed have been composed within or close to Theodore’s incumbency as archbishop of Canterbury, and while his name is stated explicitly in CE, MC, which was evidently composed twenty-eight years after Theodore’s and eight years after Hadrian’s death, attributes the argumentum more generally to a Greek origin. This makes an Irish origin unlikely while at the same time fitting perfectly with Theodore’s eastern background. Moreover, the argumentum’s initial oral transmission – deduced from the high level of variation among the earliest Insular witnesses – aligns with Bede’s and Aldhelm’s description of Theodore and Hadrian’s way of teaching (as well as with the related problem of identifying texts directly with either of the two).

BYZANTINE PARALLELS

At this point, it may still be argued that either the attribution to Theodore in CE could be spurious – especially since the Computus Digbaeanus composed in Theodore’s lifetime does not contain any ascription – or that CE simply refers to a different Theodore. Theodore of Tarsus’s authorship, however, can be corroborated further by comparison with Byzantine computistics. ⁸⁸ The most important witness for our context is the potentially oldest one, the Florilegium Coislinianum. This is an alphabetic encyclopaedia, probably of the late-ninth/early-tenth centuries, surviving in tenth-century and later manuscripts. Under letter Π, a discussion of Πάσχα is included, which contains calendrical algorithms. One of them is the bissextus algorithm under discussion here, another refers to Byzantine annus mundi 6224 = AD 716. In true encyclopaedic fashion, the author draws from a variety of sources. It may be the case that one of these was a calendrical layer of 716, but only the ongoing new edition of the Florilegium may shed more light on this. ⁸⁹ If so, this would attest to the bissextus algorithm in Byzantine sources as early as 716, within range of Theodore’s lifetime. It reads: ⁹⁰

ρξθ. περὶ τοῦ γνῶναι πόθεν ἐστὶ τὸ βίσεκστον

Δέον σε τιθεῖν τὰς ἡμέρας τοῦ ἐνιαυσιαίου κύκλου, τουτέστι τῶν τξε ἡμερῶν καὶ νυκτῶν, καὶ πολυπλασιάζειν αὐτὰς ἑκάστου νυκτοημέρου τῶν κδ ὡρῶν· καὶ ἀνατάσσουν ͵ηψξ ὧραι· ταῦτα ἀναλύειν εἰς τὸ ζ, καὶ περιττεύουσιν ὧραι τρεῖς καθ’ ἕκαστον ἐνιαυτόν, καὶ εἰς τὸν δ^ον καιρὸν γίνονται ὧραι ιβ. ἐπιλαμβάνεται οὖν ὁ Φευρουάριος μὴν τὴν περισσείαν τῆς μιᾶς ἡμέρας, καὶ λέγεται βίσεκτον.

It is interesting that the calculation proper was omitted, which could indicate that at the time of writing, this algorithm was common knowledge and did not need elaboration or additional explanation.

We are on firmer ground with two ninth-century computi, the Anonymi of 830 and 892 that have just been made available to scholarship by Gastgeber and Acerbi. ⁹¹ They largely share the same material, ⁹² including the bissextus algorithm, which has different corruptions in each version. The slightly more complete Anonymus of 830 reads: ⁹³

ὁ ἐνιαυτὸς ἔχει ἡμέρας τξε καὶ δ^ον, ὥρας ͵δτπ· ταύτας δίπλωσον· καὶ γίνεται ͵ηψξ, καὶ ὕφελε αὐτὰ εἰς ἑπτάη· οἷον ἑπτάη ͵α, ͵ζ· ζ σ, ͵αυ· καὶ μένουσι τξ· ἑπτάη ν, <τν·> μένουσι ι· <ἑπτάη μίαν, ζ·> καὶ μένουσι κατ’ ἐνιαυτὸν ὧραι γ· καὶ ἐκ {lege εἰς} τοὺς δ χρόνους γίνονται ὧραι ιβ, καὶ οὕτως γίνεται τὸ βίσεξστον.

The level of corruption, including the mistaken inclusion of the quarter-day at the beginning that is shared between the two Anonymi, point to a transmission history that had gone through numerous hands by the ninth century. Except for the excerpts preserved in the Florilegium Coislinianum and a few scattered argumenta, no Byzantine computistica between the 640s and 830 survive. ⁹⁴ Had more survived, it would surely have included the bissextus algorithm, probably as early as the seventh century, judging by the evidence just outlined. Interestingly, the manuscript transmission of all three texts (Florilegium Coislinianum and the two Anonymi) point to southern Italy for their place of composition, mirroring Pope Vitalian’s search for expertise in eastern computus south of Rome.

