10. HELPERIC, DE COMPUTO fols. 123r-135v: OVERVIEW
Location:
fols. 123r-135v
Incipit:
INCIPIT PREFATIO VENERABILIS MONACHI SVPER SEQVENTEM LIBRVM. Cum quibusdam fratribus nostris adolescentulis...
Click here for transcription of glosses.
This treatise was one of the most popular textbooks of computus of the central Middle Ages, but ironically its very popularity has obscured the identity of its author. In the manuscripts, his name assumes an almost playful variety of forms -- Helpericus, Hilpericus, Chilpericus, Albericus, Heiricus, Heriricus -- while the paedagogical ploy of making the worked examples in argumenta more relevant by substituting (not always consistently) the year in which the manuscript was copied for the annus praesens named in the exemplar, has resulted in much confusion about the date of the original.1 De computo
is furnished with two prefaces. The first is a letter to Asper, abbot of Saint-Germain in Auxerre; in it the author identifies himself as a monk of Granval, and alludes to an offer by Asper of a teaching post in Auxerre. This text does not appear in MS 17's version of
De computo
, but it is included in the only readily available edition, namely the one in PL 137.17-20.2 The connection to Auxerre, coupled with the fact that the author's name appears as "Heiricus" or "Heriricus" in some Loire valley codices, prompted Ludwig Traube to suggest that "Helperic" was actually the Carolingian scholasticusHeiric of Auxerre, a theory he later withdrew in favour of the traditional ascription.3 Helperic of Granval appears to have flourished a little later than Heiric, about 900, the date of the earliest recorded annus praesens.
MS 17's text of De computo belongs to a family of Helperic manuscripts closely associated with Fleury, and particularly with the tracts on astronomy by Abbo of Fleury which appear in the cosmographical anthology (fols. 37v-38v). It represents, in fact, a revision by Abbo himself of Helperic's original text.4 Special traits of this manuscript group include the annus praesens 978, the rendition of the author's name in its Loire valley form of Heiricus or Heriricus, and modifications of the contents to reflect Abbo's computistical doctrines, e.g. the designation of March as the beginning of the year. In the discussion of the intercalation of the leap year day, MS 17 and other manuscripts of its type contain a phrase which does not appear in the older version represented by the PL text (PL 138.22D): "Vto kalendas martii id est prope finem anni ab antiquis romanis institutus interponebatur (fol. 124ra17-19).5
Helperic's second preface, like Bede's introduction to De temporum ratione
, states that he is writing at the request of his students. But while Bede's pupils apparently wanted more detailed information,6 Helperic's longed for a text-book that would be less dense and more practical than the old classics in the field.
Et non nouum inquiunt aliquid cudere cupimus...sed ex his que ab aliis sparsim copiose
<que>
tractata asseris. poscimus utiliora queque nobisque necessariora tuo studio decer\p/ta in unum colligi. et ueluti sertum quoddam ex diuersis floribus compingi (corr. a con-). In quo opere non pompaticas uerborum faleras exigimus. quas ut ais in antiquis est inuenire commentariis. Enim uero que ab aliis sunt obscurius prolata tuo quesumus fiant manifestiora relatu.7
("We do not want you to coin anything new," they said, "but we beg you to gather and arrange like a garland composed of diverse flowers what you have chosen as being more useful and essential for us from what others, as you claim, have treated at various points and at some length. We do not demand high-flown language in this book, such as you assert is found in the old commentaries, but we ask that what they set forth darkly, your account may make more clear.")
Helperic's book falls into two sections: lunar and solar reckoning, and Paschal table. The first part discusses the solar year (ch. 1) and the zodiac (ch. 2-4), as well as the computation of solar calendar dates by regulars and concurrents (ch. 5-9). Lunar reckoning by regulars and epacts (ch. 10-14) leads to a discussion of conventional measurements of lunar months and years (ch. 16-17), the saltus lunae(ch. 18), the duration of moonlight (ch. 19), eclipses of the sun and moon (ch. 20), and the position of the moon in relation to the zodiac (ch. 21). Helperic's explanation of Paschal computation follows Bede's method of proceeding column by column through the Paschal table (ch. 22-38).
