049 - the praefatio (prologus) sancti cyrilli de paschate andthe 437 year pascal list atributed to...

Vigiliae Christianae 67 (2013) 49-78 brill.com/vc

VigiliaeChristianae

© Koninklijke Brill NV, Leiden, 2013 DOI: 10.1163/15700720-12341116

The Praefatio (Prologus) Sancti Cyrilli de Paschate and the 437-year (not 418!) Paschal list attributed

to Theophilus

Alden A. Mosshammer5693 Spearmint Way

Prescott, AZ 86305 [email protected]

AbstractThe Editio Princeps of the Prologus Sancti Cyrilli de Paschate was published by Denis Petau in 1627 from a manuscript in which the author attributed a 418-year list of dates for Passover and Easter to Theophilus of Alexandria, which the author claimed to have abbreviated to 95 years. Bruno Krusch used two additional manuscripts for his 1880 edi-tion, in which the number attributed to Theophilus is 428. Scholars have argued that 418 must be the correct original number, because 428 is not a multiple of 19. Three previously neglected manuscripts show that the number was originally 437. The author of this text deduced that the 95-year list began approximately 438 years after the birth of Christ and therefore surmised that it was a continuation of a 437-year list that began with Passover in the fĳirst year after the Nativity. The 418 years may have been substituted by a redactor who was misled by a postscript that appears in two of the manuscripts.

KeywordsComputus, Paschal Controversies, Cyril of Alexandria, Theophilus of Alexandria, 95-Year Cyrillan List

In 1513, Paul of Middelburg, the Flemish mathematician and Bishop in the Italian city of Fossombrone, published a book on the correct observance of Easter (Pascha), dedicated to Pope Leo X. Paul included a chapter on the Paschal controversies of the early church, in which he quoted extensively from ancient authorities.1 He stated that Theophilus, Bishop of Alexandria

1) Paul of Middelburg, Paulina: de recta Paschae celebratione et de die passionis Domini nostri Iesu Christi (Fossombrone 1513), 118, 123-126. I owe the reference to Ulrich Voigt,

50 A.A. Mosshammer / Vigiliae Christianae 67 (2013) 49-78

(385-412), at the request of the Emperor Theodosius (379-95), composed a Paschal list consisting of twenty-three 19-year cycles, a total of 437 years. According to Paul, Theophilus chose that period because after 23 iterations the 19-year cycle returns to the same Dominical Letter and the same Golden Number with which it began.2 Paul stated that Theophilus’ successor Cyril (412-444) drafted a shorter version consisting of fĳive 19-year cycles totalling 95 years.

Paul then quoted at length from the text now known as the Prologue of Cyril. In the quotation, the author attributes to Theophilus a cycle of 437 years and says that he has for the sake of convenience produced a 95-year abbreviation, which has no diffference from the longer list except where the sequence of bissextile years (leap-years) produces a one-unit diffferential.

The author also states that Theophilus produced a 100-year list calcu-lated from the fĳirst consulship of Theodosius (380). That list has not sur-vived, but we do have Latin translations of Theophilus’ dedicatory letter to the Emperor Theodosius and of his preface, with substantial fragments from the Greek text of the latter.3 Several sources refer to the 100-year list, including Pope Leo I of Rome and Dionysius Exiguus.4 The Cyrillan Pro-logue is the only witness to a longer list.

Zyklen und Perioden, published electronically 20 August 2010, at www.likanas.de/doc/ZyklenAugust20.pdf (accessed 28 May 2012), 122. Paulina can be consulted electronically at http://bibdig.museogalileo.it/rd/bdv?/bdviewer/bid=0000000975646 (accessed 28 May 2012).2) The “Dominical Letter” (Sunday Letter) of later medieval and modern Easter tables is a letter from “A” to “G” (1 to 7) indicating the date of the fĳirst Sunday in January. More ancient tables used a numeral from 1 to 7 indicating the weekday of a specifĳic calendar date, usually 1 January in the Roman calendar or 26 Phamenoth=22 March in the Alexandrian calendar. The “Golden Number” is the position of the year in the 19-year cycle, obtained by dividing the number of the year AD by 19 and adding “1” to the remainder. Thus the year 438 divided by 19 is 23 with no remainder. Therefore it is the fĳirst year of the cycle. From the Golden Number, one can calculate the age of the moon in days as of 22 March. For the formula see Bonnie Blackburn and Leofranc Holford-Strevens, The Oxford Companion to the Year (Oxford 1999), 810.3) Ed. Bruno Krusch, Studien zur christlich-mittelalterlichen Chronologie. Der 84-jährige Ostercyclus und seine Quellen (Berlin 1880), 220-6; hereafter cited as “Krusch, Studien (1).”4) Leo to Marcian, ed. Krusch, Studien (1), 257-261; Dionysius Exiguus, Letter to Petronius, ed. Bruno Krusch, Studien zur christlich-mittelalterlichen Chronologie: Die Entstehung unserer heutigen Zeitrechnung (Berlin 1938), 63; hereafter cited as “Krusch, Studien (2).”

The Praefatio (Prologus) Sancti Cyrilli de Paschate and the 437-year Paschal list 51

The 19-year Cycle and its Periods

Easter is the fĳirst Sunday after Passover.5 Passover is biblically defĳined as the 14th day of the fĳirst month in a lunar calendar that began in the month of “new fruits” (Aviv)—in other words, the fĳirst full moon of spring.6 The Alexandrian church since at least the end of the third century required that the 14th day of the fĳirst month should fall on or after the vernal equi-nox, which was in turn defĳined as 21 March, at least since the time of Theophilus.7

A lunar year consists of twelve months alternating between 29 and 30 days, for a total of 354 days. The 14th day of the fĳirst lunar month there-fore recedes each year with respect to the Julian calendar of 365 days by eleven days. In a leap-year the moon is assumed to have an extra day match-ing the extra day of the Julian calendar, so that the 11-day diffferential is maintained. To maintain a correspondence between the fĳirst lunar month (Ex 12.2 principium mensuum) and the springtime of the solar year, when the grain is new (Ex 23.15 mensis nouorum), one intercalates a thirteenth lunar month at approximately three-year intervals.

Such a month and year is said to be “embolismic,” from the Greek ἐμβάλλω (throw in). The embolismic month is a “full” month of 30 days, so that the embolismic lunar year consists of 384 days, 19 days longer than the Julian year.

Thus, if Passover falls on 5 April in one year, the date in the next year will be 25 March. When the subtraction of 11 days would produce a date too early to be the fĳirst month of the year—a date preceding the equinox by the Alex-andrian rule—one inserts an embolismic month, usually at the end of the lunar year. In that case, the Passover full moon advances by 19 days from one year to the next with respect to the Julian calendar. Passover on 25 March will be followed in the next year by Passover on 13 April.

To produce a repeating cycle of dates for Moon 14 in the Julian calendar year, one wants to fĳind the closest approximation between whole lunar months averaging 29½ days and whole calendar years averaging 365¼ days. The best such approximation occurs after 19 years. The Julian calendar has

5) The following discussion is based on Alden A Mosshammer, The Easter Computus and the Origins of the Christian Era (Oxford 2008), 40-55, 135-6, 148-161, 178-82.6) Exodus 12.18, Leviticus 23.5.7) See Peter of Alexandria (bishop ca 300-311) as cited in the Chronicon Paschale, ed. L. Din-dorf (Bonn 1832), 5.2-5, and the Preface of Theophilus, ed. Krusch, Studien (1), 223.


6939 days in a 19-year period that includes four leap-years, 6940 days in a period with fĳive leap-years. In the same period there are 228 lunar months averaging 29½ days for a total of 6726 days, plus four or fĳive lunar leap-days, plus seven embolismic months of 30 days each for a grand total of 6940 or 6941.8 To make the correspondence exact, one subtracts one lunar day somewhere in the cycle. The diffferential between the lunar and solar year becomes one of 12 days, instead of eleven. If 17 April was the 14th day of the moon in one year, in the next year Moon 14 will be on 5 April, and 17 April will have Moon 26, instead of Moon 25. Hence, medieval commen-tators referred to this irregularity as the saltus lunae, the “leap of the moon.”9 The word saltus fĳirst appears in this sense in the text here under study, the Prologue of Cyril.

