Cambridge, Fitzwilliam Museum, MS McClean 166
Computus and astronomy
Contents
Language(s): Latin
Full transcription:| Junius aprilis septembris necne nouember | Terdenos retinent contimiando dies . | Praeter quos omnes uno retinent sibi plures | Sed tenet in numero viginti februus octo . | Cui si bissextus fuerit super additur unus
This canonical text for using a set of computus tables often circulated with a set of computus tables and both the text and tables (known together as the Kalendarium) have been attributed to Robert Grosseteste , medieval scientist and theologian and former bishop of Lincoln in several manuscripts. The text and tables were attributed to Grosseteste by S. Harrison Thomson in The Writings of Robert Grosseteste (Cambridge, 1940), esp. pp. 94-95 and 106-107, although this particular manuscript was not known to Harrison Thomson. The tables have subsequently been rejected as authentic works of Grosseteste, and the canonical preface to the tables is now regarded as dubia in more recent scholarship, such as J. Morton's assessment of Grosseteste's computistical material where she says Grosseteste is '[p]ossibly [...] responsible for the preface which accompanies the [tables] in the ascribed texts'. See Jennifer Moreton, ‘Robert Grosseteste and the calendar’, in Robert Grosseteste: New Perspectives on his Thought and Scholarship, ed. James McEvoy (Turnhout, 1995), 77-88, esp. pp. 78-79.
The text here seems to interpolate a discussion of bissextile calculations not included in any of the versions of this text printed by Lindhagen.
The notes fall into two main groups. The larger group records calendrical and computistical information such as the aureus numerus (golden number) for a particular year (in this case 8). The smaller group records the number of years that have elapsed since a particular event and include the following information:
- Annus aborigine[sic] mundi vim.cccc.lxxix.
- Annus ab incarnatione m.cc.lxxix.
- Annus apassione[sic] domini .m.cc.xlvii.
The number of elapsed years given in the time-reckoning notes suggest that the notes were made c. 1279. The Julian calendar begins with the birth (incarnatione) of Jesus, and the notes state that 1279 years have elapsed since that event. Jesus is traditionally believed to have died in his 33rd year of life, and the notes state that it has been 1247 years since he was crucified (a passione). Subtracting the year 1279, from the number of years given since the creation of the world (ab origine mundi), 6479 gives a creation date for the world c. 5200 BCE, which accords with calculations made for the age of the world by St Jerome and Gregory of Tours.
The table on f. 1v has calculations for specific years between 1044 and 1548; the column for the year 1296 is marked in ?crayon with a red cross. The table on f. 2r has an annotation '1341' in red next to one of the rows. The tables are called 'Tabula terminorum' in a final rubric on f. 2v.
M.R. James divided this text into two, the first half on ff. 3-4 and the second part on ff. 5-8, but all of the text on ff. 3-8 is part of the Quadrans vetus. The text is imperfect due to the loss of the original 5th leaf in the quire.
Illustrated, see notes on decoration.
Tables for finding the position of the sun in:
- A bissextile year
- One year after a bissextile year
- Two years after a bissextile year
- Three years after a bissextile year
A bissextile year is a leap year. In the modern Gregorian calendar we add a leap day on the 29th March, but the practice of adding a leap day every four years (with minor adjustments) significantly predates the adoption of the Gregorian calendar in western Europe. The Romans also adjusted their calendars to the length of the solar year by adding an extra day to February every four years, but they did it by doubling the 24th of February, which was better-known in their calendar as the 6th day before the kalends of March (ante diem sextum Kalendas), causing a doubled 6th day (before the kalends of March) i.e., a bis+sextile day.
Full transcription:| Anno domini .788. bremensen funduit ecclesiam mittens Willehadum omnium doctorum promum uersus maritimas et boreales saxonie partes . qui continuo falcem predicationis illius loci misit in botros infidelitatis uindemians . ad fidem catholicam transalbinos populos et frisones prouocauit
Full transcription:| Pillule sublingua contra fluxum reumatis : Storacis Calamite Mirre(?) Olibani Laudani Calamiare maci...(?) Castorij Cynamonu Nucis muscate Cubebe Opij ...(?)