Helperic's dependence on Bede is evident throughout. Occasionally it is explicitly acknowledged, as when Helperic states that his source for the history of the Roman months in ch. 9 is that section of Macrobius'
Saturnalia
called Disputatio Chori et Praetextati
"a domno beda exinde deflorata in libro de temporibus secundo" ("excerpted by Bede in his second book on time").10 At other times the reference is implicit. In ch. 38 of De temporum ratione
, Bede issues a dire warning on the consequences for the calendar of failure to intercalate the leap-year day:
Quod si qui calculatorum facere negligens CCC solum ac LXV diebus omnes se annos agere debere putauerit, magnum sibi mox inueniet annui circuitus occurrisse dispendium ita ut, post aliquot annorum uertentium curricula, aestiuis mensibus uernum tempus, uernis brumale, brumalibus autumnale, autumnalibus aestiuum se offendisse peruersus computator horrescat.11
(For should any computist neglect to make [this intercalation], and think that all years ought to have only 365 days, he will subsequently discover that a great shortfall occurs in the course of the year; after a certain number of years have come and gone, the erring computist will be aghast to encounter spring time in the summer months, winter in the spring months, autumn in the winter months, and summer in the autumn months.)12
One might imagine that Helperic's students were disturbed by this prospect, but unable to comprehend exactly how such a reversal of the seasons could come to pass. Although he does not openly cite Bede here, Helperic's verbal echoes of
De temporum ratione
show that he had this passage in mind; however, he offers a more detailed explanation of the relationship between the calendar dates and the seasons:
Qui dies si negligatur. eueniet post aliquantulos annos ut hiem[a]e aestiui. et econtra aestate hiberni menses occurrant. Nam per CCCLXIIIIor
<annos>
tantum calculatio regradabitur. ut in kalendariis solstitiorum aequinoctia. et econtra in equinoctiorum solstitia id est cum XIImo kalendas iulii pronuntiaueris quod est solstitium aestiuum. occurrat equinoctium uernale: quod esse debet XIImo kalendas aprilis. Cumque pronuntiaueris XII kalendas aprilis et debeat esse equinoctium uernale. appeat solstitium brumale. quod est XIImo kalendas ianuarii: sicque in ceteris eueniet anni diebus. Ad hunc euitandum errorem bissectilis dies IIIIto anno semper interkalatur.13
(If this day is overlooked, it will come to pass after a number of years that the summer months will fall in winter, and the winter months, on the other hand, in summer. For in the course of 364 years the reckoning will fall behind to such an extent that the equinoxes will come on the dates of the solstices, and the solstices on the dates of the equinoxes: that is, when you state that it is the 12th kalends of July, which is the summer solstice, the spring equinox will be taking place, and when you state that it is the 12th kalends of April, which ought to be the spring equinox, the winter solstice will take place, which is on the 12th kalends of January. This will happen to all the days of the year in the same way. In order to avoid this mistake, a leap year is intercalated every fourth year.)
Finally,
De computo
closes with the suggestion that the curious reader turn to Bede for further information.14
FINIT EXCERPTIO VEL EXPOSITIO HERIRICI VIRI DOCTISSIMI.
Winchcombe
INCIPIT EXCEPTIO VEL EXPOSITIO COMPOTI
(after capitula) INCIPIT LIBER VIRI DOCTISSIMI DE COMPVTO.
(no explicit)
Cambridge
INCIPIT PREFACIO IN LIBRVM VIRI DOCTISSIMI
(after capitula) INCIPIT COMPOTVS .
EXPLICIT COMPOTVS HILPERICI.
