Peter Philomena of Dacia,also known as Petrus Dacus, Petrus Danus, Peter Nightingale

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also known as Petrus Dacus, Petrus Danus, Peter Nightingale (fl. 1290–1300)

mathematics astronomy.

Originally a canon of the cathedral in Roskilde, Denmark, Peter Nightingale first appears as the recipient of a letter from Hermann of Minden (provincial of the German Dominicans, 1286–1290) thanking him for the gift of some astronomical instruments and proposing to him that he leave Italy for Germany.1 In 1291–1292 he is listed as a member of the University of Bologna,2 where he taught mathematics and astronomy to puplis who included the astrologer Magister Romanus3 During 1292 Peter went to Paris, where in that and the following year he produced many writings. After that the sources are silent about him until 4 July 1303, when a letter from Pope Boniface VIII shows that he had returned to Denmark, in his former position as a canon of Roskilde.4 The years of Peter’s birth and death are unknown; and since he is not mentioned in the necrology of his cathedral, it is probable that he died abroad. Although he was a canon regular, he has often been considered a Dominican5 and confused with the Swedish Dominican author of the same name. This mistake was corrected by H. Schück in 1895 but nevertheless persists in more recent literature.6 His identification with another Petrus de Dacia, who in 1327 was rector of the University of Paris, has also been shown to be incorrect.7

A recent survey has revealed that there are more than 200 extant manuscripts of Peter’s numerous works.8 These can be divided into two groups, the first of which comprises the following writings:

Commentarius in Algorismum vulgarum (10 MSS). This commentary to Sacrobosco’s well-known text book of arithmetic was complepted on 31 July 1291 at Bologna and is the only work of Peter Nightingale that has been edited and printed.9 It contains some original contributions, notably a new and better method of extracting cube roots.10

Tabula multiplicationis (2 MSS). A multiplication table in the sexagesimal system and, accordingly, destined for use by astronomers

Declaratio super Compotum (2 MSS). A commentary on the twelfth-century Compotus metricus manualis of Gerlandus of Besancon. It has not yet been examined.

Kalendarium with canones (56 MSS). This calendar for the period 1292–1369 was computed in Paris as a substitute for the much-used calendar of Robert Grosseteste, which had run out.11 The appended canones give rules for adjusting the caledar for a new seventy-six-year period. Such adjustments were made in 1369 and around 1442. This calendar was intended to give more precise times of the phases of the moon than Grosseteste’s work, with which it has often been confused.12

Tractatus eclipsorii (2 MSS). This newly found treatise describes the construction and use of a volvelle or equatorium for determining eclipses. It was written in Paris but contains a reference to Roskilde and is presumably the first evidence of Peter’s interest in devising astronomical computers. It is followed by:

Tabulae coniunctionum soils et lune, that is, a table of mean conjunctions of the sun and moon;

Tabula temporis diurni, a table giving the length of the day as a function of the declination of the sun, calculated for the middle of the seventh climate (approximately the latitude of Paris);

Tabula diversitatis aspectuum lune ad solem, a table of the lunar parallax in longitude abd latitude, for the same latitude as the preceding table, and meant to be used in connection with the Tractatus eclipsorii; and

Tabula equacionis dierum, a table of the equation of time as a function of the longitude of the sun.

Tabula lune with canones (68 MSS). This was Peter’s most popular work. It exists in two versions: a numerical table and a diagram by which the approximate positions of the moon can be rapidly found from its age and the months of the year.

Tabula planetarum with canones (8 MSS). A diagram showing the governing planet for each day of the week and each hour of the day.

All the above works are well-authenticated writings by Peter Nightingale, but it is more difficult to ascertain the authorship of the treatises of the second group:

Tractatus de semissis (10 MSS). A long treatise on the construction and use of an equatorium for calculating planetary longitudes, written in Paris in 1293. No specimen of this instrument has survived, but a modern reconstruction based on the text was published in 1967.13

Tractatus novi quadrantis (18 MSS). This work was written in 1293 in Paris and describes the“new quadrant” invented some years earlier by Jacob ben Mãhir ibn Tibbon (Profatius Judaeus).14 Peter’s text seems to be a transaltion from the Hebrew original, provided with a careful introduction explaining the construction of this curious device, in which the astrolabe is transformed into a quadrant. It is not yet clear whether the other later Latin version dating from 1299 and attributed to Armengoud of Montpellier has anything to do with Peter’s treatise.

Tractatus eclipsis solis et lune (1 MS). This is a brief treatise on how the problem of computing eclipses can be solved by geometrical construction.

In many manuscripts the three writings of the second group are attributed to a Petrus de Sancto Audomaro, or Peter of St.-Omer. But two manuscripts of the Tractatus de semissis are stated to be by Petrus Danus of St. Audomaro, while another simply calls the author Petrus Danus. Internal evidence and a comparison of astronomical parameters prove the three texts to be works by the same author, who accordingly must have been a very competent astronomer working in Paris at exactly the same time as Peter Nightingale. The latter is a definitely historical person, while it has been impossible to find any other records of the former in contemporary sources. Therefore, there are good reasons to agree with the hypothesis, proposed by E. Zinner in 1932, that the two authors are identical. In that case all the works mentioned above must be attributed to Peter Nightingale, whose possible connection with St.-Omer remains to be explained.