Some text unclear due to tight binding.
Significant marginal annotation in contemporary hands.
Text accompanied by diagrams (see 'Decoration' for further information).
Significant marginal annotation in contemporary hands.
Quotations from Latin poets in the text are written as prose.
Text accompanied by diagrams (see 'Decoration' for further information).
Significant marginal annotation in contemporary hands.
Quotations from Latin poets in the text are written as prose.
Notable feasts:| 31 January - Aldegundis uirginis
Notable feasts:| 1 February - Brigide uirginis
Notable feasts:| 1 March - Albini confessoris et donati martyris| 4 March - Adriani martyris| 17 March - Gertrudis uirginis| 24 March - Quintini martyris| 26 March - Liudgeri episcopus|
Notable feasts:| 22 April - Egressio Noe de archa
Notable feasts:| 1 May - Philippi et iacobi . walpurgis| 4 May - translacio sancti godehardi| 5 May - Godehardi episcopi deposicio| 7 May - Victoris martyris| 9 May - translacio sancti nicolai | Swiperti (Swiperti in another hand)| 13 May - Seruacii episcopi . 3 lectiones . gingufli (gingulfi in another hand) 15 May - sophie virginis
Notable feasts:| 25 June - Seuere virginis et martyris . sancti eligij martyris
Notable feasts:| 4 July - Odelrici episcopi et confessoris| 8 July - Kiliani episcopi| 13 July - Margerete virginis| 14 July - Hinrici[sic] regis (in another hand)| 28 July - Panthaleonis martyris
Notable feasts:| 5 August - Dominici confessoris . osvaldi regis et martyris
Notable feasts:| 1 September - Egidii abbatis . lupi episcopi et confessoris | 2 September - Anthonii | 8 September - Adriani martyris | 28 September - Wenceslai martyris
Notable feasts:| 3 October - duorum Ewaldorum| 4 October - Francisci confessoris| 9 October - Gereonis . uictoris et sociorum eius| 21 October - Undecim milium uirginum| 22 October - Seueri episcopi| 23 October - Seuerini archiepiscopi
Notable feasts:| 6 November - Leonardi confessoris (in another hand) 7 November - Willibrordi confessoris| 19 November - Vitalis . Simplicij . elizabeth 26 November - Genouese virginis
Notable feasts:| 9 December - Godehardi episcopi (in another hand)
The calendar contains copious contemporary and later additions.
Mnemonic for the progression of ferial letters for the first day of each month written in red in the lower margin of each page of the calendar: A | dam | de | ge | bat | er | go | ci | fos | a | dri | fex (i.e., ADDGBEGCFADF)
Mneomnic poem for the dies aegyptiaci ('Egyptian days'), each line of the poem contains two numbers, the first of which should be counted (inclusively) from the beginning of the month to find the first 'Egyptian day', and the second of which should be counted backward from the end of the month to find the second. For example, the first number in the January verse is 1 (prima) and the first day counted inclusively from the first day of January is 1 January. The second number in the January verse is seven (septima) and the seventh day counted inclusively from the end of January (i.e., 31 Jan) is the 25th of January, making the 'Egyptian days' for January the 1st and 25th of the month. Full transcription:| Prima dies mensis et septima truncat ut ensis | Quarta subit mortem prosternit tertia fortem | Primus mandentem dirumpit quarta bibentem | Denus et undenus est mortis wlnere[sic] plenus| Tercius occidit et septimus hora relidit| Denus pallescit quindenus federa nescit| Tredecimus mactat julij decimus madefactat[sic] | Prima necat fortem perimitque secunda cohortem| Ternus septembris et denus fert mala membris| Tertia cum dena clamat sit integra vena| Scorpius est quintus . sed tertius ad mala cinctus | Septimus mos anguis virosus denus et anguis
Calendrical poem, one line for each month written in the lower margin close to the left edge of the leaf and preceded by a red paraph mark. Full transcription: | pocula Janus amat| Februarius algeo clamat| Marcius arua fodit| Aprilis florida prodit| Ros et flos nemorum maio sunt fomes amorem| dat iunius fena| Julio refecatur auena| Augustus spicas| September colligit vuas[sic] | Seminat october | Spoliat uirgulta nouember| Querit himere cibum porcum mactando december
Physical Description
Current foliation sequence:
i + 1-77 + [ii]
Foliated in pencil in Hindu-Arabic numerals in the upper outer corner of each recto. Where there are two uncancelled pencil folio designations on a leaf, the correct designation is the smaller of the two (both physically and numerically), and this smaller designation should be used. The final paper endleaf, f. [ii] was assigned this temporary designation in 2024 for the production of a functional tei-xml catalogue record for the Curious Cures project.