On the other hand, MS 17 and the Abbonian manuscript Cambridge, Trinity College R.15.32 (s. X-XI, Winchester) share the same explicit; as well, both call the author "Heriricus," and both omit the epistle to Asper. However, the Trinity manuscript omits the capitula found in MS 17, and treats the epilogue of the book as a final chapter, while MS 17 (like the Winchcombe computus) fuses it onto the end of ch. 38. While the Cambridge St John's College and Winchcome copies both refer to Helperic by his correct name, the Cambridge text of De computo is rather different from that found in MS 17, Winchcombe, and the Trinity manuscript, both in the order of its chapters and in its readings.16 The fact that MS 17 is relatively close to the Trinity manuscript (which has no text of De temporum ratione), and quite different from Cambridge St John's College (with which it shares many glosses to De temporum ratione), suggests that its text of Helperic derived from a different source than its text and glosses on Bede's great textbook. On the other hand, MS 17's text of Helperic broadly agrees not only with that found in the Trinity manuscript, but also with the Winchcombe computus. A collation of the preface and first chapter turned up only one instance where MS 17 read with either of these two against the third: Qui dies (MS 17, Trinity, Cambridge St John's College) versus Quibus (Winchcombe) (fol. 124ra22). MS 17 has a number of unique readings, a significant percentage of which involve the same fault, namely dropping words from the Winchcombe/Trinity text, but it is impossible to say whether the exemplar or Scribe B was guilty. However, all four manuscripts of this family share a special variant: the omission by homeoteleuton of a phrase from the end of ch. 14:
Quid ergo necesse est totiens et totiens addere XXXta et retrahere. cum lunaris aetas illo anno
< per singulas kalendas numero regularum constet? Ob hoc eo anno>
nulle pronuntiande sunt epacte.17
This phrase is also omitted by Byrhtferth when he quotes ch. 14 in his Enchiridion.18 Moreover, Byrhtferth's Proemium (MS 17 fol. 13r) refers to De computo as "heririci expositiones," a direct echo of the MS 17/Trinity rubric.19 Finally, a gloss on Helperic's text unique to MS 17 (gloss 2) appears, albeit in a slightly different form, in the Enchiridion and is not ascribed to Helperic.20 This same gloss appears in connection with the feria table on fol. 6r of MS 17.
1 The form of the author's name and the date of the annus praesens are the criteria for Ludwig Traube's classification of 33 MSS of De computo in "Computus Helperici," in Traube 1909-1920, 3.128-153, a revised version of an article which originally appeared in Neues Archiv 18 (1893):73-105.
2 This edition is of limited used for studying MS 17, because it represents the text of De computo prior to the revision by Abbo of Fleury. Moreover, Pez, from whose Thesaurus novus anecdotorum Migne took his text, did not use a trustworthy MS: see Wright (T) 1847, 69-70, Traube 1909-1920, 3.129 n. 1.
3 Traube 1909-1920, 3.146 and 128, note. Van de Vyver 1935, 149 suggested that Heiriricus, abbot of St-Mesmin de Micy (a dependency of Fleury) in the reign of Louis the Pious, may have lent his name to the Loire valley exemplars. Traube's original theory continues in circulation, thanks to its incorporation into standard reference works such as Sarton 1927-1948, 1.671-672.
5 On this point, Abbo's revision was not thorough. In ch. 9, Helperic refers to January as the beginning of the year ("Quod uero nunc annum a Ianuario ordimur...") in both the MS 17 version (fol. 126rb32-33) and the PL text (28).
8 An epigram in Munich CLM 10270 (s. XI) plays on the name Helperic/Helferich: "Computus Helperici tunc famine lenit amici. Bedam sed inde sequens iuuat hunc manifestius edens." (Helperic's computus appeases a friend's hunger. He helps by following Bede closely, but explaining him more clearly." See Traube 1909-1920, 3.144.
