Alden A. Mosshammer, The Easter computus and the origins of the Christian Era. Oxford Early Christian Studies. Xi + 474 pp (Oxford 2008): REVIEW

P. V. Kuzenkov,

School of History, Department of Church History, Moscow State Lomonosov University

From: Вестник Православного Свято-Тихоновского Гуманитарного Университета (Orthodox St. Tikhon Humanitarian University Herald) I, vol. 4 (28) (2009) 66-74.

Translated by Natalia Surina (Galway), with Dá ibhí Ó Cró iní n (Galway) & Leofranc Holford-Strevens (Oxford).

Alden A. Mosshammer, The Easter computus and the origins of the Christian Era. Oxford Early Christian Studies. Xi + 474 pp (Oxford 2008): REVIEW

This new book by Alden Mosshammer, emeritus professor of the University of California in San Diego and a renowned specialist in Byzantine chronicles, is devoted to a study of the origins of the Christian era of Dionysius Exiguus, the one that is used world-wide today. The author describes how, in the process of his research, his topic — originally defined as a study of Dionysius’s Paschal writings — grew into a much broader investigation. Encountering a problem with theories offered by modern scholarship that he found unconvincing, Mosshammer undertook a complete revision of every previous concept of the history of the development of the Easter reckonings in the 3rd to 6th centuries. While studying the problem of the origins of the Dionysian era, he discovered that it was difficult to work out on what basis so many oft-repeated scholarly statements had been made. In the Introduction (4) Mosshammer writes: ‘I came to the conclusion finally that the evidence has been misinterpreted and that much of the history of the Easter calculations of the early Christian church must be rewritten. What began as a study of the origins of the Christian era has therefore become as much a study of the origins and history of the Easter calculations’. It should be emphasised that very rarely in the world of scholarship does one encounter a work such as this, covering such a range of source-material at this level. The last such comparable work (in terms of volume) was published exactly half a century ago, and was the work of a French Byzantine scholar, Fr. Venance Grumel. [1]

The content of Mosshammer's book reflects the metamorphosis that it underwent in the process of its creation. After the first introductory part (3-58), briefly describing the basic concepts and principles of the calendar and Easter reckoning, comes Part II, entitled ‘The Easter Tables of Dionysius Exiguus’ (59-108). Clearly, this is the core that formed the basis of the author’s original plan of research. It describes at length and in great detail the Paschal works of the monk Dionysius, known by the self-deprecatory epithet of ‘small, humble’ (exiguus), who, in ad 525, took upon himself the labour of compiling a continuation of Cyril of Alexandria’s computus — the most perfect computistical system of that time — and in it numbered the years starting from ‘the Incarnation of Christ’, rather than from the era of the ‘tyrant and persecutor’, Diocletian.

However, the real central topic of the book is the most voluminous and groundbreaking part: ‘Paschal Calculations in Early Christianity’ (108 – 318). Here the evolution of the Christian computusis researched in great depth. It opens with a chapter reviewing the most ancient type of Paschal table — the 8-year cycle (mid-3rd century) and the problem of the invention of the so-called epacts (a key to the lunar calendar).

The next chapter is dedicated to the Paschal Canon of Anatolius of Laodicea (c. 277 ad), the first known computus based on a 19-year cycle. Here the author proposes his own reconstruction of Anatolius’s computus. Further on, he reviews the Paschal Letters of Bishop Athanasius of Alexandria, in which he finds attempts to adapt Anatolius’s cycle to the Western computistical tradition. In Moshammer’s view, the classical type of Alexandrian 19-year cycle was not constructed at the beginning of the 4th century — as was previously believed — but no earlier than the first decades of the 5th century, and was directly connected with the activities of the chronicler Annianus of Alexandria. In Moshammer’s opinion, Annianus’s world chronology became the system to which Cyril of Alexandria’s computus was ‘calibrated’ — the first known authentic Alexandrian computus of a classical type — which, in turn, was continued by Dionysius Exiguus.