THE TRANSMISSION OF THE THEODORE BISSEXTUS ALGORITHM

Whenever texts have been ascribed to the Canterbury school, their reception has tended to be quite limited (with exceptions, of course), usually explained by the exoticism of content. In this respect, the bissextus algorithm breaks fundamental new ground in studies on Theodore (though – with one exception – the medieval scribes themselves were not aware of its links to Theodorean teaching), not only because it proved extremely popular throughout the early Middle Ages, but also because these witnesses can be traced quite accurately due to their occurrence in datable computistical contexts. It is worth separating two transmission stages, a pre-Carolingian oral one and a codified written one in the Carolingian period.

Oral transmission stage in pre-730 texts

The witnesses to the oral stage can all be explained in a Theodorean context: A, the formularies of the 670s and 680s extending the original Dionysiac Argumenta, have been argued to be products of, possibly, Rath Melsigi in Ireland, which had strong connections to the Anglo-Saxon kingdoms. B and C, the Irish textbooks of the first two decades of the eighth century, could well have contained Theodorean learning brought to Ireland by Irish students of the Canterbury school, which is evidenced by the only surviving reference to Theodore in one of them. D and E, Victorian Computi from Neustria and Burgundy, are more curious because of their place of origin and their Victorian (as against Theodore’s Dionysiac) context; considering, however, that Theodore spent considerable time in Arles, Paris and other places in Neustria and Burgundy en route to Kent, his explanation of a calendrical phenomenon disconnected from Easter calculation could well have been absorbed by local intellectuals. To these texts should be added the tract De bissexto I attributed to Alcuin, which is a Carolingian reworking of 789 of presumably late-seventh- or early-eighth-century Irish material. ⁹⁵

1. A. Computus Digbaeanus of 675 (ed. Krusch, ‘Studien’, pp. 80–1) = Argumentum XVI

   1. 1. Oxford, Bodleian Library, Digby 63, 78v–79r (northern England, s. ix²) copied in: Computus Cottonianus of 689

   2. 2. London, British Library, Cotton Caligula A XV, 79r (north-eastern France, 743?)

2. B. Computus Einsidlensis of c. 700

   Einsiedeln, Stiftsbibliothek, 321 (647), p. 108 (St Gall?, 874?)

3. C. Munich Computus c. 41 (718/9; ed. Warntjes, Munich Computus, p. 138)

   Munich, Bayerische Staatsbibliothek, Clm 14456, 22v–23r (St Emmeram in Regensburg, 823)

4. D. Victorian Computus of 696 (ed. Cordoliani, ‘Les plus anciens manuscripts’, p. 112) ⁹⁶

   1. 1. Bern, Burgerbibliothek, 645, 50v (northern France?, 696?) copied in:

   2. 2. Cologne, Dombibliothek, 83-II, 36r (Cologne, 805)

   3. 3. Vatican, Biblioteca Apostolica Vaticana, Reg. lat. 1530, 46rb (southern France?, 1054?)

5. E. Dial. Burg. c. 14 of 727 (ed. Borst, Schriften, p. 366)

   Bern, Burgerbibliothek, 611, 95v (Corbie or Luxeuil?, 727 × 750)

6. F. Pseudo-Alcuin, De bissexto I (ed. PL 101, cols. 993–8, at 994–5)

   The manuscripts listed by Springsfeld, Alkuins Einfluß, pp. 66–80, are:

   Calibration to Septuagint annus mundi (AMII) 5989 = AD 789 (not 790):

   1. 1. Basel, Universitätsbibliothek, F III 15k, 52r–55v (Benediktbeuren?, s. ix^1/3)

   2. 2. Geneva, Bibliothèque de Genève, lat. 50, 148v–151r (Massay, 825)

   3. 3. Oxford, Bodleian Library, Bodley 309, 74r–76r (Vendôme, s. xi^ex.)

   4. 4. Vatican, Biblioteca Apostolica Vaticana, Ross. 247, 170r–173r, with reference to AMII 5889, evident scribal mistake for 5989 (because of the subsequent calculation) = AD 789 (St Chaffre, c. 1020)

   5. 5. Vatican, Biblioteca Apostolica Vaticana, Vat. lat. 642, 83r–85v (Lyon?, post-1100?)

   Calibrated to AMII 6023 = AD 823 (not 824):

   1. 6. Vatican, Biblioteca Apostolica Vaticana, Reg. lat. 226, 26v–31v (southern France?, s. x?)