16 A comparison of the prologue to De computo in MS 17 (J), the Winchcombe computus (W), the Cambridge St John's College I.15 (C) and the Trinity College manuscript (T) will illustrate this point:
123ra26 excideret JWT: excederet J²C
123ra32 insisterent JWT: instarent C
123rb5 pertinacius JWT: et pertinacius C
123rb6 cudere JWT: te cudere C
123rb10 tuo studio JWT: studio tuo C
123rb12-13 pompacitas JWT: pompacitatis C
123rb13 faleras exigimus JWT: faleras aut urbanitas exigimus ueneris C
123rb14 antiquis JWT: antiquorum C
123rb19 hoc opus JWT: que humiliter eos postulari sensi hoc opus C
123rb20 ut illud JWT: ut hoc C
123rb20 ad legendum JWT: preter se legenda C
17 MS 17 fol. 127ra29-32; Winchcombe fol 151ra14-18; Cambridge p. 254b2-5; Trinity p. 178.20-21. Cf.PL 137.21.
18 Byrhtferth 1.2 (314-316); cf. Baker and Lapidge's commentary p. 272.
10. HELPERIC, DE COMPUTO fols. 123r-135v: OVERVIEW
Location:fols. 123r-135v
Incipit:INCIPIT PREFATIO VENERABILIS MONACHI SVPER SEQVENTEM LIBRVM. Cum quibusdam fratribus nostris adolescentulis... Click here for transcription of glosses.
Scribe:B (text), A (glosses)
Related manuscripts:This treatise was one of the most popular textbooks of computus of the central Middle Ages, but ironically its very popularity has obscured the identity of its author. In the manuscripts, his name assumes an almost playful variety of forms -- Helpericus, Hilpericus, Chilpericus, Albericus, Heiricus, Heriricus -- while the paedagogical ploy of making the worked examples in argumenta more relevant by substituting (not always consistently) the year in which the manuscript was copied for the annus praesens named in the exemplar, has resulted in much confusion about the date of the original.1 De computo is furnished with two prefaces. The first is a letter to Asper, abbot of Saint-Germain in Auxerre; in it the author identifies himself as a monk of Granval, and alludes to an offer by Asper of a teaching post in Auxerre. This text does not appear in MS 17's version of De computo , but it is included in the only readily available edition, namely the one in PL 137.17-20.2 The connection to Auxerre, coupled with the fact that the author's name appears as "Heiricus" or "Heriricus" in some Loire valley codices, prompted Ludwig Traube to suggest that "Helperic" was actually the Carolingian scholasticusHeiric of Auxerre, a theory he later withdrew in favour of the traditional ascription.3 Helperic of Granval appears to have flourished a little later than Heiric, about 900, the date of the earliest recorded annus praesens.
MS 17's text of De computo belongs to a family of Helperic manuscripts closely associated with Fleury, and particularly with the tracts on astronomy by Abbo of Fleury which appear in the cosmographical anthology (fols. 37v-38v). It represents, in fact, a revision by Abbo himself of Helperic's original text.4 Special traits of this manuscript group include the annus praesens 978, the rendition of the author's name in its Loire valley form of Heiricus or Heriricus, and modifications of the contents to reflect Abbo's computistical doctrines, e.g. the designation of March as the beginning of the year. In the discussion of the intercalation of the leap year day, MS 17 and other manuscripts of its type contain a phrase which does not appear in the older version represented by the PL text (PL 138.22D): "Vto kalendas martii id est prope finem anni ab antiquis romanis institutus interponebatur (fol. 124ra17-19).5
Helperic's second preface, like Bede's introduction to De temporum ratione , states that he is writing at the request of his students. But while Bede's pupils apparently wanted more detailed information,6 Helperic's longed for a text-book that would be less dense and more practical than the old classics in the field.
Et non nouum inquiunt aliquid cudere cupimus...sed ex his que ab aliis sparsim copiose <que> tractata asseris. poscimus utiliora queque nobisque necessariora tuo studio decer\p/ta in unum colligi. et ueluti sertum quoddam ex diuersis floribus compingi (corr. a con-). In quo opere non pompaticas uerborum faleras exigimus. quas ut ais in antiquis est inuenire commentariis. Enim uero que ab aliis sunt obscurius prolata tuo quesumus fiant manifestiora relatu.7
("We do not want you to coin anything new," they said, "but we beg you to gather and arrange like a garland composed of diverse flowers what you have chosen as being more useful and essential for us from what others, as you claim, have treated at various points and at some length. We do not demand high-flown language in this book, such as you assert is found in the old commentaries, but we ask that what they set forth darkly, your account may make more clear.")