Deprecated foliation sequence.
Folios 1-79 (for ff. i + 1-77 + [ii])
Foliated in pencil in Hindu-Arabic numerals in the upper outer corner of each recto; this foliation sequence has been suspended and is no longer in use. Most of the designations in this foliation sequence have been cancelled by a single diagonal strike through the designation. Where there are two uncancelled pencil folio designations on a leaf, the designation belonging to this sequence is the larger of the two (both physically and numerically) and should not be used.
Deprecated medieval foliation sequence.
Folios 70-80 (73 omitted) for ff. 2-11, folios 1-5 (for the present ff. 12-16), folios 8-68 for the present ff. 17-77
Foliated in ink in the typical medieval forms of Hindu-Arabic numerals in the upper outer corner of each recto. This foliation sequence indicates that the quires in this volume have been rearranged since this foliation sequence was added as f. 1 in this medieval sequence is found on what is now the first leaf of Quire 2, and the present Quire 1 contains the designations that should appear at the end of the sequence. There are several things to note about this foliation sequence:- The current f. 1 was probably f. 69 in the medieval sequence as the rest of Quire 1 contains the medieval designations ff. 70-80 and the sequence would then follow on directly from the medieval designations at the end of Quire 7
- A leaf has been lost from Quire 1 after the medieval foliation sequence was added as there is an interruption in the medieval sequence; i.e., the current f. 4 is the medieval f. 72 and the current f. 5 is the medieval f. 75, but there is no leaf with a medieval f. 73 designation present in the volume.
- The medieval sequence in the present Quire 2 (ff. 12r-21v) runs from medieval folios 1-12; the present quire contains only 10 leaves and the medieval designations jump from medieval folio 5 (the present f. 16) to medieval f. 8 (very faint) on the present f. 17, indicating the loss of two leaves (medieval ff. 6-7) between the present ff. 16 and 17.
Collation
Quires of 12 and 10 leaves, with indications that some leaves have been lost since the volume was made. A medieval foliation sequence present in the volume indicates that the present Quire 1 was the 7th quire at the time the medieval foliation sequence was added to the volume. The quires are arranged as follows:
- Quire 112-1 (ff. 1-11: 5th leaf missing, stub visible)
- Quire 212-2 (ff. 12-21: 6th and 7th leaves missing)
- Quire 312 (ff. 22-33)
- Quire 410 (ff. 34-43)
- Quires 5-612 (ff. 44-67)
- Quire 710 (ff. 68-77)
112-1 (5th missing) 212-2 (6th and 7th missing)
No leaf signatures visible in the volume.
No quire signatures.
Catchwords present in the lower margin of the last verso of Quires 2-7.Condition
Layout
170 × 110 mm. Folio 1r ruled in ?leadpoint, frame and lines. Ruled in two columns, 47 lines to the column, written below top line.
130-180 × 105 mm. Folios 1v-2v, 9r-11r, and ff. 72r-77v ruled in ink in tabular formats for calendars and computus tables.
