State Library Victoria > La Trobe Journal

No 81 Autumn 2008


John N. Crossley
Ptolemy's Almagest: its dates and the dating of Oxford, All Souls College, ms. 95

The Almagest of Claudius Ptolemy was the dominant work in astronomy for over a thousand years until the publication of Copernicus's De revolutionibus in 1543. The State Library of Victoria owns a beautiful thirteenth-century manuscript of the translation Gerard of Cremona made from Arabic in the previous century. This manuscript has a number of interesting features including many glosses and two interpolations. One of these ultimately derives from Ptolemy's Canon or Handy Tables: a list of the dates of ancient kings, which was updated in the Zij of al-Khwārizmī, and includes the date of the Flood. A very similar interpolated list occurs in the manuscript in All Souls College, Oxford, also mentioning the Flood. This latter manuscript is deficient in that virtually all of the many tables are missing. On the other hand the list of dates assists us in the precise dating of that Oxford manuscript for the first time. Finally, evidence from the Huntington manuscript of the Almagest and an early book list from All Souls allow us to explain why there are no tables in the All Souls manuscript.
Ptolemy lived in Alexandria about 90–150 AD. He explained the movements of what were then called the seven planets (the sun, moon, Mercury, Venus, Mars, Jupiter and Saturn) as observed in the heavens. The movements of the planets do not fit neatly to circles around the earth, even though the sun and moon do move smoothly across the heavens. He therefore modified the basic circles by considering the planets as moving on smaller circles whose centres are on the basic circles. (The system is rather like the exciting roundabouts at funfairs where groups of seats rotate around an anchor on a platform which itself rotates.) These smaller circles were called epicycles: circles on circles.1 His main claim was that this system of epicycles fitted the observed facts of the planetary movements. It was not until well over a thousand years later that the heliocentric theory of Copernicus was developed.2 Ptolemy's work was translated into Arabic and was brought into Spain by the Arabs.
Many such Arabic works were translated into Latin in Toledo.3 One of the chief translators was Gerard of Cremona who, although he was born in Italy, lived and worked in Toledo and made over 70 translations.4 His translation was accomplished no later than 1175, and many copies of this work were made. Paul Kunitzsch, in his life-long study of the Almagest used 40 different manuscripts that contained the whole of the Almagest.5 The State Library of Victoria is fortunate in possessing one manuscript: RARESF 091 P95A (hereafter referred to as the Melbourne manuscript).6 In this essay I shall also refer to two other manuscripts of Gerard's translation: All Souls College, Oxford, MS 95 and Huntington Library, HM 65.7
The text and tables of the Melbourne manuscript are complete and the whole work is written, as Sinclair notes, in a 'first half 13c. Italian littera gothica textualis with an explicit 172va … '.8 Sinclair also adds: 'Decoration: red rubrics; small caps alternately red, with blue pen work, and blue, with red pen work', but he does not note the elaborate pen flourishes at certain places, notably near the beginnings of each of the six books. The script is very neat with very few corrections, but it has a large number of glosses. On the other hand the All Souls manuscript is nothing like as elegant or error free; nor does it have many glosses. Watson identifies this manuscript as being from the latter half of the thirteenth century, but no more precisely. The Huntington manuscript is a grand manuscript, but contains many corrections by the scribe and others. It is internally dated as being written in Southern France in 1279 (folio 184r). At some stage it belonged to 'Pier Leoni (d. 1492), physician to Lorenzo de' Medici'.