Helperic claims to cull his summary treatise from a number of sources, but in fact only Bede is mentioned by name, and indeed Helperic's readers seem to have regarded De computo as a condensed and simplified De temporum ratione .8 For this reason, the role of De computo in many computus manuscripts, including MS 17, is as an adjunct or introduction to De temporum ratione. 9 In the Winchcombe computus, British Library Royal 13.A.XI, Cambridge St John's College A.22, Cambridge St John's College I.15 and Oxford Bodleian Library F.3.14, Helperic accompanies De temporum ratione ; in British Library Cotton Cleopatra A.VII, Additional 40744, Arundel 356, Royal 12.D.IV, Royal 12.F.II, Cambridge Trinity College R.15.32, Durham Hunter 100, Paris BNF lat. 7518, lat. 12117, lat. 15170 and Munich CLM 4563, it can be argued that Helperic replaces De temporum ratione . For example, in British Library Royal 12.D.IV and Royal 12.F.II, De computo is paired with Bede's De natura rerum , the traditional companion-piece of De temporum ratione ; in Durham Hunter 100, extracts from De temporum ratione follow Helperic as an appendix, while in British Library Additional 40744 and Arundel 356, they are incorporated as glosses. MS 17's positioning of Helperic on the heels of De temporum ratione suggests that its compilers saw this text as a summary review of Bede; this pattern is followed in Cambridge St John's College A.22 and in a somewhat looser fashion in the Winchcombe computus.
Helperic's book falls into two sections: lunar and solar reckoning, and Paschal table. The first part discusses the solar year (ch. 1) and the zodiac (ch. 2-4), as well as the computation of solar calendar dates by regulars and concurrents (ch. 5-9). Lunar reckoning by regulars and epacts (ch. 10-14) leads to a discussion of conventional measurements of lunar months and years (ch. 16-17), the saltus lunae(ch. 18), the duration of moonlight (ch. 19), eclipses of the sun and moon (ch. 20), and the position of the moon in relation to the zodiac (ch. 21). Helperic's explanation of Paschal computation follows Bede's method of proceeding column by column through the Paschal table (ch. 22-38).
Helperic's dependence on Bede is evident throughout. Occasionally it is explicitly acknowledged, as when Helperic states that his source for the history of the Roman months in ch. 9 is that section of Macrobius' Saturnalia called Disputatio Chori et Praetextati "a domno beda exinde deflorata in libro de temporibus secundo" ("excerpted by Bede in his second book on time").10 At other times the reference is implicit. In ch. 38 of De temporum ratione , Bede issues a dire warning on the consequences for the calendar of failure to intercalate the leap-year day:
Quod si qui calculatorum facere negligens CCC solum ac LXV diebus omnes se annos agere debere putauerit, magnum sibi mox inueniet annui circuitus occurrisse dispendium ita ut, post aliquot annorum uertentium curricula, aestiuis mensibus uernum tempus, uernis brumale, brumalibus autumnale, autumnalibus aestiuum se offendisse peruersus computator horrescat.11
(For should any computist neglect to make [this intercalation], and think that all years ought to have only 365 days, he will subsequently discover that a great shortfall occurs in the course of the year; after a certain number of years have come and gone, the erring computist will be aghast to encounter spring time in the summer months, winter in the spring months, autumn in the winter months, and summer in the autumn months.)12
One might imagine that Helperic's students were disturbed by this prospect, but unable to comprehend exactly how such a reversal of the seasons could come to pass. Although he does not openly cite Bede here, Helperic's verbal echoes of De temporum ratione show that he had this passage in mind; however, he offers a more detailed explanation of the relationship between the calendar dates and the seasons:
Qui dies si negligatur. eueniet post aliquantulos annos ut hiem[a]e aestiui. et econtra aestate hiberni menses occurrant. Nam per CCCLXIIIIor <annos> tantum calculatio regradabitur. ut in kalendariis solstitiorum aequinoctia. et econtra in equinoctiorum solstitia id est cum XIImo kalendas iulii pronuntiaueris quod est solstitium aestiuum. occurrat equinoctium uernale: quod esse debet XIImo kalendas aprilis. Cumque pronuntiaueris XII kalendas aprilis et debeat esse equinoctium uernale. appeat solstitium brumale. quod est XIImo kalendas ianuarii: sicque in ceteris eueniet anni diebus. Ad hunc euitandum errorem bissectilis dies IIIIto anno semper interkalatur.13
(If this day is overlooked, it will come to pass after a number of years that the summer months will fall in winter, and the winter months, on the other hand, in summer. For in the course of 364 years the reckoning will fall behind to such an extent that the equinoxes will come on the dates of the solstices, and the solstices on the dates of the equinoxes: that is, when you state that it is the 12th kalends of July, which is the summer solstice, the spring equinox will be taking place, and when you state that it is the 12th kalends of April, which ought to be the spring equinox, the winter solstice will take place, which is on the 12th kalends of January. This will happen to all the days of the year in the same way. In order to avoid this mistake, a leap year is intercalated every fourth year.)
