Howlett2010 Computus in Hiberno-Latin Literature

8/19/2019 Howlett2010 Computus in Hiberno-Latin Literature

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Abstract The essay begins with an Introduction to the history of the Latin language,computus, and related disciplines in Antiquity before knowledge of thesubjects among the Irish; it proceeds with Part I, three Hiberno-Latin com-putistic texts, a note about the introduction of computus among the Irish,analysis of the beginning of Cummian’s Letter ofto Ségéne and Béccán,

and an edition, translation, and analysis of the preliminaries and dating clause of the Oxford computus of; it proceeds with Part II, a survey of Computistic Phenomena in Hiberno-Latin Literature under twenty-threeheadings, considering texts from the fifth century to the twelfth; it endswith a Conclusion.

Keywords Adomnanus, Aileranus Sapiens, Anatolius, Anonymus ad Cuimnanum, Augustinus Hibernicus, Auxilius, Béccán, Bede, Brianus Molosi Belli,Pope Celestine, Cogitosus, Columbanus, Conchubranus, Cormac, CúChuimne Sapiens, Cummianus Longus, Dicuill, Eusebius, Faustus Reien-sis, Gildas Sapiens, Gregory the Great, Gregory of Tours, Isidore, Isserni-nus, Jerome, Joseph Scottus, Laidcenn mac Baíth, Martianus Capella, MoSinu maccu Min, Muirchú moccu Macthéni, Palladius, Patricius, Pelagius,Prosper of Aquitaine, Ruben of Dairinis, Secundinus, Sedulius Scottus,Ségéne of Iona, Theodore of Canterbury, Tírechán; Ailerani Interpretatio

Mystica , Canon Euangeliorum, Annals of Ulster, Auraicept na n-éces , Cante-mus in omni die , Collectanea Pseudo-Bede , Collectanea Tirechani , CollectioCanonum Hibernensis , Columbani Carmen de mundi transitu, Precamur Patrem, Cummiani Celebra Iuda , Comm. in Marcum, De figuris apostolo-rum, De ratione conputandi , Penitentiale , De locis sanctis , De mirabilibus sacrae scripturae , De ratione paschali, Josephi Scotti Carmen figuratum, Liber

COMPUTUS IN HIBERNO-LATIN LITERATURE


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de mensura orbis terrae , Laidcenni Egloga , Lorica , Memoria abbatum nostro-rum, Patricii Epistola , Confessio, Saint Sechnall’s Hymn,Synodus episcopo-rum, Versiculi familiae Benchuir , Versus de annis a principio, VV.SS.Brigitae , Maedoci , Monenne , Patricii ; triuium, quadruuium, gematria,Hiberno-Latin grammar, computus, and literature, infixing of values of cardinal, ordinal, and calendrical numbers.

Introduction When military administrators and the legions left Britain early in

the fifth century the official language was, as elsewhere in the West-ern empire, high-register Latin, as illustrated in the literary works of the Romano-Britons Pelagius (†c. ) and Faustus, fourth son of Vortigern, abbot of Lérins, and bishop of Riez (†c. ),1 and in theepigraphic works of official inscriptions ofThe Roman Inscriptions of Britain.2 Personal inscriptions and graffiti show that Latin waswidely spoken and written in a demotic form that might haveevolved into something like the Old French of Gaul, but that lan-guage gave way to Old Welsh and Old English, leaving only thehigh-register literary Latin taught in the schools run by the civilianand ecclesiastical administrators who remained in Britain. Post-Roman Britons maintained the correctness of their Latin partly because, uniquely in the West, they learned and wrote it by thebook, without interference from a vernacular Romance language.Speakers of Vulgar Latin, proto-French in Merovingian Gaul,proto-Italian in Ostrogothic Italy, and proto-Spanish in VisigothicSpain, had to cope with a written language as far removed from

their spoken language as modern English is from the Middle Eng-lish of Chaucer, Gower, Langland, and the Gawain poet. They faceddifficulties comparable with those we would experience if we spokeas we do, but tried to write newspapers, parliamentary reports,wills, and funeral monuments in Middle English. The Briton GildasSapiens ( – c. ) continued to use Roman units of measure-ment,himina Romana andsextarius Romanus , in his Penitential, and

1 For bibliography of their works see Lapidge and Sharpe (), – . For analysissee Howlett ( a), – ; Howlett ( a), – .

2 Collingwood et al. ( ).

COMPUTUS AND ITS CULTURAL CONTEXT IN THE LATIN WEST, AD 300–1200


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in De excidio Brittanniae , published in , he wrote of Latin aslingua nostra , distinct fromlingua eorum, the Old English of theSaxons, of which he preserves the earliest written word,cyula , ‘keel’,‘boat’.3 In matters of orthography, grammar, syntax, and style theLatin of Gildas compares favourably with that of the native speakerGregory of Tours.

During the fifth century the Irish were evangelized by two mis-sions, one of the Romano-Gaul Palladius, a papal deacon sent by PopeCelestine in ,4 the other of the Romano-Briton Patricius, tradition-ally from .5 Both missions introduced converts to the literary Latinof the Bible and the liturgy. The Irish, like the Britons, learned and

wrote Latin by the book without interference from their vernacularGoidelic Old Irish. Unlike the Britons, however, they had no histori-cal experience of the Christian Roman Empire. As they were first out-with the empire to learn Latin as a completely foreign language, they needed forms of help the Britons had not needed. Recent studies by Vivien Law have shown that they had access to a wide range of LateLatin grammatical texts, sometimes in forms superior to those thathave descended directly to us.6 From these, devising a new form of Latin grammatical treatise that inculcated many things a nativespeaker would not need to be told, they created an extensive library of Insular Latin grammars,7 as well as new forms of script, half-uncial andminuscule, and either devised or developed many of the features wenow take for granted on a printed page – a hierarchy of scripts,8 dimin-uendo, separation of words by space, paragraphs, systems of punctua-tion, construe-marks, and glossing.9 As an index of the quality of Hiberno-Latin literature from its very beginnings, the Latinity of theworks of Columban of Bangor compares favourably with that of

3 Gildas,De poenitentia ; De excidio Britanniae , (Winterbottom ( ), , ).4 Lapidge and Sharpe ( ), – , and possibly Lapidge and Sharpe (),, the Synodus episcoporum.Howlett ( d); Ó Cróinín ( ); Ó Cróinín

( ).5 Lapidge and Sharpe ( ), – . Howlett ( a); Howlett ( – a).6 Law ( ); Law ( ).7

Lapidge and Sharpe ( ), – , , – , , – , , – , , – .8 For a perfect example see Faris (), text – , facsimile – .9 Stokes and Strachan ( ); for facsimiles of glossed manuscripts seeCLA ,

andCLA , and Stern ( ); Draak ( ), – ; Parkes ( ), repr. in Parkes( ), – ; Saenger ( ).



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spaces between words, coincident with the number of days from Jan-uary to March, the day of the vernal equinox. Betweensolis ascen-sum descensumque relinquentes | in line and | et solis transcensuminline there are words, coincident with the number of days from January to June, the day of the summer solstice.14 Within these

bounds there are eighty-four words before |nonnulli octoginta quattuor line , in which the thirtieth letter is the last oftriginta.

In connecting part IIII with part V, if one begins counting at| Conputa in line the seventieth word brings one to |septuaginta .

In part VI, if one begins counting at | primi in line , the one-hundredth word brings one tocentessimam| .

In part VII sentence ii the sixteenth word issextam| decimam ,and there are seventeen words before |et septimam decimam . Afterseptimam decimam| there are seventeen words to the end of the sentence.

In part VIII sentence i the nineteenth word isdecem| et | nouem,nouembeing the nineteenth word from the end of the sentence.

In part X sentence i line , conspicuous for play onand ,there are nineteen words fromdecem et nouem| to the end of the sentence.

In part XI sentence ii there are fromocto| to duodecim|twelve words, and from |id est prima pars to duodecim| twelvewords. At the end of part XI in sentences x and xi there are afterocto| eight ( ) words to the end of the chapter, betweenin octo|and |in octo sixteen ( ) words, from |in octo to | in octo thirty-two ( ) words. In the same passage there are from |duodecim

to duodecim| twelve ( ) words, from |duodecim toduodecim | twenty-four ( ) words, from |duodecim

to duodecim| twenty-four ( ) words, and from |duodecim to duodecim| thirty-six ( ) words.The Introduction to this twelve-part text consists of the title and

twelve sentences. Anatolius states the need to incorporate solar reckon-ing into calculation of the date of Easter, and the translator supportsthe calendrical subject of his author’s narrative with a title that con-tains thirty letters, for days of a solar month. The twelve sentences represent months of a solar year, and thewords the number of degrees in a circle. Including the title thewords represent the number of days of an ordinary solar year.

14 See below p .



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The Introduction both announces the subject and fixes the structure of the entire composition, the twelve introductory sentences prefiguring the twelve parts, and the reference to the eighty-four-yearcycle prefiguring the eighty-four sentences, and thewords prefi-guring the lines of the whole.

After the Introduction parts I and XII, the beginning and the end,confirm again the structure of the entire composition. Part I fixes thebeginning of the first month four ways, as reckoned by the Egyptians,by the Macedonians, and by the Romans in two ways, forward fromthe beginning of March and backward from the beginning of April.The chiastic pair to part I is part XII, which contains twelve lines, the

subject being the four seasons. The number of lines in the Intro-duction ( ) equals the number of lines in part I () added to thenumber of lines in part XII ().

