Between Crucifixion and Calendar Reform: Medieval Christian Perceptions of the Jewish Lunisolar Calendar Carl Philipp Emanuel Nothaft The moon would have played a marginal role in Christian religion, had it not been for the fact that Jesus Christ is reported by the evangelists to have been crucified on a Friday at the time of Passover. According to the Synoptic Gospels (Matthew 26:17–19; Mark 14:12–16; Luke 22:7–15), the Last Supper was conducted like a regular Passover meal, which took place on the evening that marked the transition from the 14th to the 15th day of the month of Nisan in the Jewish calendar. The Gospel of John (19:14, 31), by contrast, puts the Passion of Jesus on the ‘day of preparation’ for Passover and hence one day earlier, on 14 Nisan—a scenario that is seemingly confirmed by the Jews’ refusal to enter the Roman praetorium on the day of the crucifixion, ‘lest they should be defiled; but that they might eat the Passover’ ( John 18:28), implying that the meal lay still ahead. This striking discrepancy aside, the basic idea of a temporal connection between the Passion and Resurrection of Christ and the Jewish Passover emerges clearly from all four accounts.1 For pagan converts to Christianity who were eager to celebrate the anniversary of these events at the right time, this created a problem. After the introduction of the Julian calendar in 45 BCE, most inhabitants of the Roman empire had become used to reckoning with a solar year of 365.25 days, which did not take account of the phases of the moon, unlike the Jewish calendar, which, in Jerusalem at the time of Jesus, was in all likelihood still regulated by empirical principles such as the first sighting of the new moon crescent in the evening sky. The most straightforward way of solving the chronological problem thus posed was to make the date of Easter dependent on the Jewish calendar, either by always letting it coincide with the Passover on 14/15 Nisan (a custom later decried as the heretical doctrine of ‘quartodecimanism’) or by celebrating on the Sunday that followed it. This practice of ‘following the Jews’, common as it may have been during the first three centuries of Christianity, was eventually abandoned in favor of Easter cycles that projected lunar dates onto the grid of the Julian calendar, making it thereby possible to calculate the movable feast days long in advance and independently of the Jewish calendar. A leading role in this development was played by the church of Alexandria, which was the first to employ the 19-year lunisolar cycle that eventually became the sole basis for medieval Easter reckoning, also known as the science of computus.2 The adoption of Easter cycles fostered an increasing separation of the Christian from the Jewish pascha, which, owing to diverging standards of calculation and intercalation, were frequently celebrated a month apart. This is particularly palpable in the case of the Alexandrian style of Easter reckoning, which stressed the ‘rule of the equinox’, according to which the Easter full moon (the Christian version of 14 Nisan) could not fall earlier than 259 260 Carl Philipp Emanuel Nothaft 21 March, the assumed date of the vernal equinox, making 22 March the earliest permissible date for Easter Sunday. Scholars have occasionally come to regard this rule of the equinox, which had no direct counterpart in the Jewish calendar, as having been motivated by a deliberate attempt of the early church to sever its ties to the Synagogue, i.e. to emancipate Easter from Passover not just theologically, but also calendrically.3 While this interpretation is far from wrong, it only provides part of the picture. When Peter, who served as the patriarch of Alexandria during the first decade of the fourth century, defended his church’s method of Easter reckoning, he appealed to the divine Law that had been revealed to Moses and laid down in the book of Exodus. In Peter’s view, the Alexandrian rule of the equinox closely corresponded to the practice of the ancient Hebrews. If the Jews of his own age regularly violated the limit of the equinox, celebrating Passover a month earlier than the Christians, this was only a sign that they had abandoned the customs of their fathers—a clear sign of the degeneration that Judaism