In further separate chapters the author studies the ‘branches’ of the main stream of the computistical developments, both Western and Eastern. The chapter on 84-year-type Paschal calculations at Rome is a model piece of work, considering the scope of the sources and scholarly material used, and the author’s conclusions are convincing and clear. However, the picture he draws of 6th- and early 7th-century computistical and chronological debates in Byzantium, which culminated in the publication of the Paschal Chronicle, raises more questions. The book pays particular attention to this landmark work, whose unknown author suggested the computistically-based world chronology that became the basis for the Byzantine era.

The fourth and last part of the book (‘The Origin of the Christian Era’) brings us back to the author’s original purpose: the explanation of why Dionysius Exiguus set the 1^st year ab incarnatione domini nostri Jesu Christi (ad 1) in the year which the Greeks called the year of the 195^th Olympiad, and the Romans called the consulate of Gaius Caesar and Paul. After a brief summary of all available up-to-date scholarly data about Christ’s earthly chronology, and of the information that can be obtained from the ancient authors, Mosshammer shows that Dionysius’s date for the Incarnation strangely contradicts both the ideas of modern biblical scholars and the early Christian tradition — Eastern and Western. Nevertheless, the ‘offhand’ way in which Dionysius presents his era presupposes that not only did he not consider it necessary to prove its historical creditworthiness, he viewed it as something self-evident. This leads to the conclusion that Dionysius must have borrowed the Incarnation date from a reasonably reputable source.

In his search for this source, Mosshammer thoroughly examines three works that supposedly adopted a chronology similar to Dionysius’s: the Chronicles of Panodorus of Alexandria (c. 400 ad) and of Julius Africanus (c. 221 ad), and the Paschal Canon of Anatolius of Laodicea. None of these texts has survived. And even if the information about Christ’s chronology according to Panodorus has been passed down to us — though with some errors — by the Byzantine chronicler George Syncellus, the Incarnation date of Julius Africanus can be reconstructed only hypothetically, and the chronological anchoring of Anatolius’s Paschal Canon is even more obscure than its structure. Nevertheless, Moshammer moves confidently enough through reconstructions and hypotheses; ranging widely through such ambivalent and controversial sources as late Armenian colophons and inscriptions, he comes to the conclusion that, in his own Easter table, Dionysius Exiguus used the same ‘Christian era’ that had been proposed in the Chronicle of Julius Africanus, taken into account by Anatolius a little later in the creation of his Paschal Canon, and employed a century after that by the Egyptian Panodorus for his Chronology of the World. I take the liberty of quoting his full conclusion (437): ‘Antoine Pagi (1689: iv, xxxiii) had the right solution to the “Dionysian problem” after all. Dionysius Exiguus did not calculate or otherwise invent a new Christian era. He simply transmitted to the west a well-established tradition of the Alexandrian Church. Pagi said that Dionysius had adopted both the era of the Incarnation and the Paschal calculations of Alexandria. It is rather the case that Dionysius adopted his era of the Incarnation from the Alexandrians with their 19-year Paschal cycle. It was the Christian era of Julius Africanus, adopted by Anatolius of Laodicea, and transmitted along with the 19-year cycle to Athanasius, Andreas, Theophilus, Panodorus, and the Armenian Church, as well as to Dionysius Exiguus. ’

This is not the place for a detailed and critical evaluation of every element of Mosshammer’s theory. Even less is it necessary to point out the minor typos and errors, of which there are remarkably few in the book, which is wonderfully produced by this reputable publisher. I will only highlight the basic questions that suggest themselves in the process of reading this highly interesting, profound, and indeed ground-breaking work.

The author’s principal weakness is that he has not grasped the fundamental difference between the ancient 19-year lunisolar cycle — known as the ‘Metonic cycle’ — and the 19-year ‘lunar cycle’ of the Christian computus, adapted to the Julian Calendar. The Metonic cycle consists of exactly 6940 days, while its Julian adaptation comprises 6939¾ days, and (from the mathematical point of view) equates to the 76-year Callippic cycle. It is known that Julius Africanus was acquainted with the 19-year cycle in its classical form, which was inapplicable to the Julian calendar, and therefore to the Christian computus. Therefore, the theory of a computistical basis for Africanus’s chronology is utterly improbable (see the review of its reconstuction problem below).