The forms of corroboration are related but independent: first,confirmation of the numerical values of numerical words by theirplacement within discrete lines of text; second, confirmation of thenumerical values of numerical words by their placement within sen-tences longer than discrete lines and between adjacent sentences;third, coincidence of the numerical values of numerical words withthe numbers of the lines in which they occur, both within discretechapters and in the entire composition; fourth, coincidence of the numerical values of numerical words with the numbers of the sentences in which they occur, both within discrete chapters andin the entire composition; fifth, play with calendrical numbersof cycles, years, months, days, hours, and moments, and with thenumbers of equinoxes and solstices; sixth, incremental infixing of relations among numbers of progressively larger units, letters,

syllables, words, sentences, lines, parts or chapters, and the entire composition.This is a text with which the Irish began, from which they learned

much and forgot nothing. In addition to the calendrical reckoning learnedfrom this fundamental text, another feature that involves counting recursthroughout Hiberno-Latin literature – gematria, Hebrewℵyrj+jmyg, perhaps borrowed from Greekγεωµετρια , the calculation of numerical values of personal names, place-names, and words. As every letter of the alphabet, in Hebrew, Greek, and Latin alike, bears numerical valueas well as phonetic value,ℵ , b , g , A , B , , A , B , C , every word exhibits a number as well as a semantic


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meaning.15 The text of the Hebrew Old Testament is filled with this arti-fice, a notable example occurring in Jds: – , in which the nameblkCaleb, of which the alphanumeric value is, is the fifty-second word.16The most famous example in the Greek New Testament occurs in Apoc

: , in which the number of the beast,εξακοσιοι εξηκοντα εξ , ,exhibits descending value of the Roman numerals DCLXVI. This num-ber is the sum of the letters of the Latin name NERO CAESAR, spelled inHebrew lettersrsq !wrn, or . Theexample best known in a Latin literary text is Martianus Capella’sDe Nup-tiis Philologiae et Mercurii , in which at the beginning of book II Philologia reckons multilingual gematria on her name and that of Mercury to deter-

mine their compatibility. For a ‘smoking gun’, consider a fourteenth-century Anglo-Norman poem that refers to gematria during the practiceof it:17

Dieux soit ou vousquant vous alietz a Et de vos malx vous doynge pa rdonne b Pensez de moyquant meux porretz a Qe [i.e. setante huit] hauetza nonne. b

‘May God be where you [be] when you go,and for your sins may He grant you pardon.Think of me when best you can,you who have for a name [the number].’

In the right margin against these lines, of which the sense is clear, themetre perfect, and the rhymes pure, is a crown over the number. Inthe twenty-three-letter Latin alphabet

E D V A R D I I I or .

15 For a tabulation of the Hebrew system see Gesenius, Kautzsch and Cowley ( ), (§ . ). For evidence of knowledge of the shapes and names of letters of theHebrew alphabet see the seventh-century Old-Irish text Auraicept na n-éces (Calder( ), – , – ). For early Insular explications of the Greek system see Bede,De temporum ratione (CCSL B, – ), and the seventh-century Auraicept na n-éces (Calder ( ), – ). For actual calculation of Greek values see the eighth-century Hiberno-Latin MS Milano, Biblioteca Ambrosiana, Fsup, r.

16 Howlett ( a), – .17 Howlett ( d), – .



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Part I: Computistic TextsOn Mo Sinu maccu Min

One of the oldest extant Latin texts written in Ireland is a note, now pasted into MS Würzburg, Universitätsbibliothek, M.p.th. f., aboutthe introduction of computistic learning into Ireland during the second half of the sixth century,18 that offers valuable evidence of various forms.

Mo Sinu maccu Min scríba et àbbas Bénncuir [space]primus Hibernensium computum a Graeco quodam sapiente

memoráliter dídicitDeinde Mo Cuoroc máccu Net Sémonquem Romani doctorem totius múndi nominábant [space]alumnúsque praefàti scríbae —in insula quae dicitur Crannach Duin Lethglaisse hanc scientiam

líteris fíxitne memória làberétur.

In this text the scribe has separated the words with spaces, marking fourof the seven commas specially, two with extraordinarily long spaces,one with a dash, and the last with a punctuation point. The writer hassimultaneously fulfilled the requirements of two systems of elegantprose composition, both quantitative metricalclausulae and stressedrhythmiccursus , making patterns of the forms. The number of letters,

, coincides with the number of days from the Annunciation, cele-brated on March, to the Nativity, celebrated onDecember.19

Two cultures that exhibit long traditions of transmission in literary form, one Sanskrit, another Hebrew, also exhibit long traditions of

transmission in oral form. This note bears eloquent witness to immer-sion in both forms of transmission from the very beginnings of theHiberno-Latin tradition: primus memoraliter didicit , deinde scientiamliteris fixit ne memoria laberetur.

Epistola Cummiani

I have tried on earlier occasions to understand the oldest extant com-putistic text from Ireland, Cummian’s Letter to Ségéne abbot of Iona

18 Lapidge and Sharpe ( ), . Ó Cróinín ( a), ; Howlett ( b), – ;Howlett ( b), – .

19 For other examples see Howlett (a), n ; Howlett ( a), , – ,– ; Howlett ( b).



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and Béccán the hermit about the Paschal controversy,20 a text thatattests the author’s knowledge of ten different computational cycles, a text filled with varied forms of computistic artifice. In the Letter, thatcan be dated internally to, Cummian wrote to precede and follow his fifteen-part argument an introduction and a conclusion, chiasti-cally arranged ABC–C’B’A’, that containwords. Here follow somephenomena from the beginning of the text, the invocation, salutation,and first two sentences, not noted earlier.

IN NOMINE DIVINO DEI SUMMI CONFIDODominis sanctis et in Xpisto uenerandis Segiéno abbáti

Columbae sancti et ceterorum sanctórum successóriBeccanoque solitario caro carne et spiritu fratri cum suissápiéntibus

Cummianus supplex peccator magnis minimus apologiticam in Xpísto salútem

Verba excusationis mee in faciem sanctitatis uestre proferre procáciternon aúdeo

sed excusatum me habere uos ut pátres cúpio

testem Deum inuocans in ánimam méamquod non contemptus uestri gratia nec fastu moralis sapientiecum ceterórum despéctu

sollemnitatem festi paschalis cum ceteris sapiéntibus suscépiEgo enim primo anno quo cyclus quingentorum triginta duorumannorum a nostris celebrari orsus est non suscépi sed sílui [. . .].

From Segieno abbati | to Beccanoque solitario| there are seventy-one letters and spaces between words, coincident with the alphanumeric

value of SEGIENO, or . From |Dominis toColumbae | there are sixty-three letters and spaces between words, coin-cident with the alphanumeric value of COLUMBA,

or . BetweenColumbae | and |Beccanothere areforty-one letters and spaces between words, coincident with the alphanu-meric value of BECCANO, or . One notesthat the value of Cummian’s father’s name, FIACHNAE,

or , added to the value of his mother’sname, MUGAIN, or , equals that of his

20 Lapidge and Sharpe ( ), . This text is discussed, edited, and translated by Walsh and Ó Cróinín ( ), – . Howlett ( b), – ; Howlett ( a), – ;Howlett ( b), – .



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own name, CUMMIANUS, or.21 FromCummianus | to | Cummiani there are letters and spaces

between words. One notes further that from |Dominis sanctis et in Xpistouenerandis to Ego enim primo anno quo cyclus quingentorum triginta duo-rum | annorumthere are letters.22

Cummian wrote hisEpistola three years before the death of Isidoreof Seville in , seven years before Braulio’s publication of Isidore’sEtymologiae in . By the time someone in the circle of Cummian,probably Cummian himself, wroteDe ratione conputandi , texts of Jerome’sChronicon, Isidore’sEtymologiae , and Martianus Capella’sDe nuptiis Mercurii et Philologiae had arrived in Ireland. All are cited

explicitly in the following text.Computus Oxoniensis

MS Oxford, Bodleian Library, Bodley, r–v, a manuscript of the eleventh century from Vendôme, contains a seventh-century Hiberno-Latin computus.23 A version of the text was printed incom-pletely during the nineteenth century inPatrologia Latina XC – ,and the prologue and chapter headings were printed once during the

twentieth century.24

In the new edition of the preliminaries that fol-lows, to the left of the text Roman numerals mark numbers of sen-tences. Within the textlitterae notabiliores and punctuation marks inboldface represent features of the manuscript; acute and grave accentsmark the rhythms of the cursus ( planus , maiórum collécta ; tardus , pártes diuíditur ; uelox , paúca dictùri súmus ; medius , Iánuárii ; trispondi-acus , númerus procéssit ; dispondeus dactylicus , créscunt de minóribus );and italics suggest possible rhymes. To the right of the text letters rep-resent a possible rhyme scheme, and Arabic numerals mark numbersof lines.i De numero igitur fratres dilectissimi Deo adiuuante

paúca dictùri súmus. secundum modulumingenioli nostri sed tamen ex auctoritatemaiórum collé cta . a

21 For play on the identical values of the names of Patrick’s fatherCalfarnioand his

motherConcessa , each worth , coincident with the number of syllables from |Calfarnioto Concessa |, see Howlett ( c), .22 See below p .23 Lapidge and Sharpe ( ), .24 Jones ( ), – .