had supposedly gone through in the wake of the destruction of the Second Temple. According to Peter, one had to discern two ‘Jewish’ calendars: that of the Old Testament and that of contemporary Judaism. In this perspective, the Christian Easter calculation was not developed in order to abandon its roots, but it actually surpassed the contemporary Jewish calendar when it came to implementing Mosaic Law. The Christians, or so it seemed, were the better Hebrews.4 Most of the context of Peter’s fragmentarily preserved statements is lost, but traces of his rhetoric can be detected in a number of other late antique sources. It was still present in the fifth century, when the episcopal sees of Rome and Alexandria repeatedly quarreled over the correct dating of Easter Sunday. In 444, Paschasinus, bishop of Lilybaeum (today Marsala, Sicily), wrote a letter to Pope Leo I, in which he advertised the Alexandrian 19year Easter cycle as the ‘calculation of the Hebrews, that is the calculation according to the Law’ (Hebraeorum, hoc est legalem supputationem).5 As is well known, the Roman pontiff eventually bowed to this kind of pressure from Egypt, which resulted in the Alexandrian 19-year cycle being adopted as the standard of reckoning in the medieval Latin church. The subtleties of the Alexandrian construal of the Hebrew vs. Jewish calendar, however, got evidently lost in transmission from Greek to Latin. A general lack of available sources on the Jewish calendar other than the Old Testament soon led to a situation in which early medieval scholars ceased to properly differentiate between the biblical calendar of the Hebrews and the calendar of the Jews that they may or may not have encountered in their own time. Instead, they went on to by and large identify Jewish lunar months with the theoretical lunations of the Alexandrian 19-year cycle, thereby providing their own method of Easter reckoning with a venerable pedigree that could be tracked back to the days of Moses or even Noah.6 This anachronistic view made it possible to apply the Easter computus to biblical exegesis. One noteworthy example is an obscure chronicle of the world, written in about 814 by Claudius of Turin, a Carolingian exegete and bishop, who is otherwise better known for his leanings towards iconoclasm. In order to highlight pivotal points on the timeline of salvation, Claudius invested a lot of effort in translating into Julian dates the ‘lunar’ calendar data that could be occasionally found in the Old Testament. Basing himself on an assumed equivalence between ancient Hebrew lunar months and Alexandrian computistical months, he furnished his chronicle with weekdays and calendar dates for events such as the beginning of Noah’s flood (Saturday, 5 April), the reception of the Law at Sinai (Monday, 31 May), and the Babylonian capture of Jerusalem (Saturday, 23 June).7 Between Cruciixion and Calendar Reform 261 Claudius of Turin’s method is also present in the works of a number of eleventh and twelfth century monastic writers, who can be grouped together under the label ‘critical computists’. One of their common goals was to employ the Easter cycle in order to solve a chronological problem that had been puzzling Christian scholars for centuries: the exact date of Christ’s Passion and Resurrection. Their strategy was to search for a year in the Easter cycle in which the Julian date of the crucifixion (believed to be 23 or 25 March) and the 15th day of the moon (as posited by the Synoptic Gospels) both coincided on a Friday. In doing so, they effectively assumed that their computistical luna 15 of first spring lunation would automatically correspond to 15 Nisan as it had been observed by the Jews in first-century Jerusalem.8 Needless to say, this hypothetical Jewish calendar of the computists was very different from the type of calendar that Jews—first in Babylonia and Palestine, but eventually also in Spain and the rest of Europe—had actually adopted by the tenth century. Although the medieval Jewish calendar retained a 19-year cycle of intercalation, its method of fixing the beginning of the year represented a clear departure from the simple ‘epact’-based calendrical arithmetic that had characterized late antique Easter cycles. The technical foundation of the fixed