The fĳirst-century BC historian Diodorus of Sicily attributes the discovery of the 19-year cycle to Meton of Athens in 433/2 BC and says that people referred to it as the “Metonic cycle.”10 Eusebius of Caesarea says that Ana-tolius of Alexandria (ca. 270), who became bishop of Syrian Laodicea (now Latakia), wrote a treatise applying the 19-year cycle to Easter calculations.11 A 19-year cycle was standard in Alexandria, at least from the time of Atha-nasius (bishop, 328-373).12 Dionysius Exiguus, working in 525, adopted the 19-year cycle for use in the Roman church. He published a list of fĳive such cycles, covering 95 years beginning from the year 532. Dionysius says that this list was a continuation of a 95-year list composed by Cyril of Alexandria (bishop, 412-444) that began in the year 437. Dionysius changed the format and the data in only one respect—he substituted years numbered from the Incarnation of the Lord for the years numbered from the Roman emperor Diocletian that appeared in Cyril’s list. Thus the year 247 from Diocletian at

8) By modern astronomical calculations, a 19-year cycle produces 19x365.24219=6939.6016 solar days and 235x29.53059=6939.6887 lunar days. 9) See the discussion of Bede, De Temporum Ratione 42, ed. C.W. Jones Bedae Opera de Temporibus (Cambridge, MA 1943) hereafter cited as “Jones, BOT ”, tr. Faith Wallis, Bede: The Reckoning of time (Liverpool 1999), 113-15, hereafter cited as “Wallis, Bede.”10) Diodorus Siculus, Bibliotheca Historica 12.36.2, ed. K.T. Fischer and Fr. Vogel (5 vols., Leipzig 1906).11) Eusebius, Historia Ecclesiastica, 7.32.14-19, ed. Eduard Schwartz (Greek text) and Theodor Mommsen (translation of Rufĳinus), Eusebius: Die Kirkengeschichte (2 vols., Berlin 1908-9).12) Some of the Paschal Letters of Athanasius are extant in a Syriac translation, along with a list or “Index” that gives the dates for Easter and the age of the moon for every year of Atha-nasius’ episcopate. This Index exhibits a 19-year cycle. See “The Festal Letters of Athanasius and their Index,” Library of Nicene and Post-Nicene Fathers, vol. 4 (1891), 502-53.


the end of Cyril’s list was followed by the year 532 at the beginning of Dio-nysius’ continuation.13

The calendar dates for Passover (Moon 14) repeat in a 19-year cycle. The sequence of weekdays in the Julian calendar repeats in a 28-year cycle—the seven days of the week multiplied by the four years of the leap-year cycle. Therefore a list of dates for Easter in the Julian calendar becomes truly periodic only after 28 nineteen-year cycles, 532 years.14 Shorter peri-ods will, however, sometimes produce the same weekday for Passover and therefore the same date for Easter in the fĳirst year of the next 19-year cycle as in the fĳirst year of the period, depending on where in the period the leap-years occur. One such period is of 95 years, another of 437 years.

History of the Text

The Prologue of Cyril is an important text, because it served to introduce and defend the same 95-year list that Dionysius Exiguus used as his model and attributed to Cyril. It is probably the same list as that to which Pas-chasinus of Lilybaeum referred in a letter to Leo of Rome on the subject of the date for Easter in the year 444. Paschasinus says he consulted a list of dates for Passover that began in the consulship of Aetius and Segisvultius, AD 437.15

The fĳirst full edition of this text was published by Denis Petau (Dionysius Petavius) in 1627. Petau used a manuscript belonging to Jacques Sirmond. That text attributed to Theophilus not 437 years, but 418. In his discussion, however, Petau expressed his agreement with Paul of Middelburg that the original number must have been 437.16 Gilles Bouchier (Aegidius Buche-rius) published another edition from the same manuscript of Sirmond and divided the text into chapters.17 In 1937, Charles W. Jones identifĳied the

13) Dionysius Exiguus, Letter to Petronius, ed. Krusch, Studien (2), 63-68.14) Georgius Syncellus (ed. A.A. Mosshammer, Ecloga Chronographica Georgii Syncelli, Leipzig 1984) says (pp. 35, 382) that Annianus of Alexandria, a contemporary of Theophilus, composed eleven 532-year cycles. Victorius composed a 532-year list and stated in his Pref-ace that the Paschal data repeat after 532 years (ed. Krusch, Studien (2), 25-6). Scholars have debated whether Victorius understood the mathematics of this period or simply discovered it empirically. See Jones, BOT, 63-5; Mosshammer, Computus, 198-203, 240-1.15) Ed. Krusch, Studien (1), 247-50.16) Denis Petau, Opus de Doctrina Temporum, Diuisum in Partes Duas (Paris 1627), Part 1, 225-6 (discussion); Part 2, 881-3 (text).17) Gilles Bouchier, De Doctrina Temporum (Antwerp 1634), 481-4.


Sirmond manuscript as Oxford, Bodleian Library, MS. Bodley 309, written in the eleventh century.18 Manuscripts at Tours (Bibliothèque Municipale, MS. 334, fols. 40r-41v, ninth century) and Geneva (Bibliothèque Municipale et Universitaire, MS. 50, fols. 161v-163r, ca 805) preserve essentially the same text.19 These manuscripts, among others, constitute the so-called “Sirmond Group” of manuscripts, which contain an almost identical collection of computistical texts.20

The text purports to be the introduction to a 95-year list of Paschal data. As already noted, we know of such a list from Dionysius Exiguus, whose own 95-year list was a continuation. Dionysius attributes it to Cyril of Alexandria and says that it began in the year 153 from Diocletian (AD 437). He reproduced the last 19-year cycle, from which the remainder can be reconstructed.21 The author does not identify himself as Cyril in the text, but his name does appear in the title. The author advocates the use of the Alexandrian 19-year cycle against the 84-year cycle that was used at Rome during the fourth and fĳifth centuries.22 He also mentions a 112-year cycle. He says that the 12-day lunar increment known as the saltus should be applied at the 19th year, as Theophilus did, rather than at the 14th or 16th year as “others” did. This reference probably derives from the preface of Victorius of Aquitania to a 532-year list of Paschal data that he published in 457 at the request of Hilarus, archdeacon of Rome (later, Pope 461-8). Vic-torius erroneously stated that the authors of the 112-year list placed the saltus at the 16th year.23 The Prologue of Cyril must therefore have been

18) C.W. Jones, “The ‘Lost’ Sirmond Manuscript,” English Historical Review 52 (1937) 204-19, repr. Bede, the Schools, and the Computus, ed. Wesley Stevens (Aldershot 1994), 204-13. I thank the Bodleian Library for providing me with electronic images of the relevant pages.19) I thank the municipal libraries at Tours and Geneva for providing me with electronic images of the relevant pages.20) On the Sirmond group see Jones, BOT, 105-10; Dáibhí Ó Cróinín, “The Irish Provenance of Bede’s Computus,” Peritia 2 (1983) 229-47, repr. Early Irish History and Chronology (Dublin 2004), 173-90; Faith Wallis, Bede: The Reckoning of Time (Liverpool 1999), lxxii; Kirsten Springsfeld, Alkuins Einfluss auf die Komputistik zur Zeit Karls des Grossen (Stuttgart 2002), 66-80; Eric Grafff, “The recension of two Sirmond texts: Disputatio Morini and De diuisionibus temporum,” in Computus and Its Cultural Context in the Latin West, ed. I Warntjes and D. O Cróinin (Turnhout 2010), 112-42. I thank Professor O Cróinin for commenting on an earlier version of this paper.21) Ed. Krusch, Studien (2), 63, 69.22) On the 84-year cycle, see Wallis, Bede, xliv-xlv, and Mosshammer, Computus, 204-13.23) Ed. Krusch, Studien (2), 16-52; see p. 19. An exemplar of a 112-year cycle inscribed on the base of a seated statue was unearthed at Rome about 1550. It begins in the fĳirst year of the


written after 457 and after the death of Cyril in 444, who cannot have been its author.24

The author says that his 95-year list is an abbreviation of the longer list composed by Theophilus. The disputed number of years attributed to Theophilus appears twice—once in Chapter 2 and again in Chapter 3. The relevant clauses as they appear in the Geneva manuscript, the oldest of the witnesses to this version of the text, are as follows.

f 162r. Cuius (Theodosius) sanctissimis praeceptis obtemperans CCCCXVIII anno-rum circulum paschalem instituit eiusque clementiae a primo anno consulatus eius <us>que ad C calculans, quoto Kl uel Iduum, et quota luna Pascha debeat celebrare.

Whose (Theodosius) holy commandments obeying, he (Theophilus) established a Paschal circle of 418 years and for his clemency calculated from the fĳirst year of his consulship up to 100, on what number of the Kalends or Ides and on what quantity of the moon one should observe the Pascha.

f 162v. Et ne forte quatricentorum XVIII annorum infĳinita congeries aut fastidium cognoscendi aut pigritiam describendi quibusdam affferet, in XCV annos eundum circulum breuiaui, quos per illos annos uoluere sine ulla diffferentia recognoui. Unum tantum assem in quibusdam annis propter rationem bissexti qui occurrere non potuit usque ad illum summum circuli ultimum annum qui redit ad caput adiciendum potius dimittendum ammonui.