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ii Primum nobis interrogandum est unde primum;hec ars que numerus uel computus diciturínitiáuit . b

iii Deinde postea scire debemus ex qua radicesapientie númerus procéssit . biiii Scimus enim quod omnis sapientia siue diuina

siue humana philosóphianùncupátur . cv Et illa philosophia in tres pártes diuíditur . c

et pars philosophie que dicitur phisica in quatuorpartes diuísa uidétur ; c

vi Sic etiam et ethica secunda pars philosophiequatuor diuísiones hábet . b

vii Tertia autem logica dúas diuìsiónes; ex qua ergodiuisione hec ars númeri procédit . demonstrárinecésse est . b

viii Et postea etiam scire conuenit quis primus inuenitnumerum apud Hebreos et Chaldeos et Persoset Egiptios et apudGrécos et Latínos ; d

viiii Ac deinde inuestigari oportet quo modo numerusin linguis principálibusnùncupátur . c

hoc est apud Hebreos et Chaldeos et Persos et

Egiptios et Macedones etGrécos et Latínos ; dx Et illud nomen quod dícitur númerus dsi simplex ést an conpósi tum. esi primitiuum sit an dériuatí uum. eet quo modo definitur scíre nos cónuenit . b

xi Dehinc etiam interrogare debemus quo modonumeri nominantur apud Grecos ab uno usquead mílle et mỳriádes . d

et que note significant illos números àpud Grécos . dxii Nec non etiam scíre nos opórtet. que note

significant istos numeros ab uno usque ad milleet myriades ápudLatínos . d

xiii Deinde etiam oportunum interrogandum est quotsunt diuisiónes témporis . d

et ille diuisiones maiores créscunt de minóribus . d xiiii De athomis étiam tractándum est . bxv De momentis . dxvi De minutis . dxvii De punctis . dxviii De horis . d xviiii De quadránte naturáli . f xx De quadrante ártificiáli . f xxi De diebus . d



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xxxxvii De initio quádragési mi . f xxxxviii De terminis quádragesimálibus . dxxxxviiii De prima lúna primi ménsis . dl De términis paschálibus. et de illorum réguláribus . dli De pascha . a lii De terminis rogationum. eliii De rogátiónibus . dliiii De cóncurréntibus . dlv De cyclo solari et lunari per dígitos dèmonstrándis . dlvi De concurrentibus demonstrandis per cýclum solárem. e lvii De bissexto monstrando per cýclum solárem. elviii De zodiaco circulo et de xii signis celi et eórum

nomí nibus ; dlviiii Decursu solis et lune per xii [duódecim] sígna . a lx De vii stéllis errántibus ; dlxi De ascensu solis et descensu hoc est quo modo

crescit dies uel no x . d lxii De eclypsi sólis et lúne. hlxiii De numero momentorum et minutorum

et punctorum et horárum totìusá nni . f lxiiii De epacta monstranda et de feria querenda a

presente qualibet die: úsque ad cèntum ánnos . dlxv De computo Grecorum et Latinorum per litteraset dígitos dèmonstrándo. g

lxvi De epístolis Grecórum. e lxvii De Anatholio ét Macróbio. g lxviii De Victorio et Díonísio. g lxviiii Dé Boétio. g lxx De calculo. g

sumus deest. compotus. iniciauit. fisica. quattuor. a&hica.quattuor. loica. et persos desunt. deriuatiuumwith i written in a later hand above e. diffinitur. miriades. quot with t writtenabove erased d. diuisioniswith fourthi changed toe. astificiali.embolismi. desentiuntwith iswritten above erased first e. salareswith o writtenabove first subpuncted a. mensiswith i corrected toe. quattuor. a&as. zoziaco. anniswith o written above subpuncted i. compoto. gregorum. gregorum.

i About number, therefore, most beloved brothers, with Godhelping, we are about to say a few things according to thelittle measure of our little intellect, but neverthelessgathered together from the authority of greater men.



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ii First it must be asked by us whence first this art, which iscalled number or computus [lit. ‘reckoning together’],began.

iii Then after these things we ought to know from what rootof wisdom number proceeded.iiii For we know that all wisdom, whether divine or human,

is designated philosophy.v And that philosophy is divided into three parts,

and the part of philosophy that is called physics is seendivided into four parts.

vi And so also ethics, the second part of philosophy, has fourdivisions.

vii The third, however, logic, two divisions, from whichdivision, therefore, this art of number proceeds needsto be demonstrated.

viii And after these things it is convenient [lit. ‘it comestogether’] to know who first discovered [lit. ‘invented’,‘came upon’] number among Hebrews and Chaldeansand Persians and Egyptians and among Greeks and Latins.

viiii And then it is opportune that it be investigated in whatmanner number is designated in the principal tongues,

this is among Hebrews and Chaldeans and Persians andEgyptians and Macedonians and Greeks and Latins.x And that word [lit. ‘name’] that is called number, whether

it is simple or composite, whether it may be primitiveor derivative, and in what manner it is defined it isconvenient for us to know.

xi Then also we ought to ask in what manner numbers arenamed among the Greeks from one up to a thousandand ten thousands, and what notes signify thosenumbers among the Greeks.

xii And also it is opportune for us to know what notes signifythose numbers from one up to a thousand and tenthousands among the Latins.

xiii Then also it is opportune for it to be asked how many arethe divisions of time, and in what manner those greaterdivisions grow from the lesser.

xiiii About atoms is also to be treated.xv About moments.xvi About minutes.xvii About points.xviii About hours.xviiii About the natural quadrant.xx About the artificial quadrant.



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xxi About days.xxii About weeks [lit. ‘seven-day periods’].xxiii About lunar months.xxiiii About solar months.xxv About the order of months.xxvi About their discovery [lit. ‘invention’, ‘coming upon’].xxvii About the number of months among the ancient Romans.xxviii Then also it is to be asked from what time months were

discovered [lit. ‘invented’, ‘come upon’] and designated,and in what number of days months consist in the sunand the moon, this is in a common year and anembolismic [year] and in a solar year, and in what

manner those years disagree [lit. ‘sense or experienceapart’] and agree [lit. ‘come together’] amongthemselves, and who they are who first discovered [lit.‘invented’, ‘came upon’] solar months, and in whatmanner the months are named among Hebrews andEgyptians and Macedonians and Greeks and Latins,and how many are the causes from which monthsreceived names.

xxviiii And after these things is to be investigated about the four

times of the year.xxx Then also is to be treated about years and about kinds ofyears and about the number of years from the origin[lit. ‘rising’] of the world up to the Incarnation ofChrist.

xxxi About the number of years from the Incarnation ofChrist up to the present time.

xxxii About the bissextile [lit. ‘twice-sixth’ (day),Februaryand the following intercalary day inserted into leapyears of the Julian calendar].

xxxiii About the leap [year].xxxiiii About the indictions of the Romans.xxxv About the nineteen-year cycle.xxxvi About the lunar cycle, and who discovered [lit. ‘invented’,

‘came upon’] the first nineteen-year cycle and thelunar cycle, and in what time they were discovered[lit. ‘invented’, ‘come upon’].

xxxvii About the cycle of epacts on the eleventh of the kalendsof April.

xxxviii About the epacts that run on the kalends of January.xxxviiii About the epacts on the kalends of the twelve months.xxxx About the epacts of every single day through the

whole year.



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xxxxi About the holy day to be shown on the kalends of January.xxxxii About the holy day on the kalends of the twelve months.xxxxiii About the holy day to be sought on every day.xxxxiiii About the holy day in the term [limit] of Easter.xxxxv About the moon, in which hour or in which point it is

illuminated or its own age is changed on every day.xxxxvi About the moon, in how many hours it shines on every

single night.xxxxvii About the beginning of Lent [lit. ‘the forty-day period’].xxxxviii About Lenten terms [limits].xxxxviiii About the first moon of the first month.l About Lenten terms [limits] and their rules.

li About Easter.lii About the terms [limits] of Rogation [days].liii About Rogation [days].liiii About concurrent [numbers, lit. ‘that run together’,

e.g.concurrence between January and March,the former occurring on Sunday entailing the latteroccurring on Friday].

lv About the solar cycle and the lunar to be demonstratedon the fingers.

lvi About concurrents to be demonstrated through thesolar cycle.lvii About the bissextile to be shown through the solar cycle.lviii About the circle of the zodiac and about the twelve signs

of heaven and their names.lviiii About the course of the sun and the moon through the

twelve signs.lx About the seven wandering stars.lxi About the ascent and descent of the sun, this is in what

manner the day or night increases [lit. ‘grows’].lxii About the eclipse of the sun and the moon.lxiii About the number of moments and minutes and points

and hours of the whole year.lxiiii About the epact to be shown and about the holy day to

be sought from a certain present day up to a hundredyears.

lxv About the computus [lit. ‘reckoning together’] of the Greeksand Latins to be demonstrated through letters and fingers.

lxvi About the epistles of the Greeks.lxvii About Anatolius and Macrobius.lxviii About Victorius and Dionysius.lxviiii About Boethius.lxx About calculus.



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The short list of rejected manuscript readings suggests that this is a good copy of the original text. Three features suggest the influence of a Continental Francophone scribe, who for the author’se , as inhec ,sometimes wrotee caudata , as inque ˛ , sapientie ˛ , philosophie ˛ que ˛ ,he ˛c , hebre ˛os , que ˛ note ˛ , , ille ˛ , que ˛ , ce ˛li , lune ˛ , ,restored here toe , andiniciauit for originalinitiauit , andloica forlogica.25 To the author’s originalquatuor the scribe added a super-scriptt and wrotequattuor subsequently. Two features suggest that anexemplar was Insular. In lineastificiali implies a misreading of Insular longr as longs. In lines and gregorumillustrates theidentity of voiced g with unvoicedc among speakers of Celtic lan-

guages. If one reckons critically, the scribe miswrote sixteen charactersper thousand or, omitting consideration ofe caudata , eleven charac-ters perthousand.

Our computist’s prose is elegantly rhythmical. Of lines containing more than four syllables all but two (. of the whole) exhibit fault-less cursus rhythms, and with simple reversal of word order both of those would exhibit correct rhythms,rogatiónum términis andcréscit nox uel díes .26

Our computist made his words for cardinal and ordinal numbersexhibit their values by their placement within discrete lines.