Jewish calendar, as it is still in use today, is the time of the mean conjunction or molad, calculated on the basis of a mean lunation of 29d 12h 44m 3 1/3s = 29.530594 days. Each date of Rosh Hashanah (1 Tishri) is computed by adding multiples of this value to a fictitious calendar epoch known as molad baharad, whose time is equivalent to Sunday, 6 October 3761 BCE, at 23 hours, 11 minutes, and 20 seconds.9 For the loss of simplicity, the astronomical precision thereby achieved was considerable, especially if compared to the lunisolar calendar still in use among Christians. The old Alexandrian equation of 19 Julian years (6939.75d) with 235 months implied a mean lunation of 29.530851 days, which caused the calculated new and full moons to fall behind the observable ones at a rate of one day in roughly every three centuries. By the end of the twelfth century, Christian computists had not only noticed this discrepancy, but, aided by the influx of Arabic astronomy from the Iberian peninsula, had begun to look for new models on which to base an astronomically improved Easter computus. Under these circumstances, it could not take long until the conjunction-based Jewish calendar made its appearance on Christian scholarly radars. A meticulous comparison between the ‘Hebrew’ (i.e. Jewish), ‘Latin’ (i.e. Christian) and ‘Chaldean’ (i.e. Muslim) values for the mean synodic month can be found in a Compotus, written in 1176 by the English astronomer Roger of Hereford. In the calculated version of their lunar calendar, frequently encountered in astronomical tables, the Muslims distributed 11 intercalary days over 30 lunar years (30 × 354 + 11 = 10 631 days), thereby producing a mean month length of 29d 12h 44m = 29.530555 days. According to the divisions of time used by Roger (where there are 40 moments to an hour, 564 atoms to each moment), this was equivalent to 29 days, 12 hours, 29 moments, and 188 atoms. A slightly larger value was proposed by the Jews, who increased the number of atoms to 208 8/9. That both estimates were significantly closer to the truth than the inflated ‘Latin’ value of 29 days, 12 hours, 29 moments, and 348 atoms did not remain hidden to Roger, who admitted that the tabulated ‘ecclesiastical’ moon could differ by up to four days from the observable moon.10 The accuracy of the Muslim lunar calendar became an important source of inspiration for various medieval proposals to reform the ecclesiastical lunisolar calendar, as they were advanced in the thirteenth century by Robert Grosseteste (ca. 1170–1253), bishop of 262 Carl Philipp Emanuel Nothaft Lincoln, and the famous Franciscan scholar Roger Bacon (ca. 1214/20–ca. 1292).11 An even more suitable template, however, was provided by the Jewish calendar, whose lunisolar form resembled that of the Christian Easter cycle more strongly than the purely lunar calendar of the Arabic astronomers. In particular, both Jews and Christians used the same 19-year intercalation cycle, with the exception that the Jewish cycle began three years later than the Christian one—a fact that had already been pointed out by Abraham Ibn Ezra in his Liber de rationibus tabularum, a Latin work written especially for a Christian readership in 1154.12 That there was in his own time a lively interreligious exchange on calendrical matters is hinted at in Ibn Ezra’s ‘Letter of the Sabbath’ (Igeret ha-Shabbat, 1158), in which he criticized fellow Jews for communicating the details of their calendar to Gentiles in an inexact manner.13 The most impressive twelfth-century manifestation of such contacts is the Compotus emendatus, written in 1170 or 1171 by the Westphalian cathedral canon Reinher of Paderborn, who wanted his church to abandon its erroneous ways and return to what he regarded as the astronomically sound paschal reckoning that had once been prescribed by Moses himself. In order convince his readers of the great advantages that the Jewish conjunction-based reckoning held in store, Reinher composed a competent and elaborate exposition of its rules of operation (the first of its kind by a Christian author) along with innovative tables for easy conversion between dates calculated on the basis of the molad and the Julian calendar. These tables made ample use Hindu-Arabic numerals, including