Emperor Alexander Severus, AD 222, and consists of 14 eight-year cycles grouped in seven sets of sixteen. The saltus appears in the the third and seventh years of each 8-year cycle. The cycle is usually attributed to Hippolytus, of whom Eusebius (HE 6.22) says that he com-posed a Paschal list based on a 16-year cycle in the fĳirst year of Alexander Severus. Another version of a 112-year cycle is described by an African computist working in the year 243. It circulated under the name of Cyprian, ed. W. Hartel, S Thasci Caecili Cypriani Opera Omnia (3 vols Vienna 1868-71), 3:248-71. See Mosshammer, Computus, 121-7. Victorius correctly states that the Roman 84-year cycle had the saltus at the 12th year, adding that some placed it at the beginning of the 15th. The author of the Prologue mentions only this latter 14-year saltus. An 84-year cycle with saltus at 14-year intervals was used in Ireland. See the Introduc-tion to Immo Warntjes, The Munich computus: text and translation: Irish computistics between Isidore of Seville and the Venerable Bede and its reception in Carolingian times (Stutt-gart 2010). I thank Dr. Warntjes for commenting on an earlier draft of this paper.24) So Krusch, Studien (1), 96. The monk Leo, who addressed a compoti paschalis rationem to a deacon Sesuldus (ed. Krusch, Studien (1), 298-302), seems to have been influenced by this text. Krusch, Studien (1), 98, identifĳied the addressee as the Sesuldus who was present as a bishop at the council of Toledo in 633. Leo must therefore have been writing while Sesuldus was still a deacon, sometime before 633. I shall argue below that the Prologue of Cyril is more likely a product of the later fĳifth century, than the sixth or early seventh.


And lest an endless series of 418 years cause either weariness of reading or exhaus-tion of writing, I have abbreviated the circle to 95 years, which I ascertained to proceed through those years without any diffference. One unit only I have noted either to add or subtract in certain years because of the order of the bissextile, which cannot occur until the very last year of the circle, which returns to its head.

Johann Wilhelm Jan, in his Historia Cycli Dionysii, published in 1718, criti-cized Petau for agreeing with Paul of Middelburg in attributing 437 years to Theophilus against the witness of the manuscript.25 Meanwhile, unknown to Jan, Ludovico Muratori had in 1713 published the contents of a computis-tical manuscript in the Ambrosian Library at Milan (Biblioteca Ambrosi-ana, MS. H 150 inf., ca. 810), under the title Liber de Computo.26 The fĳirst four leaves contain a copy of the Prologus Sancti Cyrilli, followed without a break by a Ratio Bissexti. In this copy the author attributes 428 years to Theophilus.

The 418 Years

Johannes van der Hagen defended 418 as the correct original reading, because 428 is not a multiple of 19.27 Since that time, some scholars have followed Paul of Middelburg and Petau (usually without citation) in stating that Theophilus drafted a list of 437 years.28 Most, however, have accepted the witness of the Sirmond manuscript and the argument of van der Hagen that the list was of 418 years. Most earlier scholars also accepted the Pro-logue as a genuine work of Cyril in a Latin translation. They therefore treated the author’s attribution to Theophilus of a 418-year list with respect and sought to reconcile that claim with the better attested information that his work was of 100 years.

25) Johann Wilhem Jan, Historia Cycli Dionysii (Wittenberg 1718), 17; repr. Patrologia Latina 67, 453-83, col. 461. 26) Ludovici Muratori, Anecdota quae ex bibliothecae Ambrosiani Codicibus, vol. 3 (Padua 1713), 111-209; repr. Patrologia Latina 129, cols. 1273-1371.27) Johannes van der Hagen, “De Cyclo Paschali CCCCXVIII annorum Theophili Alexandri,” Observationes in Heraclii imperatoris methodum paschalem (Amsterdam 1736), 59-64.28) John James Bond, Handy-book of rules and tables for verifying dates with the Christian era (London 1869), 120; Alexander Philip, The calendar: its history, structure and improvement (Cambridge 1921), 64.


Enrico Noris thought the 418 year list must have begun in 380, the same year as the 100-year list.29 At fĳirst, van der Hagen agreed.30 Later, he argued that the 418 years began in 475, 95 years after the beginning of the 100 year list.31 Ludwig Ideler accepted the view of Noris, as did Ferdinand Piper.32

Johann Heller took a new approach. In medieval Spain, years were num-bered from a date corresponding to 1 January 38 BC and designated simply as era. Heller claimed that the Roman 84-year cycle with its base-date in a year corresponding to AD 298 and the Alexandrian 19-year cycle with a base-date corresponding to 437 (the fĳirst year of the Cyrillan 95-year cycle) would have a common starting point in 38 BC, the fĳirst year of the Spanish era. The fĳirst consulship of Theodosius (AD 380) corresponds to year 418 of the Span-ish era. Heller concluded that the Spanish era had its origin from the intro-duction to Spain of the 418-year Paschal list attributed to Theophilus.33

Bruno Krusch published what remains the only modern critical edition of the text in 1880.34 He was unable to locate the Sirmond manuscript and relied upon Petau for its readings. Krusch also used the Ambrosian manu-script and a closely related, but incomplete, copy at Cologne (Dombiblio-thek, MS. 83 (2), fols. 213v-215r, ca. 805), whose text begins in the middle of chapter 2. Like the Ambrosian manuscript, the Cologne version attributes 428 years to Theophilus and appends to the text the same Ratio Bissexti.

Krusch persuasively argued that this text cannot have been translated from a genuine work of Cyril. No other source attributes to Theophilus any-thing other than a 100-year list. The 418-year list is an invention of the author, intended to explain why Cyril drafted another list overlapping with that of Theophilus. As to why the author invented a list of 418 years from which Theophilus published only 100, Krusch remained perplexed. He

29) Enrico Noris, Historia pelagiana et dissertatio de synodo V oecumenica (Louvain 1702), 180.30) Johannes van der Hagen, Observationes in veterum patrum et pontifĳicum prologos et epis-tolas paschales (Amsterdam 1734), 65.31) van der Hagen, “De Cyclo Paschali CCCCXVIII annorum,” 61.32) Ludwig Ideler, Handbuch der mathematischen und technischen Chronologie (2 vols. Ber-lin 1825-6), 2: 258; Ferdinand Piper, Karls des Grossen Kalendarium und Ostertafel (Berlin 1858), 115.33) Johann Heller, “Ueber den Ursprung der sogenannten Spanischen Aera.” Historische Zeitschrift 31 (1874) 13-32. On the Spanish era, see Bonnie Blackburn and Leofranc Holford-Strevens, The Oxford Companion to the Year (Oxford 1999), 767. For 298 as the base-date for the Roman 84-year cycle see Krusch, Studien (1), 36-49 and Mosshammer, Computus, 205-9.34) Krusch Studien (1), 89-98 (discussion), 337-343 (text).


agreed with Heller, however, that the number is somehow to be associated with the Spanish era, so that it is clear that the author was Spanish.35

The Chartres Praefatio

C.W. Jones, in the introduction to his 1943 edition of the chronological works of Bede, published another version of the text, which he had found in a manuscript at Chartres (Bibliothèque Municipale, MS. 70, fols. 77v-79r) under the title Praefatio Sancti Cyrilli Episcopi.36 The manuscript is now lost, apparently destroyed in the bombing of the city on 26 May 1944.37 This copy included only the fĳirst sentence of Chapter 1, followed by Chapters 4 to 8, with an excerpt from Chapter 3. At the end was a postscript, which read as follows in Jones’s transcription, with his translation. The text in brackets represent Jones’s emendations.

anno cccc o et x o [xx] consolatus auferri [asterii] et protogenis circulis (sic Jones; recte circulus) ipse ad caput redit, id est a pascha quod saluator noster cum discipu-lis suis celebrauit, qm. [quem], ut arbitror, competens [completum] est. reddita ratio iam l,xlv annorum paschae dies quibus Kal., ds [nonis], vel idibus et cota luna occur-rat [-averunt], ex ordine cauculemus.

In the year 420, the consulship of Asterius and Protogenes, the cycle returned to its start, that is to the Pascha which our Lord observed with His disciples, which, I believe, was complete. We shall calculate in order when the table has completed fĳifty years, for the Easters have occurred for forty-fĳive years according to Kalends, Nones, and Ides, and according to the age of the moon.

The consulship of Asterius and Protogenes was the year 449, 420 years after the traditional Roman date of the Passion.38 Jones argued that this text was written in 482, 45 years after the beginning of the 95-year Cyrillan table that we know from Dionysius Exiguus. He took the reference in the text to a calculation with the increment of the moon at intervals of 14-years as

35) Krusch Studien (1), 93-8.36) Jones, BOT, 40-43 (text) 44-54 (discussion).37) The library has photocopies only of fols. 56-72. I thank Immo Warntjes for this information.38) For 25 March 29 (the consulship of the two Gemini) as the traditional Roman date of the Passion, see Tertullian, Aduersus Iudaeos 8.18, ed. H. Tränkle, Q.S.F. Tertulliani Aduersus Judaeos (Wiesbaden, 1964); The Chronograph of 354, ed. Th. Mommsen, Chronica Minora Saec. IV-VII (3 vols. MGH AA vols. 9, 11, 13, Berlin 1892, 1894, 1898), 1:57.


derived from the 84-year cycle with 14th-year saltus that Jones believed, following Krusch, to have been in use in Africa between the third and the fĳifth century.39 Jones concluded that this Praefatio was the original version of the Cyrillan text, written in 482 to introduce the Alexandrian cycle to Africa. The Prologue, with its erroneous attribution to Theophilus of a 418-year list, Jones thought to be an expanded version of the original text writ-ten to introduce the Alexandrian system to Spain. The author of that later version thought the reference to a 420-year period in the postscript to be a mistake, because that number is not a multiple of 19. He therefore assumed, according to Jones, that Theophilus “worked on the basis of a 418-year cycle,” beginning in the fĳirst year of the Spanish era, from which he calcu-lated a 100-year extension beginning in 380.40

V. Grumel counted the 50 years mentioned in the postscript from 399, the year that we know from other sources to have been the beginning of a 110-year list that Cyril did indeed compose and dedicated to the emperor Theodosius II.41 In fact, as A Cordoliani and Leofranc Holford-Strevens have independently pointed out, the latter portion of the postscript reads better without Jones’s emendations and without his punctuation.42

quoniam ut arbitror competens est reddita ratio iam lxlv annorum paschae dies qui-bus Kalendis uel idibus 43 et quota luna occurrat ex ordine calculemus.