The seven words of linedivide byepitritus or sesquitertian ratio: at | tres.

In line the fourth word from the end isquatuor.The ten words of linedivide into two parts atsecunda | pars.They

divide into quarters inquatuor. From |secunda to quatuor | there arefour words.

In line the five wordstertia autem logica duas diuisiones divide by

hemiolus or sesquialter ratio: at | tertia and |duas.In line the eight words divide into quarters atquatuor |.In line the twelfth syllable is the last ofduodecim, and the twelfth

letter from the end isduo | decim mensium.In line the twelfth syllable is the last ofduodecim, and the twelfth

letter from the end isduo | decim mensium.In line there are twelve syllables after xii |.


25 For other examples of the influences of Francophone scribes on early Insulartexts see Howlett and Thomas (), ; Howlett ( c), .

26 An additional argument for reversal of these words is the priority of night to day in Gen : : factumque est uespere et mane dies unus.


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Employing another form of artifice our computist wrote thirty-three letters beforeDeo , coincident with the thirty-three years of thelife of Jesus.

Our computist also made his words for cardinal and ordinal num-bers exhibit their values by their placement in units that extend beyonddiscrete lines, as in pars philosophie , secunda pars philosophie , andtertia autem .

From |unde primum hec ars to usque | ad mille there areletters.

Fromnumerus | to ab uno usque | ad mille there are lettersand spaces between words.

There are from |quadrante to quadrante | four words.In lines – there are fromcyclo| decennouenali to |cyclum decen-nouenalemnineteen syllables.

In lines – there are from | xii [duodecim] to |vii seven syllables.From |duodecim to centum| there are one hundred syllables.Fromcentum| annos to De epistolis Grecorum| there are one

hundred letters and spaces between words.Our computist has arranged words and ideas in a comprehensive

chiastic pattern.

A De numeroB ex auctoritate maiorumC computusC a diuisionesC b scire conuenitC c numerumC d apud Hebreos et Chaldeos et Persos et Egiptios et

apud Grecos et LatinosC e quo modo numerus in linguis principalibus

nuncupaturC d’ apud Hebreos et Chaldeos et Persos et Egiptios et

apud Grecos et LatinosC c’ numerusC b’ scire nos conuenitC a’ diuisionesD crescuntD – De momentis, minutis, punctis, horis

E De bissextoF cyclum decennouenalem et cyclumlunarem

G – De epactis



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H – De feria I – De luna I – De quadragesima I’ De prima luna primi mensisI’ – De pascha H’ – De rogationibusG’ De concurrentibusF’ De cyclo solari et lunariE’ De bissextoD’ crescitD’ De numero momentorum et minutorum et

punctorum et horarum

C’ computoC’ Grecorum et LatinorumB’ – De Anatholio, Macrobio, Victorio, Dionisio, Boetio A’ De calculo

The crux of the chiasmus shows the focus of the computist’s interest,the reckoning of the dates of Lent and Easter.

The text contains words. In hisEpistola , published AD ,Cummian wrote words in the Prologue and Epilogue, and in hisHistoria ecclesiastica gentis Anglorum, published AD , Bede wrotewords in the Prologue.27 If our computist did something similar,one might infer a date of composition in Anno Passionis .

Professor Dáibhí Ó Cróinín has drawn attention to the dating clause in the text of the computus that follows in MS Oxford,Bodleian Library, Bodley:28

Omnibus annis temporibus diebus ac luna maxime que iuxta Hebreos menses facit rite discussis a mundi principio usque indiem quo filii Israhel paschale mysterium initiauereanni sunt IIIDCLXXXVIIII precedente primo mense VIII kalen-das Aprilis luna XIIII VI feria Passum esse autem Dominum nostrum Ihesum Xpistum peractisV̄CCXX et VIII annis ab exortu mundi eadem cronicorum rela-tione monstratur VIII kalendas Aprilis primo mense luna XIIII VIferia

27 Howlett ( b), – . For other examples see Howlett (a), – , – ;Howlett ( a), – ; Howlett ( a), – , – , – , , ; Howlett ( c),

; Howlett ( a), – , – , – , – , – ; Howlett ( a), – .28 Ó Cróinín ( a), , repr. Ó Cróinín ( ), – .



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Inter primum pascha in Egipto et passionem Domini anni suntĪDXXXVIIII R,

Ex Domini uero passione usque in pascha quod secutum est Suib-ini filii Commainni anni sunt DCXXXI A pascha autem supradicto usque ad tempus prefinitum consum-mationis mundi id est sex milibus consummatis anni sunt CXLI

The mathematics of the text are straightforward enough: from the Pas-sion to the year of writing is(DCXXXI) years. To reduce a Victoriananno passionis date to its AD equivalent, add: AD . Thesecond clause in the dating formula provides confirmation of this: fromthe time of writing to the end of the world – traditionally set at AM(as in the poemDeus a quo facta fuit )29 – is (CXLI) years. AM

AM . To reduce this Victoriananno mundi reckoning to AD, subtract : AD . Both formulae, therefore, givethe date of writing as AD. But the date is further specified by theaddition of a most important detail: the author counted from the Passionusque ad pascha quod secutum est Suibini filii Commani , ‘the Easter of Suibine mac Commáin which has just ensued’. That is to say, the author

was referring to a Victorian Easter-table in the margin of which, besidethe data for the current year, was noted the death of one Suibine macCommáin. And the annal is preserved independently in the Annals of Innisfallens.a. AD : Kl. Dub Tíre ua Maíl Ochtraig Conaing mac Muricáin Suibne mac Commáin.30Most importantly of all, however, theIrish compiler of the computus calculated from the pasch of Suibine macCommáin, that is the Easter of the year in which he died. Easter fell on

March in AD , so the computist must have been writing after thatdate. He was undoubtedly resident in southern Ireland.

As the Prologue containswords, so this passage containslet-ters. Further confirmation of the date Anno Passionis and AnnoIncarnationis is that in the Prologue from |Deinde etiam interrogandum est to De numero annorum ab incarnatione Xpisti | usque ad presens tempus there are letters and spaces between words.

The text of the Prologue contains seventy sentences and eighty-four lines, appropriate numbers for a computist. We may observe in

29

Lapidge and Sharpe ( ), . Howlett ( a), – . This poem, composed AD , may provide both aterminus ante quemfor the arrival of Jerome’sChroniconand Isidore’sEtymologiae in Ireland and a model for our computist’s threefold mannerof dating his text. See below pp.– .

30 Mac Airt ( ), – .



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suffragans to Palladius, not to Patrick, one infers from the dedica-tions of churches to them that they worked in central and south-eastern Ireland, while Patrick worked in northern and westernIreland.33 The acts of the synod might be dated after the arrival of Palladius in and the others in , between the death of Secun-dinus in and the death of Auxilius in , perhaps to the year

, when Anno Domini.cccc o.l o.uii o. Calcedonensis senodus congrega-tus est . The acts issue from a time during which authority over a clericus qui de Brittannis ad nos uenit mattered, a time during whichmore Romano capilli tonsi mattered. The text, which is well com-posed, exhibits both the elegant quantitative metrical rhythms of

clausulae and the stressed rhythms of thecursus.In addition to many other phenomena infixed to guarantee the authenticity andintegrity of the text, the word ‘half way’ through sentence, line

, isdimidium, and the twentieth letter from the end of the line isthe first ofuiginti.There are forty sentences before canon xxviii, inwhich the second line, containing the wordquadragesimum, con-tains forty letters. Canon xxxiv contains thirty-four syllables. TheIncipit, which contains fifty-three letters, is the key to the prelimi-naries, which contain fifty-three words, and to the complete text,which contains fifty-three sentences, the penultimate sentence con-taining fifty-three letters and spaces between words. The fifty-threesentences divide by extreme and mean ratio atand , divid-ing by the same ratio at and . In the twentieth sentence, asnoted above, the twentieth letter from the end is the first ofuiginti ,and after twenty intervening sentences the thirteenth sentence fromthe end, the line that contains the wordquadragesimum, containsforty letters. From the beginning of theSalutatio to the end of the

Captatio beneuolentiae , from |Gratias agimus to Melius est arguere quam irasci | there are thirty-six words. The preliminaries endExempla definitionis nostrae inferius conscripta sunt. et sic inchoant.,two phrases which contain seventy-two letters and spaces and punc-tuation points ( ), which introduce thirty-six canons. From |Gratias agimus to salutem.; | there are letters and spaces andpunctuation marks, the key to syllables in the preliminaries.From |satius to irasci | there are letters and spaces and punctua-tion marks, the key to lines of text.

33 Thomas ( ), (fig. ).



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Patricii Epistola et Confessio

Two other fifth-century texs that certainly belong in the Patrician

dossier are Patrick’s ownEpistola ad milites Corotici andConfessio,34

thetexts of which he fixed in various ways.The Epistola is exactly CCXXII or lines long, the number of

lines in part I, , relating to that in part II,, by symmetry,: , thatin part III, , relating to that in part IIII,, by extreme and meanratio, dividing by the golden section atand . One can be cer-tain that the number of lines is correct by comparing the thirty-sixthline of part I,lupi rapaces deuorantes plebemDomini , with the thirty-sixth line of part III,lupi rapaces deglutierunt gregemDomini , andwith the the thirty-sixth line from the end of part III,tu potius interfi-cis et uendis illos genti exterae ignoranti Deum quasi inlupanar tradis membra Xpisti.Patrick refers to God thirty-three times.

In theConfessioPatrick validates his words for numbers by their place-ment. In chapter i (), relating his age at the time of his capture, he states Annorum eram tunc fere sedecim, with fifteen letters before | fere sedecim.