zero, which puts the Compotus emendatus among the earliest known Latin texts to employ such numerals for technical purposes.14 Both the Jewish calendar and the reform of the Christian Easter cycle continued to play a prominent role in the writings of Roger Bacon, who sent his famous Opus majus to Pope Clement IV in about 1267. Although he did not go as far as Reinher of Paderborn in demanding that the church should adopt some version of the Jewish calendar, Bacon spoke very highly of the Jewish astronomers and the accuracy of their value of the mean month. In fact, he was so determined to convince the pope of the importance of studying the Jewish calendar that he spared no expenses to acquire a Hebrew calendar manuscript and send it to the papal curia in Viterbo along with his pupil John as an interpreter. According to Bacon, this Hebrew calendar was ‘a wonderful work of astronomical art and highly useful for the understanding of the Law and the feasts prescribed by it. A person ignorant of it can never hope to properly understand the Law, nor can he converse with the Jews about such things, let alone convince them in any useful way’.15 That Bacon himself maintained some contact to learned Jews (and that he conversed with them about the calendar) is quite evident from his own profound knowledge on the subject, part of which reflects passages in the Babylonian Talmud. Amongst other things, he referred to the practice of the Jews in ancient Palestine, mentioned in the tractate Rosh Hashanah (22b–23b), of lighting beacons on high mountains in order to make known the beginning of a new month.16 Yet while Bacon was without a doubt a brilliant and original author, his interest in the Jewish calendar was not entirely exotic even in the thirteenth century. Another detailed and technical description of the Jewish calendar was composed in about 1294 by a certain Robert of Leicester, who is presumably identical with the scholar of the same name who later served as the 48th master of the Oxford Franciscans (1321/22) and who also penned a treatise On the Poverty of Christ.17 Aside from the reform of the calendar, biblical chronology was the other main factor Between Cruciixion and Calendar Reform 263 that motivated Christian interest in the Jewish calendar. Indeed, it is difficult to find a medieval discussion of the subject that does not in some way include an application of this knowledge to determine the exact date and year of Christ’s Passion. In order to do so, scholars had to be able to calculate the Passover dates of the first century CE, a task at which the ‘critical computists’ had failed because of their anachronistic use of the Alexandrian lunisolar cycle. Since Reinher of Paderborn rejected this cycle in favour of the medieval Jewish way of reckoning, it was only natural that he would also be the first to use the molad-calendar in an attempt to re-calculate the date of the crucifixion. This method was subsequently applied by several other medieval Christian writers, including the aforementioned Robert of Leicester, but not by Roger Bacon, who apparently understood that the Jewish lunar month of antiquity was not based on the molad or mean conjunction, but on the day of first visibility of the new moon crescent. Whereas Reinher of Paderborn had presented a static picture of the Jewish calendar, which assumed that the molad-based reckoning had already been instituted by Moses (a view presumably shared by his Jewish informants), Roger Bacon implicitly acknowledged that the Jewish calendar had a history that had to be studied carefully in order to understand biblical time reckoning. It is thus no surprise if Bacon, both in his methods and in his conclusions, came remarkably close to modern discussions of the Passion date. Using astronomical tables, he calculated that Jesus had been crucified on 3 April 33 CE, the 14th day of Nisan, a date that is still widely accepted among experts today.18 The problems posed by the chronology of the Passion also determined Christian interest in another important aspect of the Jewish calendar and the feast days attached to it: its postponement rules or deΩhiyyot. In the contemporary Jewish calendar, they make sure that the 15th day of Nisan can never fall on a Friday. If this rule had