Petrus Philomena de Dacia
by Fritz S. Pedersen
Petrus de Dacia dictus Philomena (mestre Pierre de Dace dit Rosignol, in a thirteenth-century French translation; Peder Nattergal in modern Danish) is known to have been active between 1292 and 1303, at which latter time he was a canon of Roskilde in Denmark. He is the author of three or more works concerned with algorism and astronomy, all probably written in Paris. His astronomical calendar became quite popular. Peter is the only medieval astronomer known for certain to be Danish. Three works contain Peter’s characteristic surname “Philomena” and can thus be attributed to him rather than to another of the numerous contemporary persons named Peter of Dacia. These works are described further below; their datings and locations are as follows. No. (1), on the algorism, is dated July 31, 1292, and contains allusions to Paris or France. No. (2) is a calendar valid for the years 1293–1368; some copies carry titles connecting them with Paris. No. (3), astronomical, mentions both Paris and Roskildis Dacie, and is later than 1292, probably later than the calendar, and earlier than about 1297. Other sources include an astrologi¬cal tract of uncertain date and location by one “magister Romanus, civis Romanus et urbis medicus”, who says that he composed his work on the request of mei magistri Petri Philomena(!) canonici Rolkendensis(!). Also, a papal letter dated 4 July 1303, concerning a priest in Denmark, is addressed to Petro Philomene canonico Roskildensi and two other Danish clerics; however, in a duplicate of the same letter dated 22 November 1303, Peter and one other have been replaced by clerics of Würzburg and Bourges. These sources show that Peter Philomena was a canon of Roskilde, active in Paris during most of the 1290s, most probably as a teacher of algorism and perhaps of astronomy. By 1303 he was back in Denmark, if the first papal letter is to be taken at face value. Other contemporary persons called “Petrus de Dacia” or “Petrus Dacus” call for more evidence than just the name to be identified with our author. For example, at least two Peters of Dacia were students in Bologna in 1292 and 1294, and a letter from the Dominican Hermann v. Minden to one Petro Daco in Bologna, undated but probably from the 1280s or early 1290s, acknowledges the gift of a “spera”, possibly some astronomical instrument. Our author may thus have stayed in Bologna as a student, but the evidence for this is much weaker than for his stay as a master in Paris. Of Peter’s activity before 1292 and after 1303, nothing is known. He has been connected with two anonymous astronomical notes for Roskilde, one and perhaps both from 1274, preserved as fragments of the Liber daticus Roskildensis (OTTO 1933). They imply that Roskilde has a geographical longitude of 30° to the East of the prime meridian employed. The same value is likely to be implicit in work no. (3) below. This serves to confirm that Peter was located in Roskilde before his stay in Paris, but it is unlikely that he was the one to establish the value in 1274, eighteen years before his first known work. Part of Peter’s work was influenced by William of St. Cloud, the well-known astronomer who also worked in Paris in the 1290s. In the directions for his Almanach planetarum, valid for March 1292–February 1311, William states that in 1290 he observed the precession of the equinoxes to be 10°13' (as against some 50' less according to the system in common use), and he introduces a correction of – 40 minutes of time for mean conjunctions and oppositions. This appears to have been taken into account in work (3) below but not in work (2), as will be seen. In his Kalendarium regine, covering 1292–1310 and released in 1296, William takes account of the old calendar of Grosseteste but ignores or does not know work (2). According to a conjecture by ZINNER 1932/1936, Petrus Philomena de Dacia is the same as Peter “the Dane” of St. Omer. The latter was the author of a tract on the astrolabe substitute called the New Quadrant, entitled Novus quadrans correctus a Petro Dane(!) de Sancto Audomaro and dated to 1293 or 1294, and of Tractatus de semissis, a tract on a planetary computing device, ascribed to magister Petrus de Sancto Audomaro and dated to 1294. Both texts are probably Parisian. Thus the correspondence with Peter Philomena’s activity is close to perfect both in place and time; but the two names do not overlap except as shown, and some features of contents suggest that neither author knew about the other’s work. For the present purpose, then, this identification will be disregarded. (1) Expositio super Algorismum The Expositio is a literal commentary