In chapter viii ():Et intermisi hominem cum quo fueram sex annis , withsix words beforesex , the last letter of which is sixth from the end of the line.

Still in chapter viii ():Et post triduum terram cepimuset uiginti octo dies per desertum iter fecimus

in which the third word from the beginning and from the end of thefirst line istriduum. The ten syllables divide into thirds attri |duum,and the twenty-six letters divide into thirds attri |duum. There aretwenty-eight letters before |uiginti octo.From the next line to the endof the account of Patrick’s supplying of food for his starving compan-ions there are twenty-eight lines, followed immediately by the begin-ning of the account of Patrick’s dream of trial by Satan and his dreamof release from subsequent capture, in which the twenty-eighth line isuiginti et octo dies per desertum iter fecimus.

From the beginning of the prophecy |Duobus mensibus eris cumillis | to nocte illa sexagesima | there are sixty-one letters, representing two months, one of thirty-one days and one of thirty days. Becauseof the reckoning of Gen: : factumque est uespere et mane dies unus ,


34 Lapidge and Sharpe ( ), – ; Howlett ( a); Howlett ( – a). Chapternumbers in Roman numerals refer to those of my edition; those in Arabic numeralsrefer to the traditional chapter numbers.


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the day beginning at sundown, Patrick writes punctiliously here, thetwo months of sixty-one days being fulfilled on the evening of thesixtieth.

At the beginning of chapter viiii (– ), writing of trial by his elders,Patrick statesOccasionem post annos triginta inuenerunt me aduersus , withthirty letters and spaces between words from |occasionemto triginta |.

In chapter xvii ():Breuiter dicam qualiter piissimus Deus de seruitute saepe liberauitet de periculis duodecim qua periclitata est anima mea

with twelve words before |duodecimand twelve syllables afterduodecim|.

In chapter xx (– ):Et quartodecimo die absoluit me Dominus de potes-tate eorum, in which the fourteenth letter is the last ofquartodecimo.Six lines later:

Censeo enim non minimum quam pretium quindecim hominumdistribui illis ita ut me fruamini

et ego uobis semper fruar in Deumin which the fifteenth syllable is the middle ofquindecim, and the fifteenth word from the end isquindecim.

In chapter iii () Patrick writes a Creed of thirty-three lines andwords and in the chiastic pair to that, chapter xxiiii (– ), a Doxol-ogy of forty-four lines and words. The thirty-first line of the former mentions filii Dei et coheredes Xpisti , and the thirty-first line of the latter mentions filii Dei et coheredes Xpisti , both echoing Rom: – , a text quoted only here.

The six chapters that begin part I of theConfessio, i–vi (– ), con-tain ninety-six lines of text, and the six chapters that end part V,

xxi–xxvi (– ) also contain ninety-six lines of text.The crux of the chiasmus of the central part III is also the crux of the entire text, the internally chiastic chapter xiiii, which recountsPatrick’s elevation to the episcopate. Its seventeen lines divide by extreme and mean ratio atand , and its ninety words divide by thesame ratio at and . The eleventh line isEcce dandus es | tu | ad gradum episcopatus , and the fifty-sixth word is the central wordtu. Thecentral th word of the entireConfessiois tu.

Audite omnes amantes DeumThe ‘Hymn of Saint Secundinus’ or ‘Saint Sechnall’s Hymn’ Audite omnes amantes Deumin praise of Patrick is a ninety-two-lined, pentadecasyllabic



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composition in twenty-three stanzas, of which the first letters follow theorder of the Latin alphabet from A to Z.35 As the text must be earlier thanthe seventh-century Hiberno-Latin texts which quote from it and alludeto it, the words of the hymn may represent the year of its composition, AD .

Columbani Carmen de Mundi Transitu et Precamur Patrem

The earliest Hiberno-Latin author whose works have descended to usunder his own name, Columban of Bangor, founder of Luxeuil, Annegray, and Bobbio, composedEpistolae , Sermones , a Poenitentiale ,a Regula Coenobialis , and two poems before his death in.36 One,about the transitory world,Carmen de Mundi Transitu, is calendrical,containing seven syllables in each line, for days of a week, four lines ineach stanza, for weeks in a month, thirty stanzas, for days in a month,

lines, for a decade of months, andwords, for days in a year.The other, an Easter hymn,Precamur Patrem, contains twelve syllablesin each line, six lines each in the Prologue and Epilogue, togethertwelve, two twelve-lined halves in part I, together twenty-four, andtwo twenty-four-lined halves in part II, together forty-eight. Theeighty-four-lined hymn thus exhibits repeated diminution in dupleratio : .

Versus de annis a principio

An occasional poem,Versus de annis a principio, Deus a quo facta fuit huius mundi machina , contains, like Audite omnes amantes Deum, fifteen syllables in each line.37 It considers the six ages of the world,first in the Biblical tradition and second in the Classical tradition. Atthe end of the Biblical passage the poet resumes the six ages from Abraham to Christ, and at the beginning and the end of the Classical passage he synchronizes pagan with Biblical history. Then third heconsiders the Irish tradition, dating his own time three ways, fromthe baptism of Christ to the death of Domnall king of the Irish


35 Lapidge and Sharpe ( ), . Howlett ( a), – .36 Lapidge and Sharpe ( ), , – , . Howlett ( a), – , – ;

Howlett ( b), – .37 Lapidge and Sharpe ( ), . Howlett ( a), – . See above p .


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( ) or AD , second from that date forwardto the end of the period of his reckoning ( ), andthird backwards to the Creation, with which his poem began( ). The number of the ages of the world () squaredyields the number of lines in the poem (), which squared yields thenumber of letters in the poem ( ).

Ailerani Sapientis Interpretatio Mysticaet Canon Euangeliorum

Aileranus Sapiens, lector of Clonard (†c. ), wrote two works thathave survived to modern times. One is prose, an exposition of the listof forty-two ancestors of Jesus in Matthew’s Gospel,38 extant in threemanuscripts of the ninth, tenth, and fourteenth centuries, and in twomanuscripts of a recension by Sedulius Scottus, both of the ninth century. The title

AILERANI SCOTTI INTERPRETATIO MYSTICA PRO-GENITORUM DOMINI NOSTRI IESU CHRISTI INNATIVITATE SANCTAE GENITRICIS IPSIUS LEGENDA

contains CXI or letters, which precede the Introduction ofwords and syllables.

The other work is verse, a poem, an exposition of thenum-bers in the Eusebian Canons that allow a reader to coordinate simi-lar passages in varying combinations of the four Gospels.39 This mostwidely disseminated Hiberno-Latin poem survived into the modernperiod in fifteen manuscripts. Composed in rhyming hendecasylla-bles it contains ten stanzas,– and – four lines long, two lineslong, and eight lines long, together forty-two lines, coincidentwith the number of ancestors in theInterpretatio Mystica.The stan-zaic structure and rhyme scheme coincide exactly with the sentencestructure, except in stanza, which exhibits a single sentence buttwo rhymes.

The subject is numbers, but Ailerán has presented the text as a formof mythology, in which a man, a lion, an ox, and an eagle, the symbolsof the Four Evangelists, talk with each other in ten varying combina-tions. The number of canons in the lists of both canonists is identical,

38 Lapidge and Sharpe ( ), . Howlett ( a), – .39 Lapidge and Sharpe ( ), . Howlett ( a), – ; Howlett ( b), – .



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, though Eusebius and Ailerán have disposed the canons differently.The number may represent, as well as the number of canons, the yearof composition, AD , about five years before the poet’s death. Thenumber of letters in the title,, AILERANI SAPIENTIS CANONEVANGELIORUM, an octosyllabic couplet, and in the poem,, isMCXI or , with which one may compare theletters of the titleand words of introduction in Ailerán’s other work.

Augustinus Hibernicus De mirabilibussacrae scripturae

An Irishman who named himself as Augustinus son of Eusebius wrotefor the clerics of the church of Carthage,Carthaginensis , a treatise inthree booksDe Mirabilibus Sacrae Scripturae.40 Here follows part of Book II chapter iv, about the halting of sun and moon in their coursesin Jos – , which allows us to fix the date.

Ut enim hoc manifestis approbationibus pateat cyclorum etiamab initio conditi orbis recursus in se bréuiter dìg e rémus

quos semper postquingentos triginta duosannos sole ut inprincipio et luna per omnia conuenientibus nullissubuenientibus impedimentis in id unde coeperant redíreoste ndémus

Quintonamque cyclo a mundi principio anno centesimoquarto decimo generale totius mundi diluuium súb Noe ué nit

qui post diluuium quadringentesimo decimo octáuode f é cit

Et inde alius incipiens id estsextusin octauo aetatis Abrahaeánno finítur

Et nono eius annoseptimusincipiens tricesimo quinto annoegressionis filiorum Israhel de Aegypto quinquennio antemortem Móysi conclúditur

Post quemoctauusin quo etiam istud signum in sole et lunafactum tricesimo sexto anno egressionis Israhel de Aegyptoincipiens in tricesimum primum annum Asa regis Iúdaincé dit

cuius tricesimo secundo annononusexordium capiens in quoetiam aliud signum in sole Ezechiae regis tempore de quo

paulisper dicemus fáctum lég itur centesimo octauo anno post templi restaurationem quae subDario facta est sui cursus spátiumcònsummá uit

40 Lapidge and Sharpe ( ), .



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donecdecimusinde oriens nonagesimo secundo anno postpassionem Saluatoris Auiola et Pansa consulibus cúrsibuscònsummá tur

Post quemundecimusa consulatu Paterni et Torquati adnostra usque tempora decurrens extremo annoHiberniensium moriente Manchiano inter ceteros sapiéntesperág itur

Etduodecimusnunc tertium annum agens ad futurorumscientiam se praestans a nobis qualem finem sit habitúrusignorá tur

quorum unusquisque uniformi statu peractisquingentistriginta duobusannis ín semetípsum

id est in sequentis initium reuóluitur complétis uidelicet in unoque solaribus octouicenis nónodécies et in lunaribus decemnouenalibus uicies ócties círculis

Our author composed, despite the technical nature of his subject, ele-gantly rhythmical rhyming prose. After his account of thequintus cyclus he wrote six words before |sextus , then seven syllables before |septimus , then eight letters before |octauus.In the account of theeighth cycle the thirty-second word istricesimo secundo|, and from |tricesimo secundo annothere are nine syllables before |nonus. In theaccount of the eleventh cycle the wordsextremo anno Hiberniensiummoriente Manchianorefer to the death of Manchianus of Min Droichitin AD . In the account of the twelfth cycle in the twelfth line thetwelfth letter is the last ofduodecimus |, the third year of that cycle,nunc tertium annum agens , being the year of composition, AD.From the second |quingentis triginta duobus the nineteenth word isnonodecies.In the penultimate line the nineteenth syllable isnono |

decies. Afternonodecies | the nineteenth letter is the firstn of decem-nouenalibus. Afterocties | there are eight letters to the end of the pas-sage. From | post quingentos triginta duos annos to peractis quingentis triginta duobus annis | there are exactly syllables.