   We have not systematically checked for further witnesses, but can at least add the following:

   Calibrated to AMII 5989 = AD 789:

   1. 7. Munich, Bayerische Staatsbibliothek, Clm 29790/3 (fragment, s. x) ⁹⁷

   2. 8. Paris, Bibliothèque nationale de France, Lat. 16361, pp. 279–86 (s. xii)

   Calibrated to AMII 6013 = AD 814 (slightly different algorithm to above):

   1. 9. Monza, Biblioteca capitolare, c-9/69, 47v–50r (northern Italy, 837)

   Calibrated to AMII 6033 (? the 6034 mentioned are clearly after addition of 1; then updated to 6075) = AD 834:

   1. 10. Vatican, Biblioteca Apostolica Vaticana, Reg. lat. 1723, 68r–70v (Netherlands?, s. xii^in.)

Codified written transmission post-750

This is not the place to adequately discuss the transmission of the bissextus algorithm in the Carolingian period (c. 750–900), but we want to provide some directions of travel of the idea to guide future researchers. In the end, the question is slightly premature. What is needed first is a catalogue of all computistical argumenta and tables (or ‘objects’, as they are now called) with their transmissions. ⁹⁸ More often than not, these computistical objects travelled in clusters, which are much more indicative than tracing isolated examples.

The following is likely not an exhaustive, but is, we believe, a representative list of witnesses to the Theodore algorithm before 900, with a few post-900 additions when they occurred to us (or have been brought to our attention by Jacopo Bisagni’s work on Breton manuscripts). It testifies to the influence of Theodore’s teaching in continental Europe, which would be extended considerably if computistical manuscripts post-900 were surveyed systematically.

It has been argued above that Willibrord brought the Theodore algorithm as pseudo-Dionysius Argumentum XVI §2 to the Continent as part of the Computus Cottonianus of 689, which was copied in north-eastern France in around 743 (London, British Library, Cotton Caligula A XV). Through Willibrord and his introduction of the Dionysiac Easter reckoning into the Frankish kingdoms, the region between Seine and Rhine became a hotbed for Latin computus. From here, Argumentum XVI radiated out into all parts of the Frankish Empire (A): through Arn of Salzburg it was brought to south-eastern Germany (3); there it also arrived through apparently Irish channels which were further responsible for it travelling to the Lake Constance region, or at least this is what the manuscript context of 8 and 9 suggests, the only codices to transmit the Munich Computus and the Computus Einsidlensis respectively. But it appears to have also crossed the Alps to Italy, from where it was brought back to the Reichenau (7). More importantly, it was reviewed at two of the key centres responsible for collecting and testing computistica during Charlemagne’s reign, the episcopal see of Cologne under Hildebold (4) and the palace school (5); interestingly (and understandably), this algorithm apparently was not considered worthy of inclusion in the fundamental encyclopaediae that were compiled close to imperial power (Lib. ann. of 793, Lib. comp. of 809/10, Lib. calc. of 818). ⁹⁹ From the Frankish heartland, Argumentum XVI moved to Brittany (Angers 476), and from there to southern France (10 and 11).

But the collection and systematisation of computistical thought was obviously not a royal and episcopal prerogative, it also happened in the bigger monastic centres; key for the transmission history of the Theodore algorithm is Saint-Denis under Abbot Fardulf (G): In 802, Saint-Denis produced its own collection of computistical material that survives in a copy of 804 (1). In or shortly after 810, a fresh version of this collection was sent to the Lake Constance region when Waldo, former abbot of St Gall and then Reichenau, had become abbot at Saint-Denis (2, 3). When, in 859, Saint-Denis produced its own copy of Lib. calc. of 809/10, it was updated by adding some items considered essential and missing in this encyclopaedia, including the Theodore algorithm (5). The algorithm was also copied in Saint-Denis’s vicinity (4, 6).

A re-arranged and re-worked version of what we may call the Computus Fardulfi was produced in 803 (H) and is best preserved in a Loire valley codex of the third quarter of the ninth century (3), with a reduced copy of the eleventh century (7). The early ninth-century occurrence of this algorithm in north-eastern France reflects an original Saint-Denis connection (1 and 2), as does the Italian link (4) that may be traced back to the Irish scholar Dúngal who moved from Saint-Denis to Pavia in the 810s or early 820s. The later spread of this algorithm south and east (and maybe west?) in the tenth and eleventh century is testimony to the influence of Loire valley intellectual thought (especially from Fleury) in that period. In Fleury, one variation of this algorithm from the Computus Fardulfi was composed in the mid-ninth century (I 1), which then travelled with other items of 1 further south (2) and east (3). A second variation, also from Fleury shortly after the middle of the ninth century but with Visigothic additions, can be found in J.