on John of Sacrobosco’s Algorismus, the common text-book of calculation with Hindu-Arabic numerals. Eleven manuscript copies are known, of which nine are from the fourteenth century and two from the fifteenth. The title is uncertain, since most of the copies do not carry one. Incipit Omnia que a primeva etc.: In hoc tractatu determinatur de arte numerandi sive de numero practico (T&K, 681). Explicit maximus cubicus in toto numero proposito, followed by subscription, see below. Size The text covers 82 pages in the latest edition. Editions CURTZE, M. 1897: Petri Philomeni de Dacia in algorismum vulgarem Johannis de Sacrobosco commentarius, Copenhagen. PEDERSEN 1983–1984. A well attested subscription states that the work was finished on 31 July 1292, per magistrum Petrum de Dacia dictum Philome¬nam. In two examples, the text mentions Parisian money (libras Parisienses) and a French quarter-denarius coin (picta), so it is likely to have been meant for use in Paris. As was said, the text concerns calculation with Hindu-Arabic numerals, on a dustboard or some such medium where figures can be deleted and replaced by others. Being a literal commentary, the text follows that of Sacrobosco. It has an introduction on the nature of number, then one section for each arithmetical operation, namely: positional notation (numeratio), addition, subtraction, halving, doubling, multiplication, division, summation of a difference series (progressio), extraction of square roots and of cube roots. The explanation is lucid and illustrated with worked-out numerical examples. It features the test by casting out nines, and shows an abridged method for cube root extraction that the author says he has invented himself. Literal commentaries are the typical outcome of university teaching, so Peter must be assumed to have taught algorism. The text twice alludes to astronomy, but in a vague manner, and it cannot be said whether Peter’s teaching comprised astronomy. (2) Kalendarium The Kalendarium (Calendar) is essentially a list of the times of the 940 mean conjunctions of the Sun and Moon during the years 1293–1368, expressed in hours and quarters of hours after midnight. Fifty-two manuscript copies are known, of which eleven are thirteenth or early fourteenth century; thirty are fourteenth century; nine are fifteenth century; and two are sixteenth century. The Calendar is accom¬panied by one or both of two sets of instructions (canones), namely, (A) In hoc primationum ciclo 4 linee descendentes (T&K, 680) ... et current primationes sicut prius; (B) Quere inter numeros in superiori parte istius tabule (T&K, 1191) ... dies et hore incipiunt in media nocte precedente. While the title of (B) is typically Canon supra kalendarium magistri Petri de Dacia, some central manuscripts of (A) ascribe the Calendar to magistrum Petrum Philomenam de Dacia (or equivalents). In the manuscripts, the list of conjunctions forms part of a normal calendar consisting of twelve month-pages with martyrology and other calendrical tables in varying selections, most of them taken over from the well-known calendar ascribed to Robert Grosseteste. In some early copies they came to include a table of solar positions, excerpted from William of St. Cloud’s Almanach and covering March 1296–February 1297. Such tables may, it is true, have been introduced by any scribe. The two instructions (A) and (B) are about a page each, and take account of the conjunction list only. Editions BIBLIOTHECA CASINENSIS 1880: Bibliotheca Casinensis 4, Monte Cassino, from a sixteenth century manuscript at Monte Cassino. PEDERSEN 1983–1984. There are no express indications of when the Calendar was composed. It starts with 1293, so it probably is not much earlier; it may be later, since 1293 marks the start of a nineteen-year computistical cycle and so may have been fixed by convention. Some manuscripts have headings that connect the author or the calendar with Paris, so this may be the place of composition. It is true that this location is not borne out by the time values in the Calendar; in fact these are most closely such as could be found from the common astronomical tables for Toledo, so they do not take account of the difference in geographical longitude between Toledo and Paris. Nor do they take account of the correction to conjunction times introduced about 1292 by William of St. Cloud, mentioned above. Since Peter’s work (3) below does seem to do this, the Calendar is likely to be earlier than (3), i.e., earlier than about 1297. The month-pages and instructions are intended to emulate the calendar of Grosseteste, as mentioned above. Indeed, the list of conjunctions is such that it is easy to substitute