125-140 × 75-95 mm. Non-tabular leaves between ff. 3r-77v: ruled in crayon, frame and lines. Ruled in single-column format, typically 33 lines to the leaf and written below top line. Folio 11v unruled and informally written. Folio 39r unruled.
Hand(s)
Written in a late-13th century northern textualis libraria by at least two scribes. Double-compartment a, sometimes with only a small stub for the upper compartment, particularly when a is in the initial position. Minimal 'biting' of letters. Letters f and s sometimes on the baseline, and sometimes just below it.
Annotations in several informal textualis hands and hands tending toward cursiva in the margins throughout the volume.
Decoration
- Folio 38v: Unattached sample of acanthus leaf flourishing decoration next to a diagram illustrating the mechanics of a solar eclipse
- Folio 39r: Small tinted drawing of a peacock
Numerous diagrams throughout the volume:
- Folio 6r: Geometric diagrams in the lower margin
- Folio 6v: Diagram to find the height of a turret with an illustration of a building with a turret in red and black ink
- Folios 7r-8r: Several geometric diagrams in the margins for calculating the surface area and significant angles of various shapes.
- Folio 8rv: Several diagrams for calculating the surface area and volume of 3D objects. Detailed diagrammatic illustration of a bucket on f. 8r, detailed diagrammatic illustration of a barrel and a tankard on f. 8v.
- Folio 8v: Erased diagrm of three concentric circles, the whole shape divided into quarters at the cardinals, with erased numbers written in the two outermost circles.
- Folio 17v: Geometric diagram in the lower margin
- Folio 20v: Spherical diagram of the heavens in red and black, the circles labelled from innermost to outermost as follows: spera lune, spera mercurii, spera uenis, spera solis, spera marcis, spera iouis, spera saturni, spera octaua, primum mobile
- Folio 36v: Spherical T-O map with the continents (labelled Asia, Africa, Europa) divided into the seven climate zones
- Folio 37v-38v: Several lunar and solar eclipse diagrams
- Folio 41r: Spherical diagram of the hevens in red, green and ochre with the circles labelled from innermost to outermost as follows: Spera lune, Spera mercurij, Spera ueneris, Spera solis, Spera martis, Spera iouis, Spera saturni, Spera stellarum
- Folio 44v: Spherical diagram for astronomical calculations
- Folio 48r: Metaphorical diagram illustrating the solar year; draconid ouroboros surrounded by an outer circle bearing the text 'Serpens annus ego dicti sol sic circinat inquo. + Qui fuerat pridem status est iam temporis idem +'
- Folio 51v: Diagram for comparing solar calculations in the writings of Dionysius Exiguus and Garlandus Compotista
- Folio 53r: Diagram expressing the quadripartite harmony and the connections between many natural phenomena (e.g., ages of man, humoral liquids, seasons, elements, cardinal directions)
- Folio 56rv: Diagram of lunar phases relative to the position of the sun
- Folio 69v: Circular diagram expressing the relationship between a 19-year lunisolar cycle, the claues terminorum, and the lunar epacts.
- Folio 71v: Circular diagram. Concentric circles described from innermost (text) circle to outermost (text) circle: 1) 19 year lunisolar cycle, 2) Claues terminorum 3) Cycle of epacts, 4) Cycle of embolisms, 5) Number of weeks between Christmas and the 6th Sunday before Easter
Folio 12r: Decorative initial 'O' in gold, red, blue, pink and white with an animal head among foliage in the counterspace.
Puzzle initials in red and blue with red and blue flourishing in the margins and counterspaces at the maajor divisions of the text. See e.g., f. 1r.
Plain initials in red or blue at the minor divisions of the texts, see e.g., f. 6r.
Rubrication throughout at the major divisions of the texts.
Additions
On f. 1r, 'No. 70' in ink.
Quire signatures ('1-7') in the bottom right-hand corner of the recto side of the first leaf of each quire, written in pencil by a hand of the 19th/20th century.
Binding
19th-/20th-century binding: half bound in leather with sprinkled paper sides over paste- or mill-boards. Six raised bands on spine. Spine partly covered with a torn fragment of an earlier binding, a dark leather binding with the compartments decorated with gold tools. Dimensions (L x W x H): 235 x 175 x 25 mm.