39) Krusch’s theory (Studien (1), 4-20) that such a cycle, invented by an African computist named Augustalis, was the original version of the 84-year cycle has since been discredited. The 84(14) was a product of the fĳifth century, used especially in Ireland. See Warntjes, Munich computus, xvi-xix, xxxvi-xxxvii, with references to earlier work.40) Jones, BOT, 45-50.41) V. Grumel, La Chronologie (Paris 1958), 39-40. We know of the 110-year list from an Arme-nian translation of Cyril’s dedicatory letter to Theodosius II. See F.C. Conybeare, The Arme-nian Version of Revelation and Cyril of Alexandria’s Scholia on the Incarnation and Epistle on Easter (London 1907), 215-21.42) A Cordoliani, “Textos de computo espanol del siglo VI. El Prologus Cyrilli,” Hispania Sacra 9 (1956), 127-39, 131; Holford-Strevens as cited by Mosshammer, Computus, 197.43) The Chartres manuscript, according to Jones, had kal ds uel idibus. Jones and Holford-Strevens would supply nonis for ds, while Cordoliani suggested diebus. As we shall see, the same postscript appears in Paris BNF 609 fol. 54r, where the reading is Klis uel Idibus. The author mentions only the Kalends and Ides, not the Nones, when describing the work of Theophilus. Thus it seems likely that the correct reading in the postscript is Kalendis uel Idibus, with no reference to the Nones.


Because, as I believe, an adequate account of the 95 years has now been given, let us calculate the dates of Pascha, on what Kalends or Ides it happens, and what the age of the moon.

The Roman numerals LXLV sometimes occur as an expression for “95.”44 There is no reason to divide the characters into intervals of 50 and 45. From this text one can infer only that it was written after the year 449.

The Text Quo Tempore Initium Mundi

In support of his claim that the later author of the Prologue changed the 420 years of the postscript into the 418 years attributed to Theophilus in the text, Jones cited a passage from the end of a text Quo Tempore Initium Mundi that he found in the same manuscript at Chartres. Jones thought the author might have been the same “presbiter Zacchaeus” who identifĳies him-self as the author of the Expositio Bissexti that followed upon the Quo Tem-pore in the manuscript. Jones did not transcribe more than the fĳirst sentence, but states that the author of the Expositio designates the present year as AD 635 in one passage, 784 in another.45 In the passage from the end of the Quo Tempore the author states that Theophilus composed a list of 437 years, which Cyril abbreviated to 95 years. Jones believed that this author was working from the Praefatio. Instead of changing the 420 years to 418, he chose 437, the next multiple of 19, because he was unfamiliar with the Spanish era and because he knew from Dionysius Exiguus that the 95-year list had begun in the year corresponding to AD 437. Jones tran-scribed the passage as follows. The translation is mine.

Theodosius imperator scm Theofĳilum episcm Alexandrinae aeclesiae suis litteris con-rogauit ut ei circulum paschalem ordinem annorum conscriberet. cui sanctissimus computans usque ad quadringentos triginta et septem annos et a primo anno conso-latus sui usque ad centesimum, calculans. cum suis litteris reordinabit et postea scs cirillus ecclesiae ipsius eps uidens infĳinitam congeriem et propter fastidium cogno-scendi aut pigritiam describendi siue propter falsos heriticorum lxxxiiii circuli essent disseminati, meruit, reuelante sibi dno, in nonaginta quinque annis istum circulum

44) For example in Paris, Bibliothèque Nationale de France, MS. Lat 609, fol. 48v, and Ivrea, Biblioteca Capitolare, MS. 6 (XLII), fol. 51v, in the passage where the author says he has composed a 95-year abbreviation. These manuscripts are discussed below.45) Jones, BOT, 39, n. 4.


breuiari qui per quinquies decem et nouies redit ad caput. et obseruandum est ne in nonagesimo quinto anno fallamur initium.

The emperor Theodosius asked in a letter that Theophilus, bishop of the church at Alexandria, prepare a Paschal circle for him, an order of the years. For whom in a letter the holy one made an arrangement, computing four hundred thirty seven years and calculating a hundred from the fĳirst year of his consulship. And after-wards Cyril, bishop of the same church, seeing the endless series and because of the weariness of reading or the exhaustion of writing, decided by divine revela-tion to abbreviate that same circle, which returns to its head through fĳive nine-teens. And care must be taken that we not mistake the beginning in the ninety fĳifth year.

It is more likely, as Cordoliani has persuasively argued, that the Praefatio of the Chartres manuscript consists of excerpts from the Prologue known from the other manuscripts, rather than that a later author expanded the Praefatio. Cordoliani argued that the Prologue was written in Spain some-time between 577 and 590.46

The phraseology of the text Quo Tempore Initium shows clearly that the author was working from the longer Prologue. It paraphrases chapters 2 and 3, which do not appear in the Chartres version.

Prologue (Krusch 338-339). Cuius sanctissimis praeceptis obtemperans CCCCXVIII annorum cyclum paschalem instituit eiusque clementiae, a primo anno consolatus eius usque ad centum calculans. . . . Et ne forte quadrigentorum XVIII annorum infĳinita congeries aut fastidium cognoscendi aut pigriciam discribendi quibusdam affferat, in nonaginta quinque annos eundem circulum breuiari.

Quo Tempore Initium (Jones, p. 50). cui sanctissimus computans usque ad quadrin-gentos triginta et septem annos et a primo anno consolatus sui usque ad centesimum calculans. . . . .scs cirillus ecclesiae ipsius eps. uidens infĳinitam congeriem et propter fastidium cognoscendi aut pigritiam describendi . . . meruit reuelante sibi dno, in nonaginta quinque annis istum circulum breuiauit.

The Year 418 of the Spanish Era

Cordoliani did not try to explain why the author of the Prologue attributed 418 years to Theophilus, or why the author of the Quo Tempore Initium gave the number as 437. Heller’s claim that the 418 years are to be counted from the fĳirst year of the Spanish era is arithmetically flawed. Subtracting

46) Cordoliani, “El Prologus Cyrilli,” 136-8; on Cordoliani’s argument for the date see further below.


multiples of 84 from 298 and multiples of 19 from 437 yields −38 as the common starting point. There being no “year 0”, −38 corresponds to 39 BC (not 38). Otto Neugebauer sought to revive the theory without the arith-metical error, but he does not explain why a Paschal cycle beginning in 39 BC should yield an era in its second year.47 It is possible, of course, that the inventor of the Spanish era might have thought of the Paschal cycle as beginning in a notional year “0” and numbered the following year as the fĳirst of his era. Why such a Christian inventor would have chosen to back-date the cycle to the year corresponding to 38 or 39 BC would nevertheless remain unexplained, despite Neugebauer’s effforts to fĳind a parallel in the Ethiopic Computus.48 That the Spanish era was a Christian invention is by no means uncontested.49

Krusch rejected the idea that the Spanish era had its origin from the Pas-chal tables, while nevertheless accepting a connection between era 418 and the 418-year list attributed to Theophilus. Krusch could not explain why the author, even if he did know that the fĳirst consulship of Theodosius was the Spanish year 418, should have supposed that Theophilus composed a 418-year list either beginning or ending in the year 418.50

The Number 418 as Counted from the year 114

August Strobel explained the 418-year period as resulting from adding a multiple of 19-year cycles to an 84-year cycle counted from the year of the Passion. If the author of the Prologue wrote a 95-year abbreviation of a lon-ger period, then (according to Strobel) that abbreviation probably con-sisted of the last 95-years of the earlier work. We know from Dionysius Exiguus that the 95-year list attributed to Cyril ended in the year corre-sponding to AD 531. Therefore, Strobel concluded, the 418-year cycle began in the year 532 – 418 = 114, which is one 84-year period after what Strobel regarded as the traditional and correct date for the Passion in AD 30.51 This

47) Otto Neugebauer, “On the Spanish Era,” Chiron 11 (1981) 371-80.48) Neugebauer is well known for his work on the Ethiopic Computus, which descends directly from the Alexandrian Paschal computus. See especially Otto Neugebauer, Ethiopic Astronomy and Computus (Vienna 1979).49) See Blackburn and Holford-Strevens, Oxford Companion, 767.50) Krusch, Studien (1), 93, 97-8.51) August Strobel,Ursprung und Geschichte des frühchristlichen Osterkalenders (Berlin 1977), 266-9.


ingenious construction is, however, no more convincing than the alleged connection between 418 and the Spanish era.