Finally, De computo closes with the suggestion that the curious reader turn to Bede for further information.14
This "Abbonian" text of Helperic is also found in two manuscripts which contain the text of, and glosses on, De temporum ratione closely allied with MS 17's, namely the Winchcombe computus(fols. 145r-162r) and Cambridge, St John's College I.15. (pp. 239-280) 15. However, these three manuscripts differ in their rubrics, and even in the forms they give to the author's name:
MS 17
INCIPIT PREFATIO VENERABILIS MONACHI SVPER SEQVENTEM LIBRVM.
FINIT EXCERPTIO VEL EXPOSITIO HERIRICI VIRI DOCTISSIMI.
Winchcombe
INCIPIT EXCEPTIO VEL EXPOSITIO COMPOTI
(after capitula) INCIPIT LIBER VIRI DOCTISSIMI DE COMPVTO.
(no explicit)
Cambridge
INCIPIT PREFACIO IN LIBRVM VIRI DOCTISSIMI
(after capitula) INCIPIT COMPOTVS .
EXPLICIT COMPOTVS HILPERICI.
On the other hand, MS 17 and the Abbonian manuscript Cambridge, Trinity College R.15.32 (s. X-XI, Winchester) share the same explicit; as well, both call the author "Heriricus," and both omit the epistle to Asper. However, the Trinity manuscript omits the capitula found in MS 17, and treats the epilogue of the book as a final chapter, while MS 17 (like the Winchcombe computus) fuses it onto the end of ch. 38. While the Cambridge St John's College and Winchcome copies both refer to Helperic by his correct name, the Cambridge text of De computo is rather different from that found in MS 17, Winchcombe, and the Trinity manuscript, both in the order of its chapters and in its readings.16 The fact that MS 17 is relatively close to the Trinity manuscript (which has no text of De temporum ratione), and quite different from Cambridge St John's College (with which it shares many glosses to De temporum ratione), suggests that its text of Helperic derived from a different source than its text and glosses on Bede's great textbook. On the other hand, MS 17's text of Helperic broadly agrees not only with that found in the Trinity manuscript, but also with the Winchcombe computus. A collation of the preface and first chapter turned up only one instance where MS 17 read with either of these two against the third: Qui dies (MS 17, Trinity, Cambridge St John's College) versus Quibus (Winchcombe) (fol. 124ra22). MS 17 has a number of unique readings, a significant percentage of which involve the same fault, namely dropping words from the Winchcombe/Trinity text, but it is impossible to say whether the exemplar or Scribe B was guilty. However, all four manuscripts of this family share a special variant: the omission by homeoteleuton of a phrase from the end of ch. 14:
Quid ergo necesse est totiens et totiens addere XXXta et retrahere. cum lunaris aetas illo anno < per singulas kalendas numero regularum constet? Ob hoc eo anno> nulle pronuntiande sunt epacte.17
This phrase is also omitted by Byrhtferth when he quotes ch. 14 in his Enchiridion.18 Moreover, Byrhtferth's Proemium (MS 17 fol. 13r) refers to De computo as "heririci expositiones," a direct echo of the MS 17/Trinity rubric.19 Finally, a gloss on Helperic's text unique to MS 17 (gloss 2) appears, albeit in a slightly different form, in the Enchiridion and is not ascribed to Helperic.20 This same gloss appears in connection with the feria table on fol. 6r of MS 17.