The early witness to the bissextus algorithm found in St Gall (K 1) also appears in slightly later manuscripts from north-eastern France and Wissembourg (2 and 3), and these occurrences are probably best understood as part of a general trend at the beginning of the Carolingian period, when much computistical knowledge travelled from the region between Seine and Rhine up the Rhine to the Lake Constance area; from this Carolingian heartland this algorithm spread to England (6) and Brittany (4), whence it moved south (5). This group (J) also points to three particularly outstanding witnesses for this algorithm (2, 4 and 5), each of which incorporating three versions of it in their truly encyclopaedic sections on the phenomenon of the bissextile day. These three codices are a great reminder that the transmission of individual computistical objects can only be achieved through a full-scale cluster analysis, which may well change the picture presented here.

1. A. Argumentum XVI

   1. 3. Munich, Bayerische Staatsbibliothek, Clm 14725, 8v (St Amand, 783 × 797)

   2. 4. Cologne, Dombibliothek 83-II, 35v (Cologne, 805; partly)

   3. 5. Vatican, Biblioteca Apostolica Vaticana, Pal. lat. 1447, 32r (798 × 813, Mainz; partly)

      1. 5a. Angers, Bibliothèque municipale, 476, 10r (Brittany, 926?)

   4. 6. Milan, Biblioteca Ambrosiana, H 150 inf., 18v (north-eastern France?, 810?) = Bobbio Computus c. 43 (ed. PL 129, col. 1294)

      1. 6a. Angers, Bibliothèque municipale, 476, 10v–11r (Brittany, 926?)

   5. 7. Karlsruhe, Badische Landesbibliothek, Aug. perg. 229, 30v–31v (St Stefano in Lucana or Italian scribe on the Reichenau, 821)

   6. 8. Munich, Bayerische Staatsbibliothek, Clm 14456, 65v–66r (St Emmeram in Regensburg, 823)

   7. 9. Einsiedeln, Stiftsbibliothek, 321 (647), p. 146 (St Gall?, 874?; partly)

      Later:

   8. 10. Madrid, Biblioteca Nacional de España, 9605, 68ra-b (Provence, 1026)

   9. 11. Vatican, Biblioteca Apostolica Vaticana, Barb. lat. 477, 106v (Avignon, s. xiⁱⁿ)

2. G. Computus Fardulfi A (derivative of A)

   1. 1. Vatican, Biblioteca Apostolica Vaticana, Reg. lat. 141, 157v (St Denis, 804)

   2. 2. St Gall, Stiftsbibliothek, Cod. Sang. 902, p. 162 (St Gall, 815)

   3. 3. St Gall, Stiftsbibliothek, Cod. Sang. 251, p. 10–11 (St Gall, 816)

   4. 4. Paris, Bibliothèque nationale de France, Lat. 2796, 54v, 106v–107r (northern France, c. AD 815 × 818)

   5. 5. Vatican, Biblioteca Apostolica Vaticana, Reg. lat. 309, 15r–15v (Saint-Denis, 859) = Lib. comp. i. 3f (ed. Borst, Schriften, p. 1106)

   6. 6. Berlin, Staatsbibliothek Preußischer Kulturbesitz, Phillipps 1830, 2v (Reims or Laon?, 874; partly)

3. H. Computus Fardulfi B (derivative of G)

   1. 1. Milan, Biblioteca Ambrosiana, H 150 inf., 18v (north-eastern France?, 810?) = Bobbio Computus c. 39 (ed. PL 129, col. 1293)

   2. 2. Brussels, Koninklijke Biblotheek van België/Bibliothèque royale de Belgique, 8654-72, 205r–v (northeastern France, s. ix^1/3)

   3. 3. Paris, Bibliothèque nationale de France, Lat. 894, 33v (Loire?, s. ix^3/4)

   4. 4. Padua, Biblioteca Antoniana, I 27, 49r (Verona?, s. ix/x)

      later:

   5. 5. Vatican, Biblioteca Apostolica Vaticana, Pal. lat. 235, 65r (Gandersheim? s. x¹)

   6. 6. Paris, Bibliothèque nationale de France, Lat. 6400B, 271r (Fleury?, 931?);

   7. 7. Paris, Bibliothèque nationale de France, Lat. 2183, 114v (France, s. xi);

   8. 8. Vatican, Biblioteca Apostolica Vaticana, Ross. 247, 30r (St Chaffre, c. 1020)

   9. 9. Vatican, Biblioteca Apostolica Vaticana, Reg. lat. 1263, 13v (Micy-Saint-Mesmin, 1007?)