Periods of 95 and 437 Years

Ulrich Voigt has recently argued that “437” must have been the correct orig-inal reading of this text. The author says that he has abbreviated the longer period of his predecessor “sine ulla diffferentia” except that one unit must be added or subtracted in certain years because of the position of the bissex-tus. Voigt argues that the abbreviation must have been a continuation and that the reference to a diffference of plus or minus 1 applies to the date for Easter. He says that only a period of 437 years exhibits this mathematical relationship to a 95-year continuation. He adduces Paul of Middelburg’s quotation from the text as evidence that Paul read a copy of the Prologue that had the numeral 437, instead of 418.52

A 95-year continuation of a 437-year period, when compared with the fĳirst 95 years of the longer period, will sometimes produce a date for Easter that is six days later in the calendar. It is true, as Voigt points out, that in the numbering of weekdays +6 is the equivalent of −1 and −6 is the equivalent of +1. Because the author specifĳies that the diffference is one “unit” (assem), rather than one “day,” and because he does not mention the variant of six, he is as likely to be referring to the weekday number for the year as to the date for Easter.

If we stipulate that the 95-year continuation must have begun with the same data as the fĳirst year of the longer period, and must have the same sequence of weekdays as the fĳirst 95 years of that period, plus or minus one unit, then periods of 19 × 13 = 247 and 19 × 18 = 342 years will satisfy the cri-teria, as well as 19 × 23 = 437 years. If we require that the 95-year extension must both begin and end with the same data as the fĳirst 95 years of the longer period, then the arithmetic requires the number 437.53 The diffference of plus or minus one unit can also describe any 95-year continuation of a 95-year pertiod. What we need is textual evidence to support whatever mathematical logic the author here intends.

52) Voigt, Zyklen, 116-12353) One can verify these claims by reference to the 532-year period included in Wallis, Bede, 392-404. There is a typographical error at year AD 458, where the date for Easter should be 20 April, not 20 March.


Textual Variants in Paul of Middelburg’s Quotation and in the Chartres Praefatio

The Chartres Praefatio and Paul of Middleburg’s quotation share an impor-tant set of words in the fĳirst sentence of Chapter 4, which does not appear in Krusch’s edition. Paul and Chartres MS. 70 read as follows.

A duodecimo (recte, undecimo) autem Kalendarum Aprilium die usque in octauum (recte, septimum, so Paul) Kl Maias per dies XXXV qui faciunt septimanas quinque sanctum paschae celebrari confĳirmans, ad mensem nouorum qui iam biduum de ipsa septimana (ultima add. Paul) habere manifestum est (dinoscitur Paul) reliquos eius quinque dies adiecit (adiecti Chartres).

Afffĳirming that from the eleventh day before Kalends April (22 March) until the seventh Kalends May (25 April), which are 35 days and fĳive weeks, the holy Pascha should be observed, to the month of new fruits, which manifestly has already two days from that week, he (Theophilus) added its other fĳive days also.54

The witnessess used by Krusch all omit the words “ad mensem nouorum qui iam biduum.” Paul sometimes paraphrases the text and sometimes intro-duces variants in grammar or diction in what he quotes. Clearly, however, “ad mensem nouorum qui iam biduum” is not his invention.

Paris BNF Lat. 609

The attribution to Theophilus of a cycle of 437 years in the Quo Tempore Initium, a text clearly dependent on the Prologue of Cyril, together with Paul of Middelburg’s witness to that number in a quotation from Cyril and the textual agreements between the Chartres Praefatio and Paul of Mid-delburg’s quotation, suggest that there once existed an exemplar of this text that included the words ad mensem nouorum qui iam biduum, and in which Theophilus was said to have composed a list of 437 years.

54) As the author goes on to explain, the Alexandrian limits for Moon 14 were 21 March to 18 April. Because 18 April will sometimes fall on a Sunday, the rule prohibiting the observance of Easter on the 14th day of the moon, requires postponement to 25 April. The limits for Easter Sunday are therefore 22 March to 25 April, which is an inclusive period of 35 days. The fĳirst month of a lunar calendar is a full month of 30 days, so that it already includes two days from a fĳifth week. The author says that Theophilus added fĳive more days to the fĳirst month to accommodate an Easter date on 25 March, Moon 21. See also the Preface of Theophilus, ed. Krusch, Studien (1), 224-5.


A copy from such an exemplar is in fact preserved in a manuscript in Paris, Bibliothèque Nationale de France, MS. Lat 609, fols. 44r-54r.55 This manuscript was consulted for another edition of the text, published in 1859, but overlooked by Krusch, Jones, and all the more recent commentators. That edition appeared in volume 77 of the Patrologia Graeca as Letter 87, in a supplement to the Letters of Cyril from Jean Aubert’s 1638 edition of the Opera omnia.56 The unnamed editor used Bouchier’s text, which he cor-rected and augmented from a manuscript he identifĳied as once belonging to the monastery of St. Martial in Limoges, but in his time now in the Impe-rial Library of Paris, numbered as 609. The text is listed in the catalog of 1764 as Praefatio Sancti Cyrilli de Paschate, locupletior illa quam Bucherius publici iuris fecit.57 In the catalog of 1939, the entry appears as S. Cyrillus, Epistula de festi paschalis ratione.58

As in the Chartres manuscript, the Paris copy carries the title Praefatio, rather than Prologus or Epistula. It has also the same postscript referring to the consulship of Asterius and Protogenes as in the Chartres manuscript. That text is identical to what Jones read in Chartres 70, except that it reads consolaturi et protogenis circulus instead of consolatus auferri et protogenis circulis, adds ergo between qm and ut arbitror, and reads quibus Kalis, instead of quibus kal. ds. The Paris copy supports the argument that the numeral LXLV in the Chartres manuscript is to be read as “95” and not as separate expressions of “50” and “45.” The numeral on fol. 54r in Paris 609 is not entirely legible but appears to be either LXV or LXLV.59 On folio 48v the writer unmistakably uses the fĳigure LXLV in describing the 95-year abbre-viation of Theophilus’ longer list.

The text is preserved with an Expositio Bissexti under the same title as in Chartres 70 and with a copy of the same Quo Tempore Initium Mundi,

55) For brief comments on this neglected computistical manuscript, see Walter A Gofffart, “The Supposedly ‘Frankish’ Table of Nations,” Frühmittelalterliche Studien 17 (1983), 98–130, repr. Rome’s Fall and After (London 1989), 133-66, 138-9.56) PG 77, cols 383-390. An English translation of this letter 87 may be found in John I. McEn-erney, St. Cyril of Alexandria: Letters 51-110 (Washington 1987), 122-9. McEnerney uses Krusch’s text, rather than that of the PG.57) Catalogus codicum manuscriptorum Bibliothecae Regiae, Pars Tertia, Tomus Tertius (Paris 1764), 51.58) Catalogue général des manuscrits latins, ed. Ph Lauer, vol. 1 (Paris 1939), 618. I thank the Bibliothèque Nationale de France for providing me with an electronic copy of the entire manuscript, in pdf format.59) The editor in PG 77 read the numeral as LXIV.


attributing 437 years to Theophilus. In Paris 609, fol. 54r, that text is entitled Prefatio S. Martini Dumiensis Episcopi (Martin of Braga).60 The Expositio Bis-sexti (fol. 67r) gives the current year in the Spanish era as corresponding to AD 812, the probable year of the manuscript’s composition.61

The editor of the Cyrillan text in PG 77 added the words ad mensem nouorum qui iam biduum from the Paris manuscript. Paris 609 also cor-rectly reads ab XI autem Kalendarum Aprilium, although it shares with the Chartres copy the incorrect reading usque in VIII Kl. Mai.62 The editor noted several other variants as well, including some that agree with the portions of the text that Paul of Middleburg quotes. Those variants are as follows, with the page number from Krusch’s edition. Line-numbers are added for convenience. The asterisk indicates which readings seem to be the correct ones.

Krusch Paris 609 and Paul337,2. tradita observetur inlibata* tradita inlibata337,6-7. humanam seu diuinam non humanam sed diuinam*337,8-9. ignorantiae periculum obseruantiae periculum*337,9. ita etiam a XIIII ita ut ante XIIII*341,2. ut pleno orbis circulo ut pleno orbis sui circulo*341,5. ipse XXI adsignans ipse XXI afffĳirmans*

Paris 609 (or a transcript thereof ) may have been the copy that Paul of Middleburg saw. Because Paul often takes liberties with the text, compari-son is difffĳicult.

60) Claude Barlow transcribed the text from Paris 609 in the introduction to his edition of the De Pascha attributed to Martin; Martini Episcopi Bracarensis Opera Omnia (New Haven 1950), 262-3. Barlow thought the De Pascha a genuine work of Martin. Pierre David, “Saint Martin de Braga est-il l’auteur d’un traité de comput pascal?,” Bulletin des études portugaises 14 (1950), 283-299, has argued otherwise. See also A. Cordoliani, “Textes de comput espagnol du VIe siècle: Encore le problème des traitès de comput de Martin de Braga,” Revista de archivos, bibliotecas y museos 62 (1956) 685-97. On the question of whether the Quo Tempore is Martin’s work, see my paper “Three Computistical Texts,” to be published in the proceed-ings of the Fourth International Conference on the Science of Computus, Galway 13-15 July 2012.61) The manuscript ends (fols 97r-107r) with a list of Paschal data for the years 812 through 975.62) Only the Oxford and Geneva manuscripts correctly read VII Kl. Mai, although both share the incorrect reading ab XII Kal. Apr.