Laidcenni Egloga et Lorica

The Moralia in Job, written by Gregory the Great betweenandor , was abbreviated by Laidcenn mac Baíth Bannaig of Clúain

Ferta Mo Lua, who died in .41 The work survives in nine manuscripts, seven written during the eighth and ninth centuries, one

41Lapidge and Sharpe ( ), – . Howlett, ( b), – ; Howlett ( a), – .



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during the eleventh, and one during the thirteenth, and references toit in medieval library catalogues attest its wider diffusion. Laidcennalso composed aLorica that survives in seven manuscripts writtenfrom the eighth century to the sixteenth. Part I invokes the powers of heaven to protect the poet, and part II invokes their protection ofparts of his body. Each line contains, like Ailerán’sCanon Euangelio-rum, eleven syllables. Each of the two parts is introduced by a two-lined Inuocatio of twenty-two syllables. There are twenty-twoquatrains, each containing two couplets of twenty-two syllables. Thetwenty-second stanza contains twenty-two words. The word that givesthe poem its title occurs twice, with twenty-two words from |lorica

to lorica | . The entire poem contains MMCCCCXXXXII orletters ( ).Laidcenn refers to himself fifteen times at places determined by

epogdous or sesquioctave ratio,: and / and / .The central word of a central line, capitali centro cartilagini , is

centro, and the line is an anagram with the same rhyme and the samerhythm as the verse in which it is embedded,ti[bi] practica Lorica Lait- genni ‘for you a practicalLorica of Laidcenn’.

The first six lines may suggest the date.Suffragare Trinitatis Unitas Undertake support, Unity of

Trinity,Unitatis miserere Trinitas be merciful, Trinity of Unity;Suffragare queso mihi posito undertake support, I ask, for

me placedMaris magni uelut in periculo as if in the peril of a great sea,Ut non secum trahat me so that the mortality of this

mortalitas year may notHuius anni neque mundi draw me with it nor the vanity

uanitas. of the world.The last syllable ofhuius anni is the fifty-ninth of the poem, represent-ing perhaps the year of the century. The sixth line might represent themonth of the year. The twenty-third word might represent the day of the month. In the year AD June was the second Sunday afterTrinity, the twenty-second day from Whitsun inclusive, which occurredafter the twenty-second week of that year, two years before the Annalsof Ulster record the death ofLaidggnen sapiens mac Baith Bannaigh.42

42 Mac Airt and Mac Niocaill (), – .



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mean ratio at and ), for days of a month, and letters, for daysof a year.

The grammatical tract Anonymus ad Cuimnanum,50 described by Vivien Law as ‘one of the most interesting products of seventh- andeighth-century grammatical scholarship to survive’,51 begins with a Dedicatio operis that contains twelve sentences, thirty lines, and

words.The Annals of Ulster records.a. thatCummeni Longus.lxx.ii o.anno

etatis sue quieuit .52The names CVMMENE and LADCEN survive on thesame grave slab.53

Tírecháni Episcopi Collectanea

Bishop Tírechán may have been a grandson of Amolngid, a descen-dant of Conall son of Énde, and may have come from Tirawley. Toadvance the claim of the church at Armagh to metropolitan status hecomposed theCollectanea , which he introduced with one statement inthe third person,Tirechan episcopus haec scripsit ex ore uel libro Ultani episcopi cuius ipse alumpnus uel discipulus fuit , and one statement in thefirst person,Inueni quattuor nomina in libro scripta Patricio apud Ultanum episcopum Conchuburnensium.54 As his tutor Bishop Ultándied in AD , Tírechán is often assumed to have written theCollectanea some time later, about AD . The second paragraphstates that

Patricius sexto anno babtitzatus est, uigesimo captus est, quindecimseruiuit, quadraginta legit, sexaginta unum docuit, tota uero aetas cen-tum undecim.

Haec Constans in Gallis inuenit.Tírechán’s reckoning differs from one that supposes Patrick, born about AD , to have died according to one obit in the Annals of Ulsters.a.

in about his seventy-second year, or according to another obit inthe same texts.a. when he was about .55 It differs also from the

50 Lapidge and Sharpe ( ), . Howlett ( a), – .51 Law ( ), .52 Mac Airt and Mac Niocaill (), – .53 Lionard ( ), – . Moloney ( ).54 Bieler ( ), .55 Mac Airt and Mac Niocaill (), – , – .



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-year life with which Muirchú moccu Macthéni credits Patrick, likeMoses.56 It differs more particularly from the total of years thatTírechán himself supplies. One might infer that Tírechán took thenumbers of years in distinct parts of Patrick’s career from his acknowl-edged source, but then behaved as an independent computist, reckon-ing for himself the gematria value of the name PATRICIVS as

or and attributing to Patrick a lifeof years.

Memoria abbatum nostrorum

One poem in the Antiphonary of Bangor, entitled Memoria abbatumnostrorum, beginningSancta sanctorum opera , is composed in rhyming octosyllables.57 Both diction and rhyme of the eight-lined Prologue areechoed in the eight-lined Epilogue, which with a two-lined refrain sur-round four six-lined stanzas, the initial letters of twenty-three of thetwenty-four lines following, as in Audite omnes amantes Deum, theorder of the Latin alphabet. Prologue, Epilogue, and refrains occupy twenty-four lines and seventy-five words andsyllables; the fourstanzas of alphabetic verse occupy twenty-four lines and seventy-five

words and syllables. Prologue, alphabetic stanzas, refrains, Epi-logue, and final couplet together comprisewords, being thenumber of fishes in the net in Jn: and the triangular number– .There are letters in the Prologue and letters in the Epilogue,exactly letters in the entire poem, of which theth is the firstletter of the central twenty-sixth line.

The reference to the most recent abbot Crónán in the present tensesubjunctive mood and future tense indicative mood are usually assumed to indicate composition during the period of his régime, AD

– . The number of letters in the Prologue, the four alphabeticstanzas, and the refrain in the future tense about Crónán,, total , which may suggest the year of

composition of the poem.

Versiculi Familiae Benchuir

Another poem in the Antiphonary of Bangor, entitledVersiculi fami-liae Benchuir , beginningBenchuir bona regula , is composed in rhyming

56 Howlett ( c), .57 Lapidge and Sharpe ( ), . Howlett ( a), – .



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v Quarta pórta Béniamin vi Quinta portula. hoc est páruula pórta vii Ab hac per gradus ad uallem Iósafat

descénditur viii Sexta pórta Tecúitis viiii Hic itaque ordo per earundem

portarum et turriumÍ ntercapédines. a porta Dauid supramemorata per

circuitum septémtrionem uérsus. et exinde ad oriéntem dirígitur

x Sed quamlibet sex porte in múrisnumeréntur.

Celebriores tamen ex eis portarumintróitus frèquentántur. Unus ab óccidentáli. alter a septémtrionáli. tertius ab órientàli párte, Ea uero pars murorum cum

interpósitis túrribus. que a supra descrípta Dauid pórta. per aquilonale montis Sion súpercílium.

quod a meridie superéminet cìuitáti. usque ad eam eiusdem montis fróntemdirígitur.

que prerupta rupe orientalem réspicitplágam.

Nullas habere pórtas conprobátur

quędam. quae. quae. praetermittenda. from quarum to poniturin margin with a signe de renvoi. uillae. Intercapidines.quaelibet. porte˛. numerantur. quae. quae praerupta.

ABOUT THE SITE OF JERUSALEM

About the site of Jerusalem some few things are now to be writtenfrom those which holy Arculf dictated to me;those things, however, which are found in others’ booksabout the position of the same city are to be omitted by us.

i In the great ambit of its walls the same Arculfnumbered eighty-four towers



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The words divide by symmetry atand , at per | circuitum.They divide by/ and / at and , at per | circuitum.There areseventy-two words from | portas bis ternas to sex | porte.There are sev-enty-two words from |occidentalemto | occidentali.There are twenty-five words fromseptemtrionem| to | septemtrionali.There aretwenty-five words from |orientemto orientali |.

The words divide by duple ratio: at and . There areninety-six words from |montis Sionto montis Sion|. There are alsoninety-six words from | porta Dauid to Dauid porta |, which divide by symmetry at and , at porta | Dauid.