The manuscripts vary in a number of ways, in particular in the treatment of numbers in the text.9 In the original Greek an alphabetic system was used and when it was translated into Arabic the abjad, or alphanumerical system, was used. In some manuscripts of Gerard's translation the Hindu-Arabic decimal system of numerals was employed and in some others, the Roman. In the Melbourne manuscript numbers are written out in full in Latin words in the text, but in the tables they are written in Hindu-Arabic numerals. In the All Souls manuscript they are written in Hindu-Arabic numerals throughout the text; however all of the major tables are missing in that manuscript, but those few that are included have Hindu-Arabic numerals. In the Huntington manuscript there is a variety of practices: in some places Hindu-Arabic numerals are used, in some lower case Roman numerals, and in others Latin words. There is no apparent system in the choice of notation.10
In the Melbourne manuscript there are only two interpolations in the text. One is a short and minor one elucidating some of the technical aspects (folio 33va). The other occurs on folio 44rb, immediately after the end of Book III, Chapter V, in which chapter Ptolemy has been concerned with fixing dates. He begins his calculations with Nabonassar, otherwise known as Nebuchanezzar or Nabuchonosor. The interpolation refers to another work saying in canone, that is to say, in the Canon of Kings or Handy Tables, where Ptolemy had made a list of many kings from ancient times.11 The date of the Flood, 16 February 3102 BC, comes originally from India, for this date coincides with the beginning of the Kali yuga period and was commonly used in Hindu astronomy. The Hindu interpretation of this as the era of the Flood is common in Islamic sources.12 In particular this was incorporated into the Zij or Astronomical Tables of al-Khwārizmī (died after 846 AD), which circulated widely in the Middle Ages.13 This is the source of the interpolation we are considering: it is extracted from al-Khwārizmī's Zij.
Figure 1 provides an image of the table from the Melbourne manuscript, folio 44r. The following table is taken from the right hand column of Figure 1:
years months days
What has to be added to the years of Alexander above the years of Christ 311 3 2
What are between the years of Philip and the years of Iazdaiart14 955 3 0
What are between the years of Philip and the years of the Arabs 945 3 26
What are between the years of the Flood and the years of Iazdaiart 3735 10 23
What are between the years of Nabonassar and the years of Iazdaiart 1379 3 0
What are between the years of Alexander and the years of the Arabs 932 9 17
What are between the years of Christ and the years of the Arabs 621 6 15
The All Souls manuscript additionally yields:
What is between the years of Nabonassar and Alexander 435 7 7
What is between Nabonassar and Christ 746 10 9
Together the above figures yield the following time lines:
Melbourne ms. All Souls ms.
The Flood -3102.05.04 -3102.02.17
Nabonassar -746.10.11 -746.02.26
Philip -322.09.11 -323.11.12
Alexander -311.03.02 -331.11.14
Christ 1
Arabs 622.06.15
Iazdaiart 632.05.19 632.06.16
In this last table the items in italics have been calculated from the figures given in the manuscripts. It will be noted that there are small discrepancies, even after allowing for the fact that there is an extra year to be taken into account when going from BC to AD or vice versa.
In the All Souls manuscript, the interpolated table (which I have reconstructed here), has been copied in a very awkward fashion. Part of it is in the main text and part in the margin. Indeed a note written by the scribe in the margin of folio 28r says: 'This table ought to stand between the two columns so that the three boxes ought to stand next to the words (ibi) "that they add of years, months and days".'15 In the text itself, the part corresponding to the table in the left hand column of the Melbourne manuscript folio 44r, runs on into the table in the right column. Some attempt has been made to correlate the rows by inserting Hindu-Arabic numerals. However, these numerals, as in all of the interpolation in All Souls College ms. 95, have obviously been inserted by someone other than the scribe.
In the printed version of the Almagest from 1551, a copy of which is in the State Library of Victoria, this interpolation is presented as a neat table on p. 76, which translates as follows:16