What the editor of the text in PG 77 failed to note is that Paris 609 agrees with Paul of Middelburg and with the Quo Tempore Initium in attributing to Theophilus a circle of 437 years, not 418 as in the Oxford, Tours, and Geneva copies, or 428 as in the manuscripts at Cologne and Milan. In the fĳirst instance of the number (fol. 47v), there is neither word nor numeral for “400” and the remaining numeral appears to be “XL VII” (the space is in the manuscript). Perhaps the copyist misapprehended quadrigentorum triginta septem as quadraginta septem. In the second instance (48v), the text clearly reads “ne forte CCCCXXXVII annorum infĳinita conieries.”

Ivrea, Biblioteca Capitolare, MS. 6

There is also a hitherto unnoticed copy of the fĳirst three chapters of the text and the beginning of the fourth in a manuscript in Ivrea (Biblioteca Capito-lare MS 6, olim XLII, fols. 50v-51v).63 Jones knew of the manuscript, but apparently only from the Inventario of 1894.64 In that catalog the title is listed as S. Cyrilli Epistula, and the incipit is not given. Jones therefore mis-takenly believed the text was a copy of the Pseudo-Cyrillan Epistula de Pas-cha addressed to the Synod at Carthage.65 The Ivrea manuscript also contains versions of the same Expositio Bissexti and Quo Tempore Initium Mundi that Jones found in Chartres MS. 70 and that appear also in Paris 609. Jones cited only the title, incipit, and explicit of the Expositio. Com-parison of the incipit in Chartres 70 with Ivrea 6 and Paris 609 shows that these texts shared a common source.

63) I thank Dr. Immo Warntjes of the Ernst Moritz Arndt Universität in Greifswald for pro-viding me with images of the folios containing the Expositio Bissexti and the Quo Tempore Initium, scanned from a microfĳilm in the collection at The Moore Institute of the National University of Ireland in Galway. I also thank Dr. Enrico Dal Lago of the NUI, Galway, for personally photographing on my behalf the folios containing the partial copy of the Cyrillan text.64) Alfonso Professione, Inventario dei manoscritti della Biblioteca capitolare di Ivrea (Ivrea 1894), 5. August Reiffferscheid, Bibliotheca patrum Latinorum Italica, vol. 2 (Vienna 1871), 225, provides a fuller description of the manuscript.65) Jones, BOT, 94-95, n. 5. For the Pseudo-Cyrillan Latin version of the Letter to Carthage, see Krusch, Studien (1), 101-9 (discussion), 344-9 (text). This text is based on a genuine letter of Cyril announcing the date of Easter for the year 420 (Letter 85, PG 77, 375-7).


Chartres 70 (Jones, BOT, 39, n.4). Incipit expositio bisexti uel anni coms. seu embo-lismi. Si scire uis unde sit bisextus uel annus communis siue embolismus breuiter tibi ego Zacheus in xri. nomina [sic] presbiter tibi amator sapientiae dissero.

Ivrea 6 (fol. 51v). Incipit expositio bissexti uel anni communis seu embolismi de lxlv annis circuli paschalis. scire uis unde sit bissextus uel annus communis seu embolis-mus breuiter tibi domine mi amator sapientiae disserebo.

Paris 609 (fols. 66r-v). Expositio bissexti uel anni comunis siue embolismi. Si uis scire unde sit bissextus uel annus communis seu embolismus, breuiter tibi ego domine amator sapientiae disserebo.

In the Ivrea copy, the year just completed is designated as 810 of the Span-ish era, AD 772, the likely date for the composition of the manuscript. A text with the same title existed at one time in a now lost manuscript at Ripoll.66

The Quo Tempore Initium follows immediately upon the Expositio in the Ivrea manuscript, with no intervening title. It is therefore not listed in the catalog. It has essentially the same text, with the same ending, as the ver-sions in Paris 609 and Chartres 70, attributing 437 years to Theophilus.67

This Epistola Sancti Cyrilli includes only what corresponds to the fĳirst three chapters in Krusch’s edition and part of the fourth, ending with prop-terea hos quinque dies minime dubitaui quia ipsa luna qui usque in VIII Kl Maias protenditur intra primi mensis terminos nascitur et impletur. Like Paris 609 and the Chartres Praefatio, it includes the words ad mensem nouo-rum qui iam biduum at the beginning of chapter 4. It also shares with Paris 609 the variants from Krusch’s edition already listed above, including tra-dita inlibata, obseruantiae periculum, and ita ut ante XIIII. Where Paris 609 and Paul read non humana sed diuina, however, the Ivrea copy omits non.

In the two passages where the author mentions the number of years included in the work of Theophilus, the text reads as follows.

Folio 51r. Cuius sanctissimus [sic!] praeceptis obtemperans quadringentorum XXXta annorum circulum paschalem instituit.

66) Expositio bissexti uel anni comunis seu imbolismi; Gonzalo Martinez Diez, “Dos catálogos inéditos de la Biblioteca del Monasterio de Ripoll,” Hispania Sacra 22 (1969) 333-423, 391.67) Joan Gomez Pallares found another copy of this text in an Ordo Paschalis that he tran-scibed from Paris BNF nouv. acq. Lat 2169, “El Tratado Ordo pascalis en los mss. D.I.1 y D.I.2 de la Biblioteca del Escorial y Nal 2169 de la BN de Paris,” Universitas Tarraconensis (Sección Filológica) 12 (1988-9) 127-56, reprinted in Studia chronologica: estudios sobre manuscritos latinos de cómputo (Madrid 1999), 135-55, 142; electronic edition (Barcelona 1998), hipatia.uab.cat/JG/computus.pdf (accessed 28 May 2012), 116-32, 121-22.


Folio 51v. Et ne forte CCCCXXXVII annorum infĳinita conierie aut fastidium cogno-scendi aut pegritiam discribendi quibusdam affferet in LXLV annos eundem circulum breuiaui.

The copyist apparently omitted the word or numeral for “seven” in the fĳirst passage.

Metz MS. 732

Ludwig Traube discovered a fragment of the text in uncial script at Metz, at the beginning of a compilation of fragments from several otherwise lost manuscripts of various date (Bibliothèques-Médiathèques de Metz, MS. 732). In the catalogue of manuscripts at Metz, these two leaves are described as Fragment d’une encyclique relative à la détermination et à la célébration de la fête de Pâques; cette encyclique est postérieure à la décision de l’empereur Théodose, dont elle parle.68 Paul Lehmann catalogued Traube’s collection of photographs after his untimely death in 1907 and recognized this untitled fragment at Metz as from the “Prologus S Cyrilli.”69

E.A. Lowe identifĳied another fragment from this same manuscript in the fly-leaves of a manuscript in Montpellier (Bibliothèque Universitaire de Médecine, MS. 241). A note in the Montpellier fragments, indicates that the manuscript once belonged to the abbey of St. Arnulph of Metz. Lowe dated the fragments to the sixth or seventh century.70 David Ganz, Emeri-tus Professor of Palaeography, King’s College, London, would date the hand to the seventh century, rather than the sixth, or perhaps to early in the eighth century.71 This fragment is the oldest known copy of the text.

The fragment includes chapters 1 through 3, beginning with sanctum paschae mysterium and ending with aut fastidium cognoscendi. The outer

68) Catalogue général des manuscrits des bibliothèques publiques des départements, vol. 5 (Paris 1879), 238.69) “Anhang: Die lateinischen Handschriften in alter Capitalis und in Uncialis auf Grund von L. Traubes Aufzeichnungen,” bearbeitet durch Paul Lehmann, Vorlesungen und Abhandlungen von Ludwig Traube, vol. 1, ed. Franz Boll and Paul Lehmann (Munich 1909), 157-263, 201.70) E.A. Lowe, Codices Latini Antiquiores, Part 6, France: Abbeville-Valenciennes (Oxford 1953), 27, item 789; the illustration is from the Montpellier fragment, which contains text from Eucherius, De Quaestionibus Veteris Testamenti.71) David Ganz, email correspondence of 25 October 2011. I thank Professor Ganz for responding to my request for an opinion and for providing the reference to the CLA.


edge of folio 1 has been torn away, so that a few characters are lost from the end of each line on fol. 1r and from the beginning on 1v. It shares with Paris 609 all the variants listed above, except that orbis sui has been lost from the margin. In addition, it shares with Paris 609 and Ivrea 6 the reading perfec-tae rationis cardinem against perfectae rationis ordinem (Krusch 339,5) in the Sirmond group. The Metz fragment is unique in adding currente after apostolica autoritate (338,16).