It is deeply regrettable that, amongts over 330 scholarly books and articles used by the American professor, there are none of the works of the Russian scholars, Vasilij Vasiljevič Bolotov and Protoiereus Dmitrij Alexandrovič Lebedev (the holy martyr Dimitrij), both of which would be essential for this topic. And, while the absence of Bolotov’s work can be explained by the fact that his principal publications on the Alexandrian computus were printed in an almost inaccessible publication, [2][LHS1] the silence about Lebedev’s studies, published in Византийский временник/Byzantine Chronicle and other widely-known periodicals, [3] is surprising. Of course, Russian is difficult to understand; however, Grumel had no difficulty referring to Lebedev’s works and analysing his hypotheses, and Mosshammer frequently quotes Grumel. But most importantly, this omission has a fatal consequence for the credibility of the author’s concepts.

Lebedev based his reconstruction of Anatolius’s Paschal Canon on the notion of an originally classical structure for the 19-year cycle (with distribution of embolismic years of ogdoad[LHS2] + hendecad, 3. 3. 2. 3. 3. 3. 2|, in which | is a lunar-leap [saltus]), stemming from the Metonic and Babylonian cycles and preserved in the basic variations of the Alexandrian and the Judaeo-Christian 19-year cycle (Enneacaidecaeteris)). Unaware of this concept (which, in our opinion, was very convincingly demonstrated by Lebedev), Mosshammer suggests a reconstruction of Anatolius’s cycle that not only lacks the classical order expected in the oldest variation of the Enneacaidecaeteris but astonishes by its clumsiness: 3. 3. 2. 3|3. 2. 3. Mosshammer bases this on the assumption that Anatolius took the 21st of March as the date of the vernal equinox (p. 155 and elsewhere). This is the weakest of all the hypotheses in the book, and — alas! — Mosshammer’s entire theory of the evolution of the 19-year computus is built on this assumption. The 3rd- and 4th-century sources know the equinoctial date of the 22nd of March established by Ptolemy in 140 ad. [4] It is doubtful whether Anatolius, or the 3rd-century Alexandrian astronomers who were his contemporaries, would have established a new date of the 21st of March for the vernal equinox. Observing the equinox is a difficult technical task; all experiments of that sort were known to everyone and were immediately recorded in the annals of astronomical science. However, we know of no equinoctial observations by Alexandrian astronomers after Ptolemy. It is typical that Elias of Nisibis, who was deeply interested in astronomy, and who collected data of this type, mentions, immediately after Ptolemy’s observation, one of the autumn equinox by Arabic astronomers at the court of the caliph al-Maʾ mū n[LHS3] in 829 ad. [5] It is hard to believe that such a significant achievement as a correction of the vernal equinox date would have passed unnoticed by Anatolius’s contemporaries. On the other hand, it is not difficult to demonstrate that the equinox date of the 21st of March results purely mathematically from the structure of the Alexandrian type of computus.