for a corresponding list in the Grosseteste calendar, the rest remaining equal, and in fact the early copies of Peter’s calendar are much like Grosseteste’s in general layout: thus the month-pages and instructions are typically followed by a variety of tables for ecclesiastical computus, plus a table to find the Moon’s mean place in the zodiac. The original version of this lunar table, in use since the early Middle Ages, was a 12 x 12 table to be entered with the current month and the age of the Moon. In most manuscripts of Peter’s calendar, this old lunar table is replaced by one ascribed to Peter himself. It has fourteen rows and twelve columns, and serves to find the place of the Moon by using the place of the conjunction (found from the conjunction time listed in the calendar) and the age of the Moon. Its normal title is Tabula Petri Daci de loco lune inveniendo in quolibet die anni a media nocte sui incepto. It has its own set of instructions, typically Ad locum etiam lune habendum videas quota est dies (T&K, 53) ... locum autem lune voco centrum epicicli lune. The table also occurs apart from the calendar, or associated with later calendars. The lunar table, of course, has astrological purposes; indeed, a traditional label is tabula medicorum, and a lot of medical elections depend on the Moon’s place in the zodiac. Not surprisingly, Peter’s calendar and lunar table are often followed by astrological texts, especially in the later manuscripts. The (A)-type instructions contain a rule for updating the conjunction times so as to be valid for the period 1369–1444; the difference amounts to about five hours. In four of the manuscripts, all German or Swiss of the late fourteenth or early fifteenth century, this has been carried out, purportedly, by one Johannes de Palmis. In most other late manuscripts the values have, however, been left unrevised. There exist three different French translations of the instructions of type (B) for the calendar, and two of the instructions for the lunar table, in manuscripts of the early fourteenth until the late fifteenth century. It has been suggested (SHORE 1989, 305–6) that the early translations were made by William of St. Cloud. (3) Tractatus instrumenti eclipsium magistri Petri de Dacia or Tractatus eclipsorii Petri Daci describes an instrument to be of aid in computing solar and lunar eclipses. Two manuscripts are known, namely: Napoli, BN VII.A.26, 243r (N), and Firenze, BNC II.III.24, 208r (F), both of the first half of the fourteenth century. They show the text in two versions, describing instruments that are somewhat different; the revised version appears to be that of F. The two titles just quoted are those implicit in the rubrics of N and F, respectively. Incipits and explicits Prolixitatem que quamplurimos (N; etiam plurimos F) in proiectione eclipsium laborantes (N, F: T&K, 1137) ... 7 graduum et 11 minutorum ab alterutro nodorum (N), ... solem quandoque eclipset vel infra existens eum non contingat (F). Size Each version comprises some 25 pages of text, plus 33 tables in N and 25 in F. Among the tables is a 60 x 60 multiplication table, which the author acknowledges in the text. In version F, the table shows the title Tabula magistri Petri Philomene de Dacia ad inveniendum portionem cuiuslibet numeri secundum <pro>portionem cuiuslibet alterius ad 30 vel 60... A third copy of this table, with the same heading, occurs in the manuscript Vatican B.A.V. Reg.lat. 1452, 118r, where the context seems irrelevant. Editions PEDERSEN, F.S. 1978: Petrus de Dacia: Tractatus instrumenti eclipsium (Cahiers de l’Institut du moyen-âge grec et latin 25) (version F) PEDERSEN 1983–1984 (version N). Both versions mention Paris, and version F also mentions Roskildis Dacie as being 25 minutes of time to the east of Paris. This confirms that the texts were composed in Paris, and that version F is authentic. The time difference translates to a longitude of Roskilde that is 30° east of the prime meridian, on the likely assumption that Paris is identified with Sedes regis Francorum in the Toledan Tables (long. 23°45'). The value for the precession of the equinoxes is 10 1/3° in N and 10;22° in F. These values are according to William of St. Cloud, see above; in this system, the values of N and F correspond to about 1297 and 1300, respectively. These, then, are the likely guesses at dating. The instrument is a disc that contains an outer set of circular scales, then a cursor with its own scales that may slide against the outer scales. Fixed at the centre are two revolving volvelles, with radial rulers to read across the scales. The back of the instrument also carries scales; to read across these, the