Both instances of the numeral in the discussion of the work of Theophi-lus appear on folio 2v. In clear uncial characters, both read CCCCXXXVII (see Plate 1).72

The 95-, 437-, and 532-year Periods

The author says that his 95-year cycle is an abbreviation of the work of Theophilus, sine ulla diffferentia, except for variations of plus or minus one unit, depending on the position of the bissextus. The list attributed to Theophilus is fĳictional, but the author need not have had a 437-year list before him in order to make this claim. Either or both of two considerations might have led the author to claim that Theophilus had composed a circle of 437 years.

First, if the author knew of the 532-year Great Paschal Period, either from the Preface of Victorius or from Alexandrian sources, he could easily have determined that both a 437-year period and its 95-year continuation return at the end to the same data with which they began.73 The Cyrillan 95-year table began, as we know from Dionysius Exiguus, with Moon 14 on 5 April and with feria 4 (Wednesday, the weekday of 24 March). It ended with Moon 14 on 17 April with feria 2. The author would therefore have known that the next year, like every fĳirst year of the 19-year cycle, would have Moon 14 on 5 April and, since it was a leap-year, feria 4. That same data would have appeared 532-years earlier. Thus both a 437-year list and a 95-year abbreviated continuation began with the same data and returned to that same data at the end.

72) I thank the Bibliothèques-Médiathèques de Metz for providing a high-resolution image of folio 2v and for permission to reproduce it in this article. I want especially to acknowledge the assistance of Anne Dell’Essa, Bibliothécaire Département Patrimoine-Iconographie, in responding to my requests fĳirst for jpeg images of folios 1-2 and then for a tifff image of folio 2v.73) Ulrich Voigt (Zyklen, 121) has argued that the author of the Prologue must have known the 532-year period.


Plate 1. Metz 732 fol. 2v, showing the numeral CCCCXXXVII in the fĳirst line and again in the penultimate line. Digital image courtesy of the Bibliothèques-

Médiathèques de Metz.


Years from the Incarnation and the Date of the Text

The second approach involves counting the approximate interval from the birth of Christ to the fĳirst year of the Cyrillan list. Whether or not the author calculated the mathematical relationship between 437 and 95-year periods, he would have known that the fĳirst year of the 95-year list was approxi-mately the year 438 since the birth of Christ. Adjusting that number to a multiple of 19, the author surmised that Theophilus had composed a list of 437 years beginning in the fĳirst year after the Nativity. The author might have derived that information from Dionysius Exiguus, for whom the fĳirst year of the Cyrillan list in the year 153 from Diocletian corresponded to the year 437 from the Incarnation.74 Yet nothing in the text suggests that the author knew the work of Dionysius Exiguus. Furthermore, there would have been little motivation for the author to have composed this preface and (presumably) circulated it with a copy of the Cyrillan table, except dur-ing the 95-year period covered by that list between 437 and 531.

Cordoliani argued that the text was composed between 577 and 590, well after the publication in 525 of the work of Dionysius.75 There are some sim-ilarities between the Prologue and the De Pascha falsely attributed to Mar-tin of Braga. In particular both texts claim that some communities observed Easter on 25 March, regardless of the age of the moon or the day of the week.76 Cordoliani believed that the author of the Prologue had read the De Pascha, which in turn was composed to address the problem of the date of Easter in 577, when Gregory of Tours says that Easter was observed in Spain on 21 March instead of 18 April. In 590, Gregory says, both his com-munity and the Spanish observed the Alexandrian date, following the tables of Victorius.77

Whatever the date of the De Pascha and its relationship to the Prologue, the latter more likely addresses the problem of Easter in 482 than 95 years

74) Dionysius says (ed. Krusch, Studien (2), 64) that he faithfully continued the work of Cyril, except that he substituted years from the Incarnation for years numbered from Diocletian, such that the year 248 from Diocletian was numbered instead as 532 from the Incarnation.75) Cordoliani, “El Prologus,” 136-8.76) Prologus, ed. Krusch, Studien (1), 338 (nonnulli); De Pascha, ed. Barlow, Opera Omnia, 270 (a plerisque Gallicanis episcopis). The two texts may have had a common source for this information.77) Gregory of Tours, Historia Francorum, 5.17 and 10.23, ed. Bruno Krusch and Wilhelm Levison, Gregorii episcopi Turonensis, Libri Historiarum X, Monumenta Germaniae Histor-ica, Scriptores Rerum Merovingicarum I (2 vols., 2nd edition Hannover 1951).


later in 577, as indeed Jones argued with respect to the Chartres Praefatio.78 In chapter 5, the author says that the “others” have a two-day error in their calculations for the moon.79 What they designate as the 3rd or 16th or 23rd day, Theophilus makes the 1st or 14th or 21st. They object to any date after 21 April, while Theophilus could defer Easter to as late as 25 April.80 For the year in question, the author says, they calculate the moon as in its 23rd day and refuse to observe Easter, while Theophilus makes that the 21st day and does not hesitate to observe the Pasch. What they call Moon 15 on the Saturday of the preceding week and therefore the appropriate date for the Easter Vigil, Theophilus shows to be the 13th, requiring postpone-ment to the following week.

During the period between 437 and 627 (two 95-year periods), the Alex-andrian calculations prescribe Easter for the 21st day of the moon at a date later than 21 April only in the years 455, 482, 550, and 577.81 The two-day error of which the author complains can apply only to the year 482. For that year, the Cyrillan 95-year table produces a 14th day of the moon on Sunday 18 April. By the usual rule prohibiting the observance of Easter on Moon 14, the Cyrillan table therefore prescribes Easter for 25 April, Moon 21.82 The Roman 84-year table produces Easter Sunday on 18 April, Moon 17.83 The list of Victorius has Easter on 18 April, the 15th day of the moon, with a note that the Greeks (i.e., the Alexandrians) would observe Easter on 25 April, Moon 22.84 Either date is problematic. According to Victorius, the Latins limited the 14th day of the moon to the period between 18 March and 15 April and the date for Easter Sunday to the 16th through the 22nd day of the moon.85

Jones thought the complaint was directed against the Victorian calcula-tions. The author says that his opponents counted the moon as in its 15th day on the Saturday of the week before what the author regards as the

78) Jones, BOT, 45-6.79) Ed. Krusch, Studien (1), 340-41.80) For the Roman rule prohibiting the observance of Easter after 21 April, see the letter of Leo to Marcian, ed. Krusch, Studien (1), 259.81) See the 532-year list in Wallis, Bede, 392-404.82) For this rule, see the Preface of Theophilus, ed. Krusch, Studien (1), 224.83) For reconstruction of the Roman 84-year cycle, see Mosshammer Computus, 210-211, fol-lowing Eduard Schwartz, Christliche und jüdische Ostertafeln (Berlin 1905), 46-9. In the table, the datum is for the year 482 – (84 × 2) = 314.84) Ed. Krusch, Studien (2), 49.85) Ed. Krusch, Studien (2), 19-20.


legitimate date. Jones believed that the opponents used the Victorian table, but had renumbered the moon as in its 16th day on Sunday 18 April, in order to bring it into conformity with the rule, as is the case in some of the manuscripts of the Victorian table.86

More likely, the “others” used a version of the 84-year cycle, which the author explicitly names as aberrant.87 A two-day variance from the Alexan-drian calculations occurs in the Roman 84-year table for the years between 472 and 489, except at 482. For that year of the cycle, the “Ambrosian Easter Table,” the best preserved example of the Roman 84-year cycle, dates Eas-ter to 18 April, Moon 17—not Moon 16, as in our author’s complaint.88 In fact, Moon 16 on 18 April entails Moon 14 on 16 April and would violate the Roman rule limiting Moon 14 to the period from 18 March to 15 April.

Both the Alexandrian 19-year cycle and the Roman 84-year cycle are built upon a system of “epacts.” The word derives from a Greek word mean-ing “addition”—in this case, additional days of the moon. The epact for the year gives the age of the moon as of a date corresponding to 26 Phamenoth=22 March in the Alexandrian calculations, 1 January in the Roman cycle. Easter on 18 April, Moon 17, is consistent with the epact for the year, which the Ambrosian list gives as 28; and that number is in turn consistent with the sequence of epacts for this section of the cycle.89

Moon 14 on 15 April does, however, disturb the sequence of Passover full moons for these years. Because of the diffferential of 11 days between the lunar year and the solar year, or 19 days in an embolismic year, the date of Moon 14 should either fall back by eleven days in the Julian calendar from one year to the next or advance by 19 days. Such is the case for the Alexandrian 19-year cycle. In the Roman 84-year cycle, this regularity is sometimes disturbed, and the 17th year of the cycle, corresponding to 482, is one example.90

86) Jones, BOT, 46.87) Ed. Krusch, Studien (1), 337.88) This list is preserved in Milan, Biblioteca Ambrosiana H 150 inf., fols. 135v-137r, ed. Krusch, Studien (1), 236-9; see p. 237 at the year 16 of the Ambrosian list. This is the same manuscript whose fĳirst four leaves contain a copy of the Prologue of Cyril. The Ambrosian 84-year cycle begins in the second year of what was the classical Roman cycle, so that the 16th year of the Ambrosian list is the 17th year of the classical cycle.89) On the system of epacts and the lunar calendars that they generate, see Leofranc Hol-ford-Strevens, “Paschal Lunar Calendars up to Bede,” Peritia 20 (2008) 165-208. I thank Dr. Holford-Strevens for reading and commenting upon an earlier draft of this paper.90) See Holford-Strevens, “Paschal Lunar Calendars,” 174-5.