already existed in the first century, Jesus could not have been crucified on the first day of the Feast of Unleavened Bread, as the Synoptic Gospels seemed to imply. That the Jewish calendar thus favored John’s account of the Passion was already acknowledged in the early twelfth century by Rupert of Deutz (ca. 1075–1129), who regarded the deΩhiyyot as ancient Jewish practice.19 An opposing viewpoint was expressed by an anonymous English computist, who, in 1175, dryly noted that the present-day Jewish calendar cannot have been in use at the time of Jesus precisely because it conflicted with the synoptic version of events.20 An ingenious attempt to harmonize both positions was eventually made in about 1430 by bishop Paul of Burgos (ca. 1353–1435), who had been a famous Castilian Rabbi named Solomon ha-Levi before his conversion to Christianity in 1390/91. Like others before him, Paul assumed that the Jewish calendar he was acquainted with had already been in use during the first century. Basing himself on the reckoning rules of this calendar, he found that in the year of the crucifixion (which he took to be 33 CE) the 15th of Nisan had been postponed from Friday to Sabbath. Yet according to the Synoptic Gospels, the Last Supper, held on Thursday evening, had been a Passover meal. Paul found it hard to accept the idea that Jesus, as a Jew faithful to the law of his people (Matthew 5:17), would have ever violated the Mosaic rules by celebrating Passover one day early. Luckily, all chronological problems seemingly dissolved if one looked more closely at the deΩhiyyot and the reasons for their existence. As a former Rabbi, Paul knew that the rule which prevented Passover from falling on a Friday was a mere corollary of another rule, according to which Hoshana Rabbah on 21 Tishri could never fall on a Sabbath. Since the interval between Nisan and Tishri was always constant in the fixed Jewish calendar, a shift of Hoshana Rabbah from 264 Carl Philipp Emanuel Nothaft Sabbath to Sunday automatically implied that the preceding 15 Nisan had to move from Friday to Sabbath. Yet this meant that the postponement of Passover in the year of the crucifixion was contingent upon a feast (Hoshana Rabbah) that still lay several months ahead, belonging to a future in which, due to Christ’s self-sacrifice, mankind had been redeemed and the law of the Old Covenant abolished. The calendrical rules attached to Hoshana Rabbah, Paul argued, were hence null and void in this near future and this was the reason why Jesus, knowing what would happen, refrained from postponing the Passover shortly before his death.21 Paul’s fame as a commentator on the Bible ensured that his solution for the Passion chronology would remain the object of scholarly debate for at least the next two centuries. To name just one example, we find his views discussed at the University of Louvain in the late 1480s, where Paul of Middelburg (1446–1534), a Dutchman who later became bishop of Fossombrone, and the philosopher Peter de Rivo (ca. 1420–1499) fought a heated controversy over the date of Christ’s crucifixion. Paul of Middelburg added further substance to the theory of his namesake Paul of Burgos by presenting an array of obscure medieval Hebrew texts, which to him proved that the present-day Jewish calendar, including its deΩhiyyot, had been in existence since the days of the founding of the Second Temple. His Hebrew citations in this context represent the earliest known instance of Hebrew printing in the Netherlands.22 Peter de Rivo, on the other hand, dismissed this evidence as well as Paul of Burgos’s entire strand of reasoning. In his view, the present-day Jewish calendar, with its astronomical precision, showed clear signs of Arabic influence and could only have been conceived after the rise of Islam, maybe even only after the development of the Alfonsine tables in the thirteenth century.23 Discussions of this kind would continue well into the sixteenth century and beyond, during a period that saw important developments in the field of Christian Hebraism.24 As we have seen, however, scholarly interest in the calendar as a particular aspect of Judaism clearly predates the Renaissance. Owing to the joint roots of both calendars, Christian intellectual engagement with