The reconstruction of the Anatolian cycle suggested by Mosshammer raises a lot of questions. First of all, Anatolius’s manipulations of the classical structure of the Enneacaidecaeteris cycle established in the ancient world seem quite strange, considering that he was the first to promote the cycle — if he was not [indeed] its inventor[6] — assuming that he took the 22nd of March (26th of Phamenoth) for the beginning of the cycle, as a lunar equivalent of the last day of epagomenon (28th of August). But what is the practical convenience of this construction? It does not rid him of the necessity to calculate the annual lunar epact (i. e. the epact of the 1st of March, equivalent to that of the 1st of January). Besides that, there is no explanation of Anatolius’s words that, by the 22nd of March, the sun was already in its fourth day[LHS4] of passage through the sign of Aries. Considering that the entire quotation from Anatolius’s Paschal Canon, preserved in Eusebius’s Historia Ecclesiastica, [7] was dedicated to the necessity of placing the Paschal full-moon after the equinox, there is a question: why did Anatolius not mention his allegedly new date for this astronomical turning-point, the 21st of March? Furthermore, Mosshammer’s hypothesis of a transformation of Anatolius’s cycle into the Alexandrian cycle, which supposedly[LHS5] reverts to the classical form by retaining the limit of the 21st of March, suggests a very strange ‘evolution’ from the complex to the simple. No support for Moshammer's position is afforded either by references to the Ethiopian computus (which serves simply as a Coptic and an Ethiopian reflection of the Alexandrian cycle) or by debatable parallels with the cycle of ‘multipying by five and six’ (where the 12th-year analogue of the saltus follows automatically from the annual addition in their system of epacts of 5/60 day — 5/60 × 12 = 1 — that resulted of itself from considerations that had nothing to do with the Anatolian cycle). As for the reference to a 30-year Paschal cycle in a Verona manuscript, in the Easter dates presented there it is easier to discern a hybrid of an Alexandrian cycle with the Anatolian cycle in Eduard Schwartz’s reconstruction (of 45 Easter full-moons mentioned there, 25 dates coincide with them), than a resemblance to Mosshammer’s reconstruction (17 coincidences); besides, the use of this table in this context does not appear to be justified.

The next problematical subject relates to a new theory of the origins of the Alexandrian computus. Scholars since Ludwig Ideler have connected the origins of the Alexandrian 19-year cycle, starting from the 1st day of the 1st year of the Diocletian era (1st of Thoth, year 284), directly to the Diocletian era, whereas (according to Moshammer) the beginning of the Alexandrian cycle with the 1st year of the so-called Diocletian era is purely coincidental. To support this argument he offers a theory explaining the establishment of the Diocletian era through political reforms, which came about due to the loss of Egypt’s special status in the Roman Empire (174). However, it does not answer the question of why the years of Diocletian’s rule were used for the purpose of calculating the computus. True, ‘the Diocletian era’ was widely used in 4th-century Egypt, but there were other eras used along with it as well; for example, the Eras of Philippus and Augustus. For what other reason would Christians use the name of Diocletian — their principal persecutor — in their computus, if not as an obvious practical convenience?

It is clear from the Paschal prologues of Theophilus and Cyril that Alexandrian archbishops tried to dissociate Diocletian’s name from the computus, replacing it with the names of more pious emperors. Thus Theophilus, after starting his reckoning of years from the 1st consulate of Theodosius I (ad 380) in his Easter tables, solemnly writes to the emperor, saying that those wishing to know the exact date of the Easter ‘should use your name’, which ‘thus will remain in people’s memory forever’. His successor, Cyril, in order to connect the computus to Theodosius II’s name, uses ad 403, when the Emperor Arcadius proclaimed his new-born son a consul. Thus Mosshammer’s speculation that it was Cyril of Alexandria who ‘calibrated’ the Alexandrian cycle to the Era of Diocletian (193) looks particularly strange. At any rate, the fact that a new moon of the first cycle fell on the 1st of Thoth in the 1st year of the Era of Diocletian is too convenient for us to assume that its origins are coincidental.

It would be more logical to assume that Anatolius of Laodicea’s cycle was re-calibrated by his pupils at the beginning of the 4th century. If Anatolius set the beginning of the cycle at the new moon of the 26th of Phamenoth, which, as regards the lunar phase, is the same as the day before the 1st of Thoth, then the beginning of the Alexandrian cycle is the new moon of the 27th of Phamenoth, which, in terms of phases, is the same as the 1st of Thoth. The transition from one system to another is a mathematically graceful operation. If the cycle has a classical structure, the 21st of March naturally appears there as the boundary of the Easter limit. And it hardly bothered anyone that this date for the equinox agreed with astronomical realia of the 4th century much better. Any calendar is primarily a mathematical construct, in which the convenience of computations is valued much more highly than astronomical accuracy.