Apart from his works in pure mathematics, Peter Nightingale made two important contributions to medieval science. One was his work on astronomical computing instruments, for which he occupies a very important position in the history of astronomical computing machines. He was not the first Latin writer in this field, which in the later Middle Ages increasingly attracted the attention of astronomers. About 1260 the Paris astronomer Campanus of Novara had constructed a set of six equatoria for calculating longitudes.15 Peter, however, was the first to invent a computer that solved this problem for all the planets with a single instrument. This device reduced the number of graduated circles and facilitated the construction of the instrument, the main principle of which was later adopted by John of Lignèrs and Chaucer.16 The Tractatus de semissis also contains Peter’s efforts to correct traditional astronomical parameters by new observations.

Peter’s second achievement was in the field of astronomical tables, in which his calendar remained in constant use for 150 years. This calendar had the peculiar feature that for each day of the year it listed both the declination of the sun and the length of the day. The same features are found in a contemporary calendar by the Paris astronomer Guillaume de St.-Cloud, who seems to have collaborated with Peter Nightingale during the latter’s sojourn in Paris.17 The prehistory of this calendar was put into perspective by A. Otto, who in 1933 drew attention to a passage in the partly extant Liber daticus of Roskilde cathedral. It appears that in 1274 an unnamed astronomer belonging to the chapter made a series of observations, unique for his time, of the altitude of the sun at noon, from which he calculated the length of the day by a kardagas sinuum (a trigonometrical diagram replacing a sine table).18 Both the altitude and the length of the day were tabulated in the now lost calendar of the cathedral. In this respect the Roskilde calendar may be considered the prototype of the calendar calculated by Peter Nightingale in Paris. This is not to say that he was identical with the unknown Roskilde astronomer of 1274; but there is no doubt that it was he who brought the principle from Denmark to France, thus creating a hitherto unknown link between Scandinavian astronomy and European science in general.


1. Published in Paul Lehmann, “Skandinaviens Anteil an der lateinischen Literatur und Wissenschaft des Mittelalters,” in Sitzungsberichte der Bayerischen Akademie der Wissenschaften zu München, Phil.-hist. Abt. (1936), 53-54.

2. Ellen Jørgensen, “Om nogle middelalderlige forfattere der naevnes som hjemmehørende i Dacia,” in Historisk tidsskrift, 8th ser., 3 (1910–1912), 253–260.

3. Lynn Thorndike, History of Magic and Experimental Science, III (New York, 1934), 647–649.

4. A. Krarup, in Bullarium danicum, no. 947 (1932), 834–835.

5. J. Quétif and J. Echard, Scriptores ordinis PraedicatorumII (Paris, 1721).

6. H. Schück, Illustrerad Svensk literaturhistoria, I (Stockholm, 1895), 343; G. Sarton, Introduction to the History of Science, II (Baltimore, 1931), 996–997.

7. C. E. Bulaeus, Historia Universitatis Parisiensis, II (Paris, 1668), 210, 982; cf. H. Denifle and A. Chatelain, Chartularium Universitatis Parisiensis, II (Paris, 1891), nos. 863, 955.

8. This survey, by Olaf Pedersen, is not yet completed. It supersedes previous inventories by G. Eneström, “Anteckningar om matematikern Petrus de Dacia och hans skrifter,” in Öfversigt af K. Vetenskapsakademiens förhandlingar (1885), 15–27, 65–70, and (1886), 57–60; and E. Zinner, Verzeichnis der astronomischen Handschriften des deutschen Kulturgebietes (Munich, 1925), nos. 2055–2082.

9. Maximilian Curtze, Petri Philomeni de Dacia in Algorismum vulgarem Johannis de Sacrobosco commentarius una cum algorismo ipso (Copenhagen, 1897).

10. G. Eneström, “Über die Geschichte der Kubikwurzelausziehung im Mittelalter,” in Bibliotheca mathematica, 3rd ser., 14 (1914), 83–84; cf. M. Cantor, Geschichte der Mathematik, 2nd ed., II (Leipzig, 1899–1900), 90

11. E. Zinner, “Petrus de Dacia, en middelalderlig dansk astronom,” in Nordisk astronomisk tidsskrift, 13 (1932), 136–146; German trans. in Archeion, 18 (1936), 318–329.

12. First by J. Langebek, in Scriptores rerum Danicarum, IV (Copenhagen, 1786), 260 f., where Grosseteste’s calendar was edited and attributed to Petrus de Dacia.

13. O. Pederson, “The Life and Work of Peter Nightingale,” in Vistas in Astronomy, 9 (1967), 3–10; cf. O. Pedersen, “Peder Nattergal og hans astronomiske regneinstrument.”

14. This text has been edited in an unpublished thesis by Lydik Garm, “Profatius Judaeus’ traktat om kvadranten” (Aarhus, Institute for the History of Science, 1966).

15. F. J. Benjamin and G. J. Toomer, Campanus of Novara and Medieval Planetary Theory (Madison, Wis., 1971).

16. D. J. de Solla Price, The Equatorie of the Planetis (Cambridge, 1955), 17 f. (Chaucer) and 188 f. (John of Lignères).

17. P. Duhem, Le système du monde, new ed., IV (Paris, 1954), 14 f.; cf. Zinner, loc. cit.

18. A. Otto, Liber daticus Roskildensis (Copenhagen, 1933), 32–33. The importance of the Roskilde astronomer was first pointed out by A. A. Bjørnbo, “Die mathematischen S. Marco-Handschriften in Florenz,” in Bibliotheca mathematica, 3rd ser., 12 (1912), 116

Olaf Pedersen