Fig. 1. State Library of Victoria MS RARESF 091 P95A, fol 44r.

Differences of time from one reign to another:
Years Weekday From to Years Months Days
¶ Philippi 1 Flood Iazdaiart 3725 10 23
¶ Alexander 2 Nabuchodon. Iazdaiart 1379 3 0
Iazdaiart King
of the Persians 3 Philip Iazdaiart 955 3 0
Nabuchodonasar 4 Philip Arabs 945 3 26
Flood, Arabs 5 Alexander Arabs 932 9 17
Diocletian 5 Alexander Christ 311 3 2
Christ Arabs 621 6 15
Philip Alexander 12 6 9
The relevant numbers are exactly the same as those in the Melbourne manuscript.
There is a further addition to Gerard of Cremona's text in the All Souls manuscript on folio 27r, which unfortunately has no correlate in the Melbourne manuscript. This interpolation is very distinctive in that, while the basic text is written in two columns, this insertion spreads across the whole of the bottom of folio 27r. Lines have been deliberately ruled for it and, although the script is smaller, it appears to be in the hand of the main scribe. In this addition we read:
It is believed that these years agree:
The year of Our Lord Jesus Christ 1250 and 6 months.
The Arab year 648 and 3 months and 9 days. These are lunar.
The year of the prophets or of Iazdaiart 619 and 5 months and 19 days.
The year of Alexander or the Greeks 1461 and 9 months.
The year of Nabuchdonozor or the Egyptians 1998 and 8 months and 19 days.
Lines 1 and 4 are joined to: These are [years] of 365 days and a quarter.
Lines 3 and 5 are joined to: These are [years] of 365 days without the quarter.
The references here are to 365 days per year versus 365 and a quarter.17 However, even allowing for that there are small discrepancies in each of the last four lines. Neglecting months and days, 648 should be 628, 1461 should be 1561, and 1998 should be 1997. The first two can be explained as copying errors: there is a similar error in the table in the margin where we find 855 instead of 955, and 445 instead of 945. The last error is almost negligible, though it may be a simple confusion between the writing of 4 and 5, something that causes difficulty to readers of manuscripts to this day.
There is one important conclusion we can make from the choice of 1250 and 6 months AD in the top row of the table: it strongly suggests that the scribe was writing this text in the sixth month, i.e. June, 1250 AD.
Finally, there is the question of the missing tables in the All Souls manuscript. There are book lists from the time of the co-founder (with Henry II) of All Souls, Archbishop Chichele, who died in 1443, a few years after the college was founded in 1438. In List II, the books are arranged first according to whether they are chained (cathenati) or not, and within those classifications, according to subject.18 The books are listed by the incipits of the second folios, since many of the opening pages of early books got damaged and were unreadable. There we find, among the thirteen chained books under Astronomia Cath' [Cathenati]:
*135 124 Tholomeus in almagesti 2 fo tatim genus
136 125 Liber astronomiae 2 fo tabula
137 126 2 fo eciam diuinitas
The bold numbers, due to Ker (see n. 18), have an asterisk if they were extant at the time of preparation of the list. Thus the book next to the Almagest, one of several astronomical works, is missing. Ptolemy's Quadripartitum is also listed as 132 121, and there were five other books on astronomy classified as distribuendi, i.e. for circulation.
In the Huntington manuscript HM 65 the tables occur after the main text, beginning on folio 219r, and they are marked with tie marks.19 However, I did not observe any such tie marks in the All Souls manuscript. The next book in the All Souls list is recorded as a book on astronomy and is missing, but the incipit of the second folio reads: tabula. We therefore infer that the tables from the All Souls Almagest were bound in a second volume, which was in the college in the first half of the fifteenth century but disappeared shortly thereafter.
The three manuscripts therefore illuminate each other. Both the Melbourne and the Huntington manuscripts include all the tables. However the ones in the Huntington are collected together at the end of the work, while the Melbourne ones are integrated into the body of the text. This enables us to see why there were no tables in the All Souls College Almagest: they were in the second, now missing, volume of the Almagest. Next, the Melbourne manuscript has the interpolated Canon of Kings neatly presented. This allows us to make sense of the All Souls one, for although the table is present in the All Souls manuscript, it is badly arranged and is virtually incomprehensible on its own. Finally, the All Souls manuscript has an extra interpolation, which depends on the interpolated table for its explanation. This interpolation is very valuable since it has led me to discover the date of the All Souls Almagest, but this would not have been possible without the clarification provided by the Melbourne Almagest manuscript.


I would like to thank the Rare Books librarians at the State Library of Victoria, All Souls College, Oxford and the Huntington Library, Pasadena, CA, for their generous assistance, and Charles Burnett for his careful reading of a draft and providing valuable additional information. I would also to like to thank the Warden and Fellows of All Souls College, Oxford for permission to reproduce the text of their manuscript.


For an English version, translated from the original Greek, see Gerald James Toomer, (translator and annotator), Ptolemy's Almagest, London: Duckworth, 1984.


See Nicolai Copernici Torinensis De revolutionibus orbium coelestium, libri VI, Norimbergae, apud Ioh. Petreium, 1543. The State Library of Victoria possesses a copy of the second edition of 1566 and also a facsimile of the first.


See Charles Burnett, 'The coherence of the Arabic-Latin translation program in Toledo in the twelfth century', Science in Context, 14(1/2): pp. 249-288, 2001.


See e.g. Burnett, 2001, and Richard Lemay, 'Gerard of Cremona', in Charles Coulson Gillispie, editor, Dictionary of Scientific Biography, volume XV (Supplement I), Roger Adams—Ludwik Zejszner: topical essays, pp. 173-192, New York: Charles Scribner's Sons, 1978.