Furthermore, Mosshammer’s comparison of the Parisian computus published by André Van de Vyver with the data in the headings, and in the index to Athanasius the Great’s Paschal Letters, shows that they have a similar alternation of epacts 29, 11, 22 (in years 9-11 of Van de Vyver’s computus), which corresponds to epacts 30, 11, 22 in the first three years of the Alexandrian cycle. Mosshammer suggests (187-89) that a 95-year table for ad 334-428, and van de Vyver's computus, continuing it, are the cycle used by the anonymous author of the Index to Athanasius’s Easter Letters, if not by Athanasius the Great himself. This was supposedly a modification of Anatolius’s cycle, created with the aim of matching the dates of the 84-year Roman cycle for ad 343-345 and featured at the Council of Sardica in ad 353. However, our knowledge of the genesis of the Alexandrian cycle does not provide us with any basis for such an unusual step in its development. In Van de Vyver’s cycle the saltus is clearly in the wrong place, breaking up the already abnormal structure (3. 3. 1 | 1. 3. 3. 2. 3). This implies a hybrid variation of a 19-year cycle, in which the Anatolian cycle was adapted to the Alexandrian computus. This was done by a mechanical transfer of the saltus between the 9th and 10th years, and a shift of the embolismic month from the 17th to the 16th year. The fact that the saltus was placed after the 9th year, not after the 10th (which would make the entire sequence of Paschal full-moons identical with the Alexandrian) is puzzling. The modern Armenian computus, based on Andreas of Byzantium’s cycle, looks exactly the same. In our opinion, Van de Vyver’s table reflects this computus exactly. Mosshammer’s reasoning is acute; however, by his own admission, it is not compelling (189). No single reform could bring the 19-year cycle into harmony with the Roman 84-year cycle, and Athanasius’s Paschal Letters are a perfect proof of that. Their elements of adaptation to Roman practice are unsophisticated additions and corruptions, and make no pretensions to being systematic; on the contrary, the systematic occurrence of epact 29 in ad 342 and ad 361 (instead of the Alexandrian 30) is strangely not reflected in the Easter-date itself[LHS6].

In Mosshammer’s view, the coincidence of the beginning of the 19-year cycle with the beginning of the Era of Diocletian first occurred in Cyril of Alexandria’s computus, as a side-effect of the adaptation of the Anatolian cycle to Annianus’s chronological system developed between 392 and 412 ad. In this theory (198-203), it was precisely this era of Annianus that determined the classical look of the Alexandrian cycle that we encounter for the first time in Cyril of Alexandria’s computus. Cyril allegedly reformed the 19-year Anatolian cycle (which, in Mosshammer’s reconstruction, hardly differs from the Alexandrian) and brought its beginning forward by 8 years in order to align Annianus’s World Era (March 5492 bc) with the 1st year of the Paschal cycle. For that reason, Cyril had to add 4 ‘proleptic’ years before the opening date of his computus (Theodosius II’s first consulate, ad 403), which turned out to be the 5th year of the cycle. To justify this discord he states that the Paschal Canon must start from the beginning of the 19-year cycle. [8] But in that case Cyril's predecessor, Theophilus of Alexandria, should have started his computus from the 1st year of the cycle. This means that it is not a coincidence that the opening of Theophilus’s computus is dated to the first consulate of Theodosius I (ad 380), and not to his installation (ad 379); ad 380 fell exactly in the first year of the 19-year cycle. This can only mean that the Alexandrian Cycle ‘calibrated’ to the Diocletian era had already existed in the Theophilan computus that had been created before the system of Annianus, who was active in Arcadius’s times (between ad 395 and 412). And we have a direct proof of that in the source: the prologue to Cyril’s computus directly states that the cycle of Theophilus has a saltus at the end of the 19th year, like the Alexandrian cycle.