   10. 10. Vatican, Biblioteca Apostolica Vaticana, Barb. lat. 477, 103v, 106v (Avignon, s. xiⁱⁿ)

   11. 11. Madrid, Biblioteca Nacional de España, 9605, 67rb–67va (Provence, 1026)

   12. 12. Vatican, Biblioteca Apostolica Vaticana, Reg. lat. 1530, 38vb–39ra (southern France?, 1054?; with noteworthy variation, arriving at a bissextus of 24 hours rather than the 12 hours common to this algorithm)

4. I. Fleury version I (variation of H and G)

   1. 1. Paris, Bibliothèque nationale de France, Lat. 5543, 118v–119r (Fleury, 847)

   2. 2. Paris, Bibliothèque nationale de France, Lat. 5239, 111r (Limoges, s. x^1/3)

   3. 3. Strasbourg, Bibliothèque nationale et universitaire, 326, 154r (Limoges/Angoulême?, c. 1000?)

5. J. Fleury version II (variation of H and G, with Visigothic additions)

   1. 1. London, British Library, Harley 3017, 46r–46v (Fleury?, 864)

6. K. Austrasian version

   1. 1. St Gall, Stiftsbibliothek, 225, p. 122 (St Gall, 773?)

   2. 2. Milan, Biblioteca Ambrosiana, H 150 inf., 18r (north-eastern France?, 810?) = Bobbio Computus c. 40 (ed. PL 129, col. 1293–4)

   3. 3. Wolfenbüttel, Herzog-August-Bibliothek, Cod. Guelf. 91 Weiss., 95r, (Worms?, s. ixⁱⁿ)

   4. 4. Angers, Bibliothèque municipale, 476, 10v (Brittany, 926?)

   5. 5. Madrid, Biblioteca Nacional de España, 9605, 67v (Provence, 1026)

   6. 6. Rouen, Bibliothèque municipale, Y 6 (274), 23r (England, s. xiⁱⁿ). ¹⁰⁰

CONCLUSION

The ascriptions to Theodore in CE of c. 700 and to ‘the Greeks’ in MC of 718/9, combined with the fact that the earliest occurrences are the Computus Digbaeanus of 675 and Computus Cottonianus of 689, point to a Greek origin of the bissextus algorithm introduced into Latin computistics by Theodore of Tarsus. This is corroborated by later occurrences of the algorithm in Byzantine computi, whose phrasing and transmission suggest these to be younger witnesses of a long tradition that may well go back to the seventh century. Theodore would have learned the argumentum himself either at one of his Eastern stations or in the Greek milieu of Italy before teaching it at Canterbury. His Irish students brought it to the regiones Scottorum. From there it then moved in Willibrord’s bags to the Continent, where it enjoyed a wide transmission in written form from the mid-eighth century onwards.

These results obviously raise the question of how much more Theodorean teaching may be found in Insular computistics of the late-seventh and early-eighth centuries. As this study suggests, the answer can only be found by a full-scale comparison of the Insular corpus (especially the major texts: CE, MC, DRC, Computus Digbaeanus and Computus Cottonianus, and Bede’s DT and DTR) with eastern computi, especially Georgios Presbyter and Maximus Confessor, but also the Anonymi of 830 and 892. This will place on a more solid footing the few scattered suggestions concerning the Canterbury school’s and its pupils’ astronomical/computistical material, ¹⁰¹ and may lead to some more surprising results. Here, the Anglo-Saxon evidence may actually prove more promising than the Irish corpus. The algorithms found in Bede and the Digbaeanus and Cottonianus are based on Dionysius’ calculations, which, being translations from Greek, will have featured prominently in Theodore’s teaching. The Irish, on the other hand, remained suspicious of the incarnation era, and employed calendrical methods that already worked for earlier Easter reckonings before the introduction of the Alexandrian/Dionysiac system. The focus should move away from trying to connect full-scale texts to Theodore to a more fine-grained study of individual ideas (like the bissextus algorithm in this study), for instance, to seriously and systematically consider how much of Bede may actually be Canterbury thought.