As Adomnán knew from Apoc: that the walls of the heavenly

Jerusalem contain cubits, his account of the walls of the earthly Jerusalem occupies words. As Adomnán knew from Apoc: thatthe heavenly Jerusalem has twelve gates, he writes, after stating that theearthly Jerusalem has only portas bis ternas , the word porta twelve times. As Adomnán states twice that he is taking us per circuitum‘through a cir-cuit’, his account occupies as many syllables as there are degrees in a cir-cle, . The words of the account divide by extreme and mean ratioat and . Betweencircuitum | and | circuitumthere are fifty-fivewords. From |dirigitur to dirigitur | inclusive there are fifty-five words.On the circuit of the walls are eighty-four towers, appropriate for anIrish computist who reckoned Easter on a cycle of eighty-four years. Theuse of space to separate words is a convention devised in these islandsnot later than the sixth century, exhibited above in the note about MoSinu maccu Min and easily demonstrable in a wide range of Cambro-,Hiberno-, and Anglo-Latin texts of the seventh century. In Adomnán’sprose we observe that the number of letters,, added to the number of spaces between words and before the first word and after the last word is

, so that the number of letters and spaces is the cube of the numberof sentences, perfection.The number of lines in the passage is a perfect number,. All but

three lines end in good clausular rhythms, two,and , exhibiting hexameter endings, and one,, exhibiting acursus tardus.

Cogitosus of Kildare Vita Sanctae Brigitae

To advance the claim of the church at Kildare to metropolitan statusCogitosus published in AD a Vita Sanctae Brigitae in thirty-twochapters. Here follows the beginning and the end of the thirty-secondchapter.



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Part I XXX II [i.e. triginta duo]

Nec et de miraculo in reparatione eclesiae fácto tacéndum est a in qua gloriosaamborumhoc est archiepiscopi Conleathet huius uirginis florentissimaeBrígitaecórpora b

a dextris et a sinistris altaris decorati in monuméntis pósita bornatis uario cultu auri et argenti et gemmarum et pretiosi

lapidis atque coronis aureis et argenteisdé super pendéntibus cac diuersis imaginibus cum celaturis uariis et colóribus

rèquiéscunt cca

Part VIVeniam peto a fratribus ac lectoribus haéc legéntibus immo émendá ntibus qui causa obediéntiae coáctus nulla praerogatiua sciéntiae subfúltus pelagus inmensum uirtutum beátaeBrígitaeet uiris peritíssimis fòrmidándumhis paucis rustico sérmone díctis

uirtutibus de maximis et innúmerabílibus parua líntre cucúrriOrate promé | Cogitósonepote culpábili Aéd oet ut audaciae méae indùlgeá tis atque orationum uestrarum clipeo Dominome

commendétis exóroEtDeusuos pacem euangelicam sectántes exaúdiat AmenExplicit Vita Sanctae Brígitae uírginis

Part I XXX II [Thirty-two]Nor, also, is it fit for silence to be kept about a miracle

performed in the repair of the churchin which the glorious bodies of both, this is of

Archbishop Conlaed and of this most flourishingBrigit, restplaced in monuments on the right and on the left [sides]

of a decorated altar



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with ornaments hanging from above with variedadornment of gold and silver and gems and precious stoneand crowns gilded and silvered

and with diverse images with varied carvings[or ‘paintings’,‘panellings’,‘canopies’] and colours.

Part VIPardon I seek from brothers and readers reading these thingsindeed emending who compelled for the sake of obediencesupported by no prerogative of learning the immense sea of the virtues of blessed Brigit

to be feared by the most learned menwith these few sayings in rustic speechabout very great and innumerable virtueswith a small boat I have run on to.Pray for me, Cogitosus,reprehensible nephew to Áedand that you may be indulgent to my audacity and that you may commend me to the Lord with the

shield of your prayers I pray earnestly.

And may God hear you out pursuing evangelical peace. Amen.The Life of holy Brigit the virgin ends.

Reckoning one line and two words for the chapter number XXX II,trig-inta duo, and five lines and sixty-two words of narrative, there are six lines and sixty-four words. The six lines prefigure the six parts of the nar-rative. The sixty-four words represent the alphanumeric value of thename BRIGITA, or , which divide by extremeand mean ratio at and , at florentissimae | Brigitae.In line thethirty-second syllable is the central syllable ofBrigitae , coincident withher commemoration onFebruary, the thirty-second day of the year, thethirty-second line of a calendar that begins at January. The entire para-graph contains letters, one for each day of an ordinary solar year.

In Part VI coincident with the alphanumeric value of the nameBRIGITA, there are sixty-four syllables from the beginning to |Brigi-tae , and sixty-four syllables fromBrigitae | to Cogitoso nepote culpabili

Aedo|. Coincident with the alphanumeric value of the nominative

form of the name COGITOSVS, or, there are syllables from the beginning toCogitoso|. Coincident

with the alphanumeric value of the ablative form COGITOSO,



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or , there are ninety-eight letters andspaces between words from the space before | pro me Cogitosoto thespace afterme |. Coincident with the alphanumeric value of the name AEDO, or , the twenty-fourth word afterBrigitae | is Aedo |. Coincident with the alphanumeric value of DEVS,

or , there are from the space before |Deus to the spaceafterexaudiat | forty-seven letters and spaces between words.

Let us recapitulate. Part I of the concluding chapter suggests by itsnumber, , the day of the year on which Brigit is commemorated. Itsuggests by the number of its words,, the alphanumeric value of Brigit’s name, which relates to the former number by duple ratio: ,

: . It suggests by the number of its lines the number of parts in thechapter, , and by the number of its letters the number of days in anordinary solar year, . It describes three artefacts, one altar flankedby two tombs, one of Conlaed and one of Brigit.

The last lines of part VI contain six words, which recall the six linesof part I. The seventy-three words of part VI confirm the line number

, with which part VI begins.From the beginning of chapter XXXII toOrate pro me | Cogitoso

there are words, suggesting perhaps that Cogitosus published hisVita Sanctae Brigitae in AD , about thirty years after publication of Ailerán’sVita Sanctae Brigitae , six or seven years before Muirchú pub-lished hisVita Sancti Patricii not later than the year . The yearwas slightly more than years after the birth of Patrick, supposing that to have occurred about , slightly more than years after thebirth of Brigit, supposing that to have occurred about.

Muirchú moccu Macthéni, Vita Sancti Patricii

To supersede the claim of the church at Kildare and to advance theclaim of the church at Armagh to metropolitan status Muirchú moccuMacthéni published not later than ADhisVita Sancti Patricii , of which chapter X follows.60

In illis autem diebus quibus haec gesta suntin praedictis regionibus fuit rex quidam magnus ferox gentilisqueinperator barbarorum regnansin Temoria quae erat caput Scotorum.Loiguire nomine filius Neill

60 Lapidge and Sharpe ( ), . Howlett ( c), – , – .



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origostirpis regiae huius paene insulaeHic autem sciuos. et magos. et aruspices.et incantatores et omnis malae artisinuentores habuerat.qui poterant omnia scire et prouidere ex more gentilitatis etidolatriae antequam essent.e quibus duo prae caeteris praeferebantur quorum nomina haecsuntLothroch qui et Lochru. et Lucetmail qui et Ronal.et hii duo ex sua arte magica crebrius prophetabant morem quendam

exterumf uturumin modum regni cumig nota quadam doctrina molesta longinquo trans maria aduectum

a paucis dictatum.a multis susceptum.ab omnibus honorandum.regna subuersurum.resistentes reges occisurum. turbas seducturum.omnes eorum deos destructurum.et eiectis omnibus illorum artis operibus. in

saecula regnaturum.

Portantem quoquesuadentemque huncmorem signaueruntet prophetauerunt hiis uerbis quasiin modum uersiculi crebro ab hiisdem dictis.maximein antecedentibus aduentum Patricii duobus

aut tribusa nnis.Haecautemsunt uersiculi uerba pro pter linguae idioma

non tam manifesta:.“ A duenietascicaputcum suo ligno curuicapiteEx sua domu capite perforataincantabit nefas A sua tabula ex anteriore parte domus suae.respondebit ei sua familia tota ‘.Fiat Fiat .’”Quod nostris uerbis potest manifestius exprimi.Q uando ergo haec omnia fiant.regnum nostrum quod estg entile non stabit quodsic postea euenerat.euersis enimin aduentuPatricii idolorum culturis.fides Xpisti catholica nostra repleuit omnia.D e hiis ista sufficiant .Redeamus ad propositum. In those days, however, in which these things were accomplishedin the foresaid regions there was a certain king great, fierce,

and gentile



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an emperor of the barbarians reigning in Tara which was the capital [lit. ‘head’] of the Scots [i.e. Irish]Loiguire by name, son of Neill the origin [lit. ‘rising’] of the royal lineage of almostall this island.This man, however, had men possessing knowledge and

magi [or ‘druids’] and divinersand enchanters and finders of every evil artwho could know all things and foresee by the custom of

gentile belief and idolatry before they would befrom among whom two before the others were preferred, whose names are these,

Lothroch, who also [was named] Lochru, and Lucetmail,who also [was named] Ronaland these two by their own magic [or ‘druidic’] art used

rather frequently to prophesy that a certain alien customwas coming

in the manner of a realm with a certain unknowndistressing teaching

borne across the seas from a long way away, preached by few,

undertaken by many,to be honoured by all,about to subvert realms,about to kill resisting kings, about to seduce throngs,about to destroy all their gods,and with all the works of the art of those men hurled away

about to reign for ages. Also the one bearing and persuading to this custom they signaledand prophesied in these words, as if in the manner of a little verse frequently in these same wordsespecially in the two or three years leading up to the coming

here of Patrick.These, however, are the words of the little verse, not very manifest

on account of the idiom of the language.‘Adze-head will come here with his own curve-headed woodfrom his own house with the head perforated he will sing

something unutterable from his own table from the forward part of his own houseall his own family will respond to him “let it be done, let it be done”’which can be expressed more manifestly in our words:when therefore all these things may be doneour realm, because it is pagan, will not stand which came about thus afterward



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for with the cults of idols overturned at the coming here of Patrick our catholic faith of Christ refilled all things. About these matters those things suffice.Let us return to the proposed matter.