See e.g. Paul Kunitzsch, Der Almagest, Göttingen: Vandenhoeck und Ruprecht, 1974.


See manuscript no. 224 in Keith V. Sinclair, Descriptive catalogue of medieval and renaissance western manuscripts in Australia, Sydney: Sydney University Press,1969.


See Manuscript 95 in Andrew George Watson, A descriptive catalogue of the medieval manuscripts of All Souls College, Oxford, Oxford University Press, Oxford, 1997, and Huntington Library, HM 65, in Consuelo W. Dutschke with the assistance of Richard H. Rouse et al., Guide To Medieval and Renaissance Manuscripts in the Huntington Library, Henry E. Huntington Library and Art Gallery, San Marino, California, 1989. Electronic version encoded by Sharon K. Goetz, 2003 available at, accessed 30.iii.2006.


See Sinclair, no. 224, p.382 and cf. also Keith V. Sinclair, 'An unnoticed astronomical and astrological manuscript', Isis, 54, pp. 396-99, 1963.


The numbers in the tables are uniformly in Hindu-Arabic numerals, apart from when they occur in notes appended to the tables. For example Roman numerals occur in notes to tables on folio 100va, and Latin number words and Roman numerals occur in a note to a table on folio 101rb.


See also my 'Reading and writing numbers: 1200-1400', unpublished paper, currently submitted for publication.


Roger Bacon, c. 1214-1294, the Franciscan monk, notes in his Opus majus that Ptolemy is the authority for dates from Nabuchonossor through Alexander the Great to Hadrian: Nam Ptolemaeus in Almagesti certificat nos de tempore a Nabugodonosor usque ad Alexandrum, et ab eo usque ad Octavianum Augustum, et ab eo usque ad Adrianum principem. See John Sherren Brewer, ed., Opera hactenus inedita Fr. Rogeri Bacon, Number 15 in the Roll Series, London: Longman, Green, Longman and Roberts, 1859, p. 189.


See Lynn Thorndike, 'Astronomical and chronological calculations at Newminster in 1428', Annals of Science, 7, pp. 275-283, 1951 (pp. 277 and 281) and compare Otto Neugebauer and Olaf Schmidt, 'Hindu astronomy at Newminster in 1428', Annals of Science, 8, pp. 221-228, 1952 (pp. 221-222).


See Heinrich Suter, Die astronomischen Tafeln des Muhammad ibn Musa al-Khwârizmî in der Bearbeitung des Maslama ibn Ahmed al-Majrîtî und der lateinischen Uebersetzung des Athelard von Bath, Det Kongelige Danske Videnskabernes Selskabs Skrifter, 7. Reihe, Historisk og Filosofisk Afdeling 3,1 (1914), reprinted in Heinrich Suter, Beiträge zur Geschichte der Mathematik und Astronomie im Islam, vol. I, Frankfurt a. M., Institut für Geschichte der Arabisch-Islamischen Wissenschaften, 1986; translation and commentary by O. Neugebauer, The Astronomical Tables of al-Khwarizmi, Copenhagen: I kommission hos Munksgaard, 1962.


Iazdaiart was the spelling of the name of the Sassanian King, Yazdigird III, the first day of whose reign is used as the epoch of many Arabic astronomical tables. (This is why it is necessary to have a table showing how to convert years, months and days from Yazdigird to the same from the hijra.)


Hec tabula deberet stare inter duas columpnas itaque tres arce deberent stare iuxta ibi Quid addunt videlicet annorum. mensium. dierum. This quotation clearly takes up the phrase "What has to be added" in the table at the top of p. 120: Quid addunt anni Alexandri super annos Christi, etc.


Claudij Ptolemaei Pelusiensis Alexandrini Omnia quae extant opera, praeter Geographiam, quam non dissimili forma nuperrimè aedidimus / summa cura & diligentia castigata ab Erasmo Osualdo Schrekhenfuchsio, & ab eodem Isagoica [sic] in Almagestum praefatione, & fidelissimis in priores libros annotationibus illustrata, quemadmodum sequens pagina catalogo indicat, in officina Henrichi Petri, Basileae, mense Martio, 1551. (RARESF 520.8 P95.)


Egyptian years were counted as just 365 days.


The list is reproduced beginning on p. 8, of Neil Ripley Ker, Records of All Souls College Library 1437-1600, Oxford: Oxford University Press, 1971.


See the illustration at