the Jewish calendar was kept alive throughout the Middle Ages, ranging from the naive identification of Alexandrian Easter reckoning with the calendar of Moses that characterizes the earlier period to the refined and erudite treatment we encounter in the works of Roger Bacon. To give up such pursuits was to impede a proper understanding of Scripture, at least according to Bacon, who reminded the pope that ‘our Lord and the Apostles were Jews [Hebraei], as were the Patriarchs and Prophets’.25 Notes 1. See Strobel (1977), pp. 17–64; Finegan (1998), pp. 353–358. The following abbreviations are used throughout: PL = Patrologia Latina; CCSL = Corpus Christianorum Series Latina; CCCM = Corpus Christianorum Continuatio Mediaevalis. 2. For a comprehensive overview, see Pedersen (1983) and Thornton (1989). 3. Zerubavel (1982), p. 286; Simon (1996), pp. 310–322; Steel (2000), pp. 98–101. 4. Peter’s arguments are cited in the seventh century Chronicon Paschale: Dindorf (1832), pp. 4–10. 5. See Paschasinus’s Epistola ad Papam Leonem in Krusch (1880), p. 248. Photius, in his Bibliotheca (cod. 115), mentions a book entitled ‘Discourse against the Jews and the heretics who follow them and against those [...] who do not celebrate Easter in the first month according to the Hebrews’. See Henry (1960), p. 86. On the general background, see Gerlach (1998). 6. See Bede, De temporum ratione, CCSL 123B: 312–315, 326–327, 420–422; ps.-Bede, De argumentis lunae, PL 90: 723, and Wiesenbach (1986), pp. 119–122. See also Warntjes (2010), pp. 242–243, for Between Cruciixion and Calendar Reform 265 further source references. 7. Claudius of Turin, Brevis Chronica, PL 104: 917–926. See further Allen (1998) and Nothaft (forthcoming). 8. The standard monography is now Verbist (2010). See further the editions by Weikmann (2004) and Wiesenbach (1986), who coined the term ‘kritische Komputisten’. 9. For a useful introduction into the present-day Jewish calendar, see Feldman (1978), pp. 185–210. On its medieval origins, see Stern (2001), pp. 180–210; Stern and Mancuso (2007); Carlebach (2011), pp. 11–24. 10. MS Cambridge, University Library, K.K.1.1, f. 238r; Moreton (1995), pp. 581–586. 11. See the texts edited in Steele (1926); Brewer (1859), pp. 274–295; Bridges (1897), pp. 269–285. 12. See the edition by Millás Vallicrosa (1947), pp. 99–100. 13. Friedländer (1894/95), p. 71; Sela (1996), pp. 216–217. 14. The Compotus emendatus was edited by van Wijk (1951). See also Honselmann (1962) and Herold (2005). On the reception of Hindu numerals in the West, see Burnett (2006). 15. Brewer (1859), p. 220: ‘Et in hac tabula est mirum artificium astronomiae, et summa legis intelligendae utilitas, et omnium festorum legalium, quam qui nescit numquam potest scire intellectum legis, ut oportet, nec cum Judaeis conferre de talibus, nec eius persuadere utiliter’. 16. Bridges (1897), p. 196: ‘Et ideo Hebraei antiquitus per astronomiam certificaverunt primationem lunae, et cum non fuerat in visione novae lunae, nec potuit per visum cognosci, accenderunt faces in Jerusalem in monte alto, ut sciretur quod tunc fuit tempus primationis, quatenus homines essent parati facere solemnitates et festa quae habebant expedire’. 17. See MS Oxford, Bodleian Library, Digby 212, ff. 2r–10r; MS Erfurt, Universitätsbibliothek, Amploniana, Quart. 361, ff. 80rb–85rb; Russell (1936), p. 139; Walmsley (1953); North (1992), pp. 132–133. 18. See Bridges (1897), pp. 195–198, 206–210. For modern estimates of the crucifixion date see Finegan (1998), pp. 359–369. A comprehensive account of pre-modern attempts at dating the Passion is provided in Nothaft (2012). 19. Rupert of Deutz, De sancta trinitate, CCCM 22: 900; Idem, De gloria et honore filii hominis super Mattheum, CCCM 29: 300–301. On the deΩhiyyot, see Stern (2001), pp. 166–167, 194–195; Belenkiy (2002). 20. MS London, British Library, Cotton Vitellius A.XII, f. 96ra. On the Compotus constabularii, see Moreton (1999). 21. See the commentary on Matthew 26 in Paul of Burgos (1634), cols. 441–446. 22. Paul of Middelburg (1513), sigs. D6v–E6r; Offenberg (1974). 23. Peter de Rivo (1488), sigs. c4r–6r; (1492), sigs. e5r–6v. 24. Weinberg (2000). On Christian Hebraism in the early modern period, see Coudert and Shoulson (2004). 