In 481, Moon 14 occurs on 28 March. Moon 14 in the year 483 falls on 5 April. The intervening year should be either 28 March minus 11 days, 17 March, or 28 March plus 19 days, 16 April, both of which violate the Roman limits for Moon 14. Either the author of the Cyrillan Prologue imputed to his opponents the same two-day diffferential in the age of the moon for the year 482 that is evident in the surrounding years, or these “others” used a lunar list that preserved the usual 19- or 11-day diffferentials in the calendar date of the Passover full moon during these years, even at the expense of exceeding the Roman limit of 15 April for Moon 14 in the year 482.

The match between the author’s discussion and the data for the year 482 is not perfect, but the fĳit is better than any of the other three possibilities. In 577, the disputed Paschal date to which Gregory of Tours referred, the Alexandrian Easter again falls on 25 April, Moon 21. For that year the Roman 84-year table would produce Easter on 18 April, Moon 19—a fĳive-day difffer-ence from the Alexandrian lunar count. If the date was still at issue when this text was written, the year 455 (the subject of Leo’s appeal to Marcian), when the Alexandrian Easter was 24 April, Moon 21, can be excluded. The text shows the influence of the Preface of Victorius, written in 457. In any case, both in 455 and 95-years later in 550, the 84-year cycle produces Moon 25 on 24 April 455, not the Moon 23 of the author’s complaint, with Easter on 17 April, Moon 18, a four-day diffference from the Alexandrian calculation.91

The 437 Years as Counted from the Nativity

The Cyrillan Prologue therefore probably predates Dionysius Exiguus. One need not have known the work of Dionysius to approximate his date of AD 437 for the beginning of the Cyrillan 95-year table in the year 153 from Diocletian. It was well known in late antiquity that Jesus was born in approximately the year corresponding to 1 or 2 BC. That date follows from the statement in Luke’s Gospel (3.1 and 3.23) that Jesus began his ministry at about the age of 30 after having received John’s baptism in the 15th year of Tiberius (AD 29). The author might have known the date corresponding to 1 BC from Julius Africanus, who dated the Passion to AD 31, at the end

91) If a date for Easter after 21 April was not at issue, four other years become candidates. Roman Easter was on Moon 16 and Alexandrian Easter on Moon 21 a week later in the years 468, 472, 478, and 498.


of the year 5531 from Adam and the Incarnation to the beginning of the year 5501.92

The author might also have known that approximate date either from Jerome’s version of the Chronicle of Eusebius, or from the Ecclesiastical His-tory of Eusebius in the translation of Rufĳinus. In the Chronicle, the note Christus nascitur appears at the third year of the 194th Olympiad (2/1 BC) and the fĳirst year of Diocletian at the second year of Olympiad 266 (AD 286/7), so that Diocletian 153 would be 439 years from Christ.93 In the Ecclesiastical History, Eusebius says at the end of Book 7 (7.32.32) that he has covered 305 years since the birth of Christ, and at the beginning of Book 8 (8.2.4) that the Great Persecution began in March of the 19th year of Dio-cletian. If the 19th year of Diocletian was approximately the year 305 or 306 from Christ, then the 153rd year was approximately the year 439 or 440. The author of the Prologue would have adjusted the number to 438, so as to make the beginning of the 95-year list the fĳirst year of the 24th 19-year cycle from the birth of Christ.94

The author claimed that this 95-year list was an abbreviated continua-tion of a list that included 437 years from the Nativity. He attributed that 437-year list to Theophilus, to whom he also correctly attributed a calcula-tion covering one hundred years from the fĳirst consulship of Theodosius, without explaining what he thought was the relationship between the two lists.

The 418 Years—Corruption or Redaction?

The number 418 in the Geneva-Oxford-Tours group of manuscripts and 428 in the Cologne and Ambrosian copies could have resulted from a process of

92) Julius Africanus, F93, ed. Martin Wallrafff et al., Julius Africanus Chronographiae: The Extant Fragments (Berlin 2007), 276-286, esp. 282, line 58 (from Eusebius), and 284, lines 80-81 (from Syncellus), where the date is the second year of Olympiad 202, AD 30/31. Syncel-lus adds (286, line 109) that 5531 years had been completed since Adam. See also F15 (p. 24, line 13) and T92 (274, line 4) for the 5500 years from Adam to the Incarnation. Mosshammer (Computus, 407) has argued that 5501, not 5500, was the year of the Incarnation.93) Ed. Rudolf Helm, Die Chronik des Hieronymus (3rd edition, Berlin 1984), 169, 225.94) Daniel McCarthy has argued that the Christian era was in fact derived from some such inference derived from the works of Eusebius, “The emergence of Anno Domini,” in Time and Eternity—The Medieval Discourse, ed. G. Jaritz and G. Moreno-Riaño (Turnhout 2003), 31–53.


scribal corruption.95 The numeral CCCCXXXVII (437) might have been cor-rupted fĳirst to CCCCXXVIII (428), then “corrected” to 418 to make it a mul-tiple of 19.

Since it is a multiple of 19, the number 418 looks like a deliberate choice. There is therefore another possibility, more speculative but worth consid-eration. Both the complete copy in Paris 609 and the excerpts in Chartres 70 end with the statement that “the circle returns to its head in the 410th year (anno autem CCCCmo et Xmo), in the consulship of Asterius and Proto-genes, that is to the Pascha that our Saviour celebrated with his disciples.” Jones amended the numeral to CCCC et XX, because the consulship of Aste-rius and Protogenes is 420 years after the traditional Roman date of the Passion on Friday 25 March, AD 29. Jones argued that the author of this text, who advocated the Alexandrian 19-year cycle against the Roman 84-year cycle, wanted nevertheless to show that in the year 449 the Alexan-drian calculations produced the same recapitulation of the data for the year of the Passion as did the Roman 84-year cycle, namely a 14th day of the moon on Thursday, 24 March.96 The author had read the Preface of Theophilus and repeats, with emphasis, the teaching of Theophilus that the Passion had occurred on the 15th day of the moon.97

For this author to have conceded a periodicity after 420 years, a multiple of 84 rather than 19, would have undermined, not strengthened his case. It is possible that a later redactor, who would perhaps not have been troubled by the interval of 420 years, added the postscript. It is likely, however, to belong to the original author. His purpose is to introduce and defend a Lati-nized version of the Alexandrian computus. In Alexandria the traditional date of the Passion was in the year corresponding to AD 31.98 The consul-ship of Asterius and Protogenes, 418 years after that date, is the only year within the 95-year scope of the Cyrillan list that produces Moon 15 on a Friday at a multiple of 19-years from the Alexandrian date for the Passion and at an acceptable date in March. In 449 that date was 25 March. In 31,

95) On careless transcription of numerals, see the comments of Augustine, De Ciuitate Dei, 15.13, ed. Barhard Dombart (2 vols. Leipzig 1863) 2: 71.26-29. I thank Leofranc Holford-Strevens for the reference.96) Jones, BOT 46-7.97) Ed. Krusch, Studien (1), 225 (Theophilus), 342 (Cyrillus).98) Chronicon Paschale, ed. L. Dindorf (Bonn 1832), 415.9-14. On this date as traditional in the Greek church since the time of Julius Africanus, see Grumel, La Chronologie, 20-22; Moss-hammer, Computus, 49; C. Philipp E. Nothaft, Dating the Passion: The Life of Jesus and the Emergence of Scientifĳic Chronology (Leiden 2011), 57-58, 77.


23 March was a Friday and the 13th day of the moon by Alexandrian calcu-lations. The author of the Prologue need not have calculated the data for AD 31, nor have been bothered by the discrepancies if he did.

By this hypothesis, the numeral in the postscript should be amended to CCCCmo et Xmo et VIIIuo. In the exemplar common to Paris 609 and Char-tres 70, the word or numeral for “eighth” was omitted, just as the word or numeral for “seven” was overlooked in the transcription of the fĳirst instance of the number 437 in the Ivrea manuscript. The writer of the exemplar ancestral to the Sirmond group saw the periodicity of 418 years in the post-script and decided to attribute that number to Theophilus in the text, instead of 437, while nevertheless omitting the postscript. The number 428 in the Cologne and Ambrosian manuscripts would in that case be a second-ary corruption.

Whatever the reason for the author’s invention of a Paschal list of more than 400 years as the work of Theophilus and however that number came to be corrupted or redacted to 418 or 428, there can be no doubt that 437 was the original number. Paris 609, Metz 732, Ivrea 6, and the lost Chartres 70 constitute a family of manuscripts attesting to an older and better ver-sion of the text than any of the Sirmond group. In acccordance with their witness, we should refer to the text as the Praefatio Sancti Cyrilli, rather than the Prologus.

049 - the praefatio (prologus) sancti cyrilli de paschate andthe 437 year pascal list atributed to...

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