1 The form of the author's name and the date of the annus praesens are the criteria for Ludwig Traube's classification of 33 MSS of De computo in "Computus Helperici," in Traube 1909-1920, 3.128-153, a revised version of an article which originally appeared in Neues Archiv 18 (1893):73-105.
2 This edition is of limited used for studying MS 17, because it represents the text of De computo prior to the revision by Abbo of Fleury. Moreover, Pez, from whose Thesaurus novus anecdotorum Migne took his text, did not use a trustworthy MS: see Wright (T) 1847, 69-70, Traube 1909-1920, 3.129 n. 1.
3 Traube 1909-1920, 3.146 and 128, note. Van de Vyver 1935, 149 suggested that Heiriricus, abbot of St-Mesmin de Micy (a dependency of Fleury) in the reign of Louis the Pious, may have lent his name to the Loire valley exemplars. Traube's original theory continues in circulation, thanks to its incorporation into standard reference works such as Sarton 1927-1948, 1.671-672.
4 Van de Vyver 1935, 148-149.
5 On this point, Abbo's revision was not thorough. In ch. 9, Helperic refers to January as the beginning of the year ("Quod uero nunc annum a Ianuario ordimur...") in both the MS 17 version (fol. 126rb32-33) and the PL text (28).
6 Bede, De temporum ratione praefatio (263.2-12).
7 MS 17 fol. 123rb5-16; cf. PL 137.19D.
8 An epigram in Munich CLM 10270 (s. XI) plays on the name Helperic/Helferich: "Computus Helperici tunc famine lenit amici. Bedam sed inde sequens iuuat hunc manifestius edens." (Helperic's computus appeases a friend's hunger. He helps by following Bede closely, but explaining him more clearly." See Traube 1909-1920, 3.144.
9 Jones 1939, 56.
10 MS 17 fol. 126va8-9; PL 137.28D. Cf.Bede, De temporum ratione ch. 12.
11 Bede, De temporum ratione 38 (400.33-39).
12 trans. Wallis 1999, 106.
13 MS 17 fol. 124ra22-35; PL 137.23A.
14 MS 17 fol. 135rb5-11; PL 137.48B.
15 McGurk 1974, 1-2.
16 A comparison of the prologue to De computo in MS 17 (J), the Winchcombe computus (W), the Cambridge St John's College I.15 (C) and the Trinity College manuscript (T) will illustrate this point:
123ra26 excideret JWT: excederet J²C
123ra32 insisterent JWT: instarent C
123rb5 pertinacius JWT: et pertinacius C
123rb6 cudere JWT: te cudere C
123rb10 tuo studio JWT: studio tuo C
123rb12-13 pompacitas JWT: pompacitatis C
123rb13 faleras exigimus JWT: faleras aut urbanitas exigimus ueneris C
123rb14 antiquis JWT: antiquorum C
123rb19 hoc opus JWT: que humiliter eos postulari sensi hoc opus C
123rb20 ut illud JWT: ut hoc C
123rb20 ad legendum JWT: preter se legenda C
17 MS 17 fol. 127ra29-32; Winchcombe fol 151ra14-18; Cambridge p. 254b2-5; Trinity p. 178.20-21. Cf.PL 137.21.
18 Byrhtferth 1.2 (314-316); cf. Baker and Lapidge's commentary p. 272.
19 ed. Baker and Lapidge, 379.87.
20 Byrhtferth 1.2 (38.241-249); see also Baker and Lapidge's commentary p. 269.