Chapter X is remarkable for many reasons. One cannot read this pas-sage aloud without noting Muirchú’s close attention to rhythm andrhyme and many other structural phenomena. In lines– there arefrom | fuit to Neill | forty-six syllables and from |Neill to insulae | forty-six letters and spaces between words, coincident with the alphanumericvalue in the eighteen-letter Irish system of NEILL, or

. The twenty-eighth line of the chapter introduces four verses thatcontain twenty-eight words, the verses before the caesuras containing twenty-eight syllables.61 The number is a perfect number and also a triangular number . The verses are noteworthy octodecasyllables. The verses in the first couplet share an identicalnumber of syllables arranged on each side of the caesura (– ) and anidentical number of letters (). The verses in the second couplet sharean identical number of syllables arranged on each side of the caesura ( – ) and an identical number of letters (). The verses end with theword FIAT, which bears a numerical value of or . As theword occurs twice, its value ofcoincides with the number of syllablesin the verses it ends. The numberis half of the number of cubits inthe wall of the heavenly Jerusalem,.

The entire passage contains words, which divide into/ and/ and and , at duobus aut tribus |. From |Et hii duo [...]

prophetabant to fides Xpisti | there are exactly units, coincidentwith the value in the Greek alphanumeric system of the nameIHCOYC or .62 From |e quibus duotohii duo | inclusive there are twenty-two words.

The most securely fixed date in Patrician scholarship is AD, theyear in which Prosper of Aquitaine wrote in his Chroniclead Scotos in Xpistum credentes ordinatus a Papa Caelestino Palladius primus episcopus mittitur.63 Under the year the Annals of Ulster record thatPatricius peruenit ad Hiberniam.64 In this chapter there are from prophetabant |

61 For other examples of this see Howlett (a), – ; Howlett ( a), .62 For other examples of this see Howlett (b), ; Howlett ( a), ;

Howlett ( b), – ; Howlett ( a), – , – ; Howlett ( a), ;Howlett ( a), – ; Howlett ( a), – , – .

63 MGH Auct. ant., .64 Mac Airt and Mac Niocaill (), – .



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to aduentum | Patricii exactly letters, coincident with the year AD , between which and AD there are three years. Muirchúhas infixed a letter count as a means of confirming his statement thatthe druids prophesied Patrick’s advent during three years before hisarrival, and set that within a larger pattern coincident with thealphanumeric value of the name of Jesus.

Collectanea Pseudo-Bedae

The text now known asCollectanea Pseudo-Bedae first took shape in Irelandduring the seventh century.65 Two passages suffice to illustrate the com-putistic nature of this remarkable text. First, some questions about Adam.

Dic mihi quis primus prophetauit? Adam quando dixit ‘Hoc nunc os ex ossibus meis et

caro de carne mea’.Omnis homo qui in dolore positus est memor

sit illius sententiae ‘Ne quid nimis’.Vidi filium cum matre manducantem cuius pellis

pendebat in pariete.Sedeo super equum non natum cuius matrem in manu teneo.

Quaero barbarum quem inuenire non possum.In aquilonali parte ciuitatis ubi aqua attingit parietem tolle saxumquadratum ibi inuenies barbarum.

Dic mihi quae est illa res quae cum augetur minor erit et dumminuitur augmentum accipit?

Nemo in ecclesia amplius nocet quam qui nomen et opinionemsanctitatis habet.

Cui plus creditur plus ab eo exigitur.Potentes potenter tormenta patiuntur.

Sic ut per prophetam dicitur ‘Ducunt in bonis dies suos et inpuncto ad inferna descendunt’.Quattuor claues sunt sapientia uel industria legendi assiduitas

interrogandi honor doctoris contemptio facultatum.Dic quot annos uixit primus parens Adam? Noningentos triginta.Qui sunt tres amici et inimici sine quibus uiuere nemo potest?

Ignis aqua et ferrum.

In § between Adam| and |mea ‘mine’, that is ‘of Adam’, there are forty-six letters, coincident with the alphanumeric value in the Greek system of A AM, or . In § the sixty-first letter is the first ofnimis ,coincident with the alphanumeric value in the Latin system of NIMIS,

65 Lapidge and Sharpe ( ), . Bayliss and Lapidge ( ); Howlett ( b).



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or . In § there are twenty words. There are forty syllables before |quadratumand four words from |quadratumto the end.In § the sixteen words divide by extreme and mean ratio atand , sothat the minor part of the golden section begins atminor |. The six wordsof the minor part divide by the same ratio atand , so that the minorpart of the minor part begins atminuitur |. From the space before |Dic mihi quis primus prophetauit? Adam§ to theN ofNoningentos triginta § there are letters and spaces between words. In §the third wordistres.From the space before |qui to ferrum| there are eighty-three lettersand spaces between words, coincident with the alphanumeric value of FERRUM, or .

Second, some observations about the Three Wise Men, whosenames appear here for the first time in a Latin text.

Magi sunt qui munera Domino dederunt.Primus fuisse Melchior senex et canus barba prolix et capillistunica hyacinthina sagoque milenoet calceamentis hyacinthino et albo mixto opere pro mitrario

uariae compositionis indutusaurum obtulit Regi Domino.Secundus nomine Caspar iuuenis imberbisrubicundus milenica tunica sago rubeocalceamentis hyacinthinis uestitusthure quasi Deo oblatione digna Deum honorabat.Tertius fuscus integre barbatus Balthasar nominehabens tunicam rubeam albo uario sagocalceamentis milenicis amictusper myrrham filius hominis moriturum professus est.Omnia autem uestimenta eorum Syriaca sunt.

This passage about the threemagi is introduced by a sentence of six words and concluded by a sentence of six words, together twelve words,which surround twelve lines of description, in three parts, introducedPrimus , Secundus , andTertius.The names of themagi bear alphanumericvalues, MELCHIOR or , CASPAR

or , BALTHASARor , together . Their gifts bear alphanumeric values, AURUM

or , THUS or , MYRRHA or , together .66The threemagi represent the


66 Compare the play in Rhygyfarch ap Sulien’sVita Sancti Dauid § (Howlett( a), – , – ) on the identical alphanumeric value of DAVID and AQUA as

, and on the values of the antenatal gifts, FAVUS, PISCIS, and CERVUS.


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ne meo iudicio qué uidebá ntur c uelut commendaticia déscriberéntur [.] c

II [S]ingulorum nomina [.] singulistestimoniis prescrípta pósui : b

[n]e uelut incertum [. q ]uisque quoddicat [. m]ínus lúceat : d

III Sed hoc lectórem nón fallat . d

ut [. c]um [.] ad generales titulos quosnecessario preposúimus recúrrat [.] d

numeros diligénter obsér uet . e q uibus obseruatis [:] questiónem

quam uolúerit e sine ulla cunctatióne repériet ; e

FINIT PROLOGUS.

excluding line including line

IT BEGINS IN THE NAME OF THE FATHER AND OF THESON AND OF THE HOLY SPIRIT AMEN.I

Gazing together on the numerousness of the model judgementsof synods,

and foreseeing dark confusion, less useful, from the very crudestates of very many of them,

and also gazing with an eye to the future on the diversity ofothers, unharmonious and destructive rather than constructive,

I have set in order an exposition, brief and clear and harmonious,into a text of one volume, from an immense forest of writers,adding to many [of the judgements],reducing many,arranging in order many in the same course,[setting in a row many, from sense to sense, with the course of the

words not followed,]striving therefore toward this alone before all things,so that things might be written down as commendatory,

which were not seen [so] by my judgement [alone].III have placed the forewritten names of individual men in individual

testimonies,



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so that what anyone would say might shine as less uncertain.III

But this should not deceive the reader,as when he would recur to the general titles that we have necessarilyplaced before,he should diligently observe the numbers,which observed, any question that he will have wished,without any delay he will find.THE PROLOGUE ENDS.

The two most recent authorities named in theCollectioare Theodorearchbishop of Canterbury, who died AD, and Adomnán abbot of Iona, who died AD . Thomas Charles-Edwards has suggested68

‘the A recension is where the work had got to when one of the compil-ers, Ruben, died in [. . .]. It may have been his collaborator, CúChuimne, who revised and expanded the text [. . .]. The prologue intwo B recension MSS and one A recension copy appears to have beenwritten by a single person. [. . .] Since the work on the B recension is a completion of the unfinished labours on the A, it is likely that the Brecension was compiled in Ireland and in a centre associated with theproduction of the A recension.’

In the twenty-three-letter alphabetic system the name CU CUIMNEIAE bears a numerical value of and and

or or . The numerical value of his complete nameCú Cuimne Iae coincides with the number of words in the Prologueproper, . From |Incipit to Finit prologus | there are letters, whichmay represent the year in which Cú Chuimne published the text, tenyears after the death of Ruben and twelve years before his own death.

The only significant variant is line, absent from the text of threemanuscripts of recension B, but present in two manuscripts of recen-sion A. The additional text raises the number of words in the Prologueproper to , which coincides with the numerical value of the nameCU CHUIMNE IAE, and andor or . In this expanded form of the Prologue there arefrom |Sinodorum to Finit Prologus | inclusive letters.

Both forms of the Prologue may have issued from the mind of a

single orderly legist, who described accurately what he and his late col-league had done. The text extant in three

Documents

Howlett2010 Computus in Hiberno-Latin Literature