In my opinion, the relationship between the Annianus era and the Alexandrian cycle is exactly the opposite to the one offered by Mosshammer — the era followed the cycle, not the other way around. Not only can it be concluded logically, but it is also proven by the source texts. As was said above, Theophilus’s computus already corresponded to the Alexandrian cycle. For Cyril, his successor, the calculation of the years was unshakeable, and did not depend on any world era (to which he would not have omitted to refer, in order to justify a not very elegant opening of a computus dedicated to the emperor). As for Annianus, he uses the Alexandrian 19-year cycle as the main element of his system, criticising Eusebius of Caesarea for failing to place the Creation in the first year of the cycle in his chronology. [9] It is obvious that, in order to rebuke Eusebius with the help of what he calls a ‘cyclic Paschal tome’, Annianus would not only have had to be acquainted with the Alexandrian computus, he must also have been absolutely certain that this cycle has the only possible order of the years. Hence, by ad 412, when Annianus finished his work, the Alexandrian Enneacaidecaeteris must already have enjoyed an unquestioned authority, whereas, according to Mosshammer, it first appeared in Cyril’s computus, compiled around ad 430.

Let us look now at Mosshammer’s reconstruction of Julius Africanus’s chronological system (402-18). He suggests the 25th of March 5501 bc as the opening of Africanus’s era, dating the Incarnation to the 25th of March 1 bc, and the Resurrection to 25th March 31 ad. The dates themselves do not give rise to any objections; however, their conclusion is drawn on a very shaky basis. The main thrust of the proposed theory is an assumption that in Africanus the year starts in the middle of the Olympic year[LHS7]. However, Africanus conceives the Olympiad, not as a stretch of time, but as a single event. This indicates a regularly used verb ἤ χ θ η (meaning ‘passed’, ‘was carried out’), which is usually used for sports and feast-days. [10] It is the Olympiad that takes place in a particular year, not the year that begins in such-and-such an Olympiad. This is obviously proven by the example of the 189th Olympiad (ignored by Mosshammer). [11] Apart from that, a number of postulates in the same hypothesis (Philinus’ being an archon in the 1st year of the 250th Olympiad; the fall of Alexandria in the 2nd year of the 187th Olympiad) contradict the source text.

The 25th of March, the ‘key’ date for Moshammer's reconstruction, raises numerous questions. Every available source proves that, in the Eastern Christian tradition, this date did not have any significance until the end of the 4th century. In the first decades of the 3rd century, when Julius Africanus was working on his Chronicle, the 25th of March, having no connection either to the Creation or to the Incarnation, only barely begins to enter into the Western ecclesiastical calendar as the date of Christ’s Passion. [12]

In conclusion, it must be reiterated that the student of computus and chronology has at his disposal not only the texts (often corrupted by the scribes) but also the systems — mathematical calendar constructions based on various formal principles. On the one hand, this makes the task easier, since it provides additional tools to verify the text; but, on the other, it condemns the researcher to formulate hypothetical constructions and theories, based not so much on the particular evidence of the sources as on general logic — and in historical studies logical consistency is not valued nearly as highly as in science. Nevertheless, only a skilful combination of close adherence to the letter of the sources, so necessary for the historian, and an understanding of the mathematical logic of calendrical paschal systems, allows a successful advance. Alas! Alden Moshammer's fundamental work is vulnerable to the very criticisms of being hypothetical and of misinterpreting the sources that drove him to rewrite the history of the origins of the Christian computus and chronology in the first place. While meticulously following only the data that rest on a specific source, and trying to avoid speculative constructions as much as possible, Mosshammer was still obliged to propose a number of hypothetical reconstructions. But this made his theory lose the systematic and logical coherence that we find in Venance Grumel’s and Dimitri Lebedev’s concepts. However, the appearance of this new fundamental work in the history of chronology is undoubtedly a landmark event in historical science, and from now on Mosshammer's book is sure to become the new basis on which future researchers will build their works. Faciant meliora potentes!

[1] Venance Grumel, La chronologie (Paris 1958).

[2] V. V. Bolotov, [A report at a meeting on 31st of May 1899]// Russian Astronomical Society, The Journal of Russian Calendar Reform Committee. 1899. Appendix V. Re-published as ‘The Alexandrian computus: logic and aestethics’, in А. Чхартишвили (ed), Календарный вопрос (Мoscow 2000) c. 105-144 / Болотов В. В. [Доклад в заседании 31 мая 1899 г. ]// Журнал комиссии Русского Астрономического общества по вопросу о реформе календаря в России. 1899. Приложение V. Переиздано под названием «Александрийская пасхалия: логика и эстетика» в сб.: Календарный вопрос/ А. Чхартишвили, ред. М., 2000. С. 105-144.