25. Brewer (1859), p. 213: ‘Nam Dominus noster et apostoli fuerunt Hebraei, sicut patriarchae et prophetae’. References Allen, M. I., 1998, “The Chronicle of Claudius of Turin”, in A. C. Murray (ed.), After Rome’s Fall: Narrators and Sources of Early Medieval History (Toronto: University of Toronto Press), 288–319. Belenkiy, A., 2002, “A Unique Feature of the Jewish Calendar – Deĥiyot”, Culture and Cosmos 6, 3–22. Brewer, J. S. (ed.), 1859, Fr. Rogeri Bacon Opera quaedam hactenus inedita, vol. 1, Rerum Britannicarum Medii Aevi Scriptores (Rolls Series) 15 (London: Longman, Green, Longman, and Roberts). Bridges, J. H. (ed.), 1897, The Opus Majus of Roger Bacon 1 (Oxford: Clarendon Press). Burnett, C., 2006, “The Semantics of Indian Numerals in Arabic, Greek and Latin”, Journal of Indian Philosophy 34, 15–30. Carlebach, E., 2011, Palaces of Time: Jewish Calendar and Culture in Early Modern Europe (Cambridge, MA: The Belknap Press of Harvard University Press). Coudert, A. P., and Shoulson, J. S. (eds.), 2004, Hebraica Veritas? Christian Hebraists and the Study of Judaism 266 Carl Philipp Emanuel Nothaft in Early Modern Europe (Philadelphia: University of Pennsylvania Press). Dindorf, L. (ed.), 1832, Chronicon Paschale 1 (Bonn: Weber). Feldman, W. M., 1978, Rabbinical Mathematics and Astronomy, 3rd ed. (New York: Hermon Press). Finegan, J., 1998, Handbook of Biblical Chronology: Principles of Time Reckoning in the Ancient World and Problems of Chronology in the Bible, revised ed. (Peabody, MA: Hendrickson Publishers). Friedländer, M., 1894/95, “Ibn Ezra in England”, Transactions of the Jewish Historical Society of England 2, 47–75. Gerlach, K., 1998, The Antenicene Pascha: A Rhetorical History, Liturgia condenda 7 (Louvain: Peeters). Henry, R. (ed.), 1960, Photius: Bibliothèque 2 (Paris: Société d’Édition «Les Belles Lettres»). Herold, W., 2005, “Der computus emendatus des Reinher von Paderborn”, in W. Chobrak and K. Hausberger (eds.), Kulturarbeit und Kirche. Festschrift Msgr. Dr. Paul Mai zum 70. Geburtstag, Beiträge zur Geschichte des Bistums Regensburg 39 (Regensburg: Verlag des Vereins für Regensburger Bistumsgeschichte), 39– 47. Honselmann, K., 1962, “Magister Reinher. Schrittmacher für die Kalenderreform und die moderne Rechenkunst”, in K. Honselmann (ed.), Von der Domschule zum Gymnasium Theodorianum in Paderborn, Studen und Quellen zur Westfälischen Geschichte 3 (Paderborn: Verein für Geschichte und Altertumskunde Westfalens), 107–126. Krusch, B., 1880, Studien zur christlich-mittelalterlichen Chronologie: Der 84-jährige Osterzyklus und seine Quellen (Leipzig: Von Veit & Comp). Millás Vallicrosa, J. M., 1947, El libro de los fundamentos de las Tablas astronómicas de R. Abraham ibn Ezra (Madrid, Barcelona: Casa Provincial de Caridad). Moreton, J., 1995, “Before Grosseteste. Roger of Hereford and Calendar Reform in Eleventh- and TwelfthCentury England”, Isis 86, 562–586. ——, 1999, “The Compotus of «Constabularius» (1175): A Preliminary Study”, in J. Biard (ed.), Langage, Sciences, Philosophie au XIIe siècle (Paris: Vrin), 61–82. North, J. D., 1992, “Astronomy and Mathematics”, in J. I. Catto and R. Evans (eds.), The History of the University of Oxford. Vol. II: Late Medieval Oxford (Oxford: Clarendon Press), 103–174. Nothaft, C. P. E., 2012, Dating the Passion: The Life of Jesus and the Emergence of Scientific Chronology (200– 1600), Texts and Studies on Time, Astronomy, and Calendars 1 (Leiden: Brill). ——, forthcoming, “Chronologically Confused: Claudius of Turin and the Date of Christ’s Passion,” in I. Warntjes and D. Ó Cróinín (eds.), Proceedings of the 3rd Galway Computus Conference (Turnhout: Brepols). Offenberg, A. K., 1974, “The First Use of Hebrew in a Book Printed in the Netherlands”, Quaerendo 4, 44– 54. Paul of Burgos, 1634, “Additiones”, in Biblia Sacra cum Glossa Ordinaria 5 (Antwerp: Meursius). Paul of Middelburg, 1513, Paulina de recta Paschae celebratione: et de die passionis domini nostri Iesu Christi (Fossombrone: Petrutius). Pedersen, O., 1983, “The Ecclesiastical Calendar and the Life of the Church”, in G. V. Coyne et al (ed.), Gregorian Reform of the Calendar (Vatican City: Specola Vaticana), 17–74. Peter de Rivo, 1488, Opus responsivum ad Epistolam apologeticam M. 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