The covers contain several labels and annotations:
- '4' written in ink on the front cover
- A label fixed to the front cover with an adhesive bearing the annotation 'MS. IV.' in ink
- A number '324' written in white ink on the front cover
- Two pieces of a torn printed label, one on each cover, the first bearing 'B. BON' and '3', the second bearing 'GNI' and '3', probably originally a larger label bearing the words 'BONCOMPAGNI' and '323'
Paper pastedowns pasted over the turn ins. The front pastedown contains:
- '166' written in pencil
- A blind-embossed unidentified heraldic achievement on a small oval piece of paper pasted onto the pastedown
- A note in pencil 'CLX.198'
- A note in pencil 'Ce.79'
- A McClean Collection bookplate ('FROM THE COLLECTION OF FRANK MCCLEAN') with engraving by J. A. C. Harrison S.C. The bookplate has two pencil annotations: 'Boncompagni Catatlogue 323'; and 'MS McCl. 166'
- Annotation in pencil '6/'
- Annotation in ink 'C.C.v.8.ti'
- A note in pencil:| 77 ff| aug.14.08| H.A.C
- A note in pencil: Mc MSS. 166
A paper endleaf probably contemporary with the binding present at each end of the volume. The front endleaf, f. i contains several small annotations in ink and pencil on the recto, perhaps former prices and bookseller notes. On f. i verso there is a partial list of the contents of the volume in ink in two hands:
- Tabula terminorum
- Libellus de usu quadrantis
- Tabulae astronomicae div argumenti
- Algorismus Magni Johannis de Sacro Busto[sic]
- folia XXVIII in charta pergam.| Ej. Ejusdem liber de sphaera foll.19. Compotus totidem 33 foll.
Stored in a dark brown hard-cased box bearing a handwritten label 'McClean 166 16.3.9.23'.
Traces of a former binding present on f. 11v as a rust-stain in the centre of the outer margin. The present Quire 1 was once the final quire in the volume, and as such folio 11v was once one of the final leaves in the volume, the rust mark in the outer margin of f. 11v suggests that prior to the displacement of Quire 1, the leaves were bound between boards fastened with a metal clasp positioned at the centre of the fore edge.
History
Date of production based on palaeographical features and cluster of late 13th century dates given in annalistic entries on f. 11v. Place of production assigned to France based on palaeographical features, and to Verdu n by M. R. James based on specific feasts in the calendar on ff. 72r-77v
Provenance and Acquisition
Owned by the German mineralogist and geologist Georg Amadeus Carl Friedrich Naumann (1797-1873) . According to the M.R. James Catalogue, Fitzwilliam Museum MS McClean 166 was MS 14 in Naumann's collection
Owned by the Italian mathematician and historian of science Baldassarre Boncompagni (1821–1894) . Fitzwilliam Museum MS McClean 166 was MS 323 in Boncompagni's collection.
Owned by Frank McClean (1837-1904) : sold to him by the booksellers Wesley & Son of Essex Street, London, probably c. 1894-1904.
Bequeathed to the Fitzwilliam Museum by Frank McClean , together with the rest of his collection, in 1904.
Additional Information
Record Sources
Availability
Visitors to the Fitzwilliam Museum who wish to consult Collection material are required to apply to the Museum in advance of their visit. For information on eligibility and admission procedures see: Fitzwilliam Museum: Study Room.
Bibliography
-
A Critical Edition of 'Tractatus Quadrantis', Britt, Frances Nan Long (GA: Atlanta, 1972, PhD)
Practical Geometry in the High Middle Ages: Artis Cuiuslibet Consummatio and the Pratike
de
Geometrie Memoirs of the American Philosophical Society, Victor, Stephen K. (Philadelphia, 1979)
Funding of Cataloguing
Wellcome
Digital Images
Abbreviations
View list of abbreviations and editorial conventions.