volvelles are transferred to the back in version N whereas version F provides for two extra volvelles on the back. To use the instrument, one should first find the time and place of the mean conjunction or opposition. Tables are provided for this; they are said to be for Paris, and apparently they take account of William’s correction for mean conjunction times, from about 1292, mentioned above. The operations done on the instrument mainly simulate table look-ups, certain additions and subtractions, and multiplications by constants. Thus the instrument may be used for finding the solar and lunar equations and thence the elongation between Sun and Moon at mean conjunction or opposition, so as to obtain the true conjunction or opposition. Other uses include finding eclipse magnitudes. However, for such a complicated task as finding parallax for solar eclipses, the instrument is not used; instead the text provides the common Toledan parallax table (for the seventh climate, which includes Paris) and describes how to use it in the normal manner. All told, the instrument does far from the whole work of calculation, but it does facilitate certain operations. The text, as is usual in instrument descriptions, contains a section describing the construction of the instrument, then one on its use. A third and final chapter yields the propter quid of the construction and the operations, showing how they are in accordance with the theory of eclipses. This theory is the normal one from Albattani, via the Toledan Tables. The rules for the construction of the instrument have much phrasing in common with other such rules, most notably perhaps with those concerning the Quadrans vetus or Quadrans cum cursore. Dubious works Editions All printed in PEDERSEN 1983–1984. A few early manuscripts of instruction (A) for the Calendar (cf. work (2) above) include a passage on renewing the Calendar by finding the first conjunction in 1369 per tabulas meas (not mediarum) coniunctionum supra Parisius. The stated result, however, is consistent with the original Calendar and with the Toledan Tables rather than with, e.g., the conjunction tables in the Eclipsorium or other tables valid for Paris. The passage is probably an interpolation. In three Italian manuscripts of the fifteenth century, the versified compotus metricus manualis attributed to Anianus (inc. Compotus est talis, T&K, 243) is accompanied by a commentary Ut habetur circa primum De Anima, scientia est de bonis et de difficillimis. The preamble contains the sentence Causa efficiens sive compilator huius opusculi fuit magister Petrus de Dacia. This ought to mean that the commentator attributes the computus verses to Peter of Dacia. However, one of the three manuscripts has some rubrics and a subscription by one magistrum Nicolaum de Ripis Venetum, of 1494, ascribing the computus to Gerlandus and the commentary to Peter of Dacia. The rest of the text offers no better evidence for place, date or authorship. Hic est tabula planetarum secundum magistrum Petrum de Dacia Parisius facta and Consequenter hic sequuntur expositiones signorum secundum predictum magistrum Petrum de Dacia are the headings for two astrological pieces that accompany Peter’s lunar table (see work (2) above) in London, British Library, Egerton 831, 9v; incipits, Septem sunt planete scilicet Saturnus (T&K, 1433) and Multum prodest scire in quo signo (T&K, 891). Other manuscripts offer parallels to these texts but do not carry ascriptions. Bibliography ENESTRÖM, G. 1885–1886: Anteckningar om matematikern Petrus de Dacia och hans skrifter. Öfversigt af Kongl. Vetenskaps-Akademiens Förhandlingar 1885: no. 3; 1885 no. 8; 1886 no. 3, Stockholm. OTTO, A. 1933: Liber daticus Roskildensis, Copenhagen. PEDERSEN, O. 1970 ff.: “Peter Philomena of Dacia,” in Dictionary of Scientific Biography, ed. C.G. Gillispie, 16 vols., New York 1970–1981. PEDERSEN, O. 1976: Petrus Philomena de Dacia: A problem of identity. With a survey of the manuscripts (Cahiers de l’Institut du moyen-âge grec et latin 19), Copenhagen. PEDERSEN, F.S. 1983–1984: Petri Philomenae de Dacia et Petri de S. Audomaro opera quadrivialia (CPhD 10, I–II), Copenhagen. SHORE, L.A. 1989: “A case study in medieval nonliterary translation: Scientific texts from Latin to French,” in Medieval translators and their craft, ed. J. Beer, Kalamazoo, 297–327. T&K = THORNDIKE, L. & KIBRE, P. 1963: A catalogue of incipits of mediaeval scientific writings in Latin. Cambridge, Mass.. ZINNER, E. 1932: “Petrus de Dacia, en middelalderlig dansk Astronom,” Nordisk astronomisk Tidsskrift n.s. 13, 136–46. ZINNER, E. 1936: “Petrus de Dacia, ein mittelalterlicher dänischer Astronom,” Archeion 18, 318–29.