[3] D. A. Lebedev, ‘On the history of ancient paschal cycles: the 19-year cycle of Anatolius of Laodicea’, Византийский временник/ Byzantine Chronicle 18/1 (1911 [1913]) 148-389 [Лебедев Д. А. Из истории древних пасхальных циклов: 19-летний цикл Анатолия Лаодикийского// Византийский временник. 1911 [1913] Т. 18. Отд. 1. С. 148-389]; idem, ‘Chronologicalnotes’, ibid, 18/2, 91-95 [он же Хронологические заметки // Там же. Отд. 2. С. 91-95]; idem, ‘More on the pseudo-Anatolius cycle’, Byzantine Chronicle 19 (1912) [1915] 152-158 [он же. Еще о цикле псевдо-Анатолия// ВВ. 1912 [1915]. Т. 19. С. 152-158]; idem, ‘The cycle of Anatolius of Laodicea according to V. V. Bolotov/ [он же. Цикл Анатолия Лаодикийского по В. В. Болотову. Etc... ]

[4]Accusing the author of the Constitutiones apostolicae of accepting the 22nd of March as a wrong date for the vernal equinox, Mosshammer forgets that the same statement is found in Epiphanus of Cyprus (Epiphanus, Panarion LI, 26-27 = Die griechieschen christlichen Schriftsteller 2 (Leipzig 1922) 297-98.

[5]E. W. Brooks (ed), Elia Nisibenus. Opus Chronologicum II (Louvain 1910) 45-46; Versio. P. 70

[6]Lebedev, ‘From the history of the ancient Paschal cycles, 238-99’ (Appendix A).

[7]Eusebius Caesariensis, Historia ecclesiastica VII. 32.

[8]Burns W. H., É vieux P. (eds), Cyrillus Alexandrinus. Epistulae paschales sive Homiliae paschales. Cyrille d'Alexandrie, Lettres Festales (Paris 1991) 220-21.

[9]A. A. Mosshammer (ed), Georgius Syncellus. Ecloga chronographica (Leipzig 1984) 36.

[10]See, for example, ibid., 231, 252, 255, 286 (three times) 297.

[11]ibid., 372-73.

[12]Tertullian, Adversus Judaeos 8. 18.

[LHS1]In the note: a policy matter whether Russian bibliography should be translated in Russian, English, or both. My inclination would be to keep titles at least in Russian (after all, if you can’t read it the article is no use to you anyway).

[LHS2]Or ogdoas and hendecas italic, as preferred.

[LHS3]The correct transliteration of ا ل م أ م و ن.

[LHS4]It is essential to retain the ordinal of Kuzenkov’s Russian, and Anatolius’ Greek, to indicate that the sun entered on 19 March, since ‘four days’ might mean that it entered on the 18th and this is its fifth day there.

[LHS5]An attempt at rendering (?! ); when I am feeling really rude, I say ‘forsooth’., but not may other people do.

[LHS6]The translation ‘final result’ is correct, but not too clear. The point is that even with epact 29, and hence luna XIIII on 11 Pharmouthi = 6 April instead of the 10th = 5th, in those two years Easter still falls on the same date (16 and 13 Pharmouthi = 11 and 8 April respectively; the first year in which it would have made a difference was 475, when Easter would have been celebarated on 18 Pharmouthi instead of the 11th. (This is, expressed in Alexandrian terms, the reckoning used by the non-Chalcedonian churches of Asia that led to their celebrating on 13 April instead of the 6th four years in every 532 down to 1824. )

[LHS7]That is what Kuzenkov says, unequivocally (literally ‘in the middle of the year of the Olympiad’): and it is true, insofar as Mosshammer takes Africanus to have operated with Roman years beginning on 1 January, cosmic years beginning on 24 March, and Olympic years beginning in summer. Admittedly the translation is more coherent, but it improves on the original.