Dr%20Philipp%20Nothaft: List of publications

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A Medieval Value for the Circumference of the Earth

July 2020

Journal article

Early Science and Medicine: a journal for the study of science, technology and medicine in the pre-modern period

‘With utmost certainty’: two late medieval pioneers of technical chronology

May 2020

Journal article

Journal of Medieval History

© 2020, © 2020 Informa UK Limited, trading as Taylor & Francis Group. This article focuses on the chronological methods developed and deployed by two little known medieval scholars, Giles of Lessines (active in the 1260s) and Heinrich Selder (1370s), both of whom made noteworthy advances in the use of astronomy to establish dates and intervals between events in ancient history. Based on their reading of Ptolemy's Almagest, both authors emphasised the importance of dated astronomical observations, such as eclipses, arguing that the recorded intervals between these observations were endowed with a unique degree of reliability. Several key examples of how they mobilised Ptolemy's astronomical data to rectify parts of the timeline between the creation of the world and the present will be discussed. These show that the technical arguments contained in Giles’ and Selder's writings reached a level of sophistication and accuracy that has previously only been associated with chronologers of the early modern and later periods.

Medieval Europe’s satanic ciphers: on the genesis of a modern myth

May 2020

Journal article

British Journal for the History of Mathematics

© 2020, © 2020 British Journal for the History of Mathematics. The purpose of this article is to investigate the genesis and growth of a historical canard that can be encountered in numerous popular as well as some scholarly publications devoted to the history of mathematics. According to one of the core elements of this story, the number or symbol for zero was the cause of much anxiety in medieval Europe, as its unusual properties caused it to be associated with the Devil or with black magic. This anxiety is supposed to have extended to the entire system of Hindu-Arabic numerals, such that the use of these numerals was banned by the Church or by other powerful institutions. I shall argue that this narrative is false or unsubstantiated at nearly every level of analysis. Some elements arose from an unwarranted interpretation of medieval sources, while others are based on the unbridled imagination of certain modern authors.

The Liber Theoreumacie (1214) and the Early History of the Quadrans Vetus

February 2020

Journal article

JOURNAL FOR THE HISTORY OF ASTRONOMY

Astronomical instruments, quadrant, astrolabe, precession, John of Seville, thirteenth-century astronomy

An Overlooked Construction Manual for the Quadrans Vetustissimus

December 2019

Journal article

NUNCIUS-JOURNAL OF THE HISTORY OF SCIENCE

medieval astronomical instruments, quadrant, Worcester Cathedral Priory

Pierre d’Ailly’s Tractatus de vero cyclo lunari: Introduction and Edition

May 2019

Journal article

Comptes rendus des séances de l’Académie des Inscriptions et Belles-Lettres

The Astrological Autobiography of a Medieval Philosopher: Henry Bate's Nativitas (1280-81).

May 2019

Journal article

JOURNAL FOR THE HISTORY OF ASTRONOMY

Glorious Science or “Dead Dog”? Jean de Jandun and the Quarrel over Astrology in Fourteenth-Century Paris

April 2019

Journal article

Vivarium

Robert Grosseteste’s Compotus

March 2019

Scholarly edition

An Alfonsine universe: Nicolo Conti and Georg Peurbach on the threefold motion of the fixed stars

February 2019

Journal article

CENTAURUS

Alfonsine Tables, astrology, Georg Peurbach, Nicolo Conti, precession, Renaissance astronomy

Astronomical and Cosmological 'Dubia' in the Cistercian Pierre Ceffons’ 'In II Sententiarum', distinctio 1

January 2019

Journal article

Cahiers de l’Institut du Moyen-Âge Grec et Latin

Jean des Murs's canones tabularum alfonsii of 1339

January 2019

Journal article

Erudition and the Republic of Letters

© 2019 by Koninklijke Brill NV, Leiden, The Netherlands. Among the works by Jean des Murs that have yet to be printed are his Canones tabularum Alfonsii, which he wrote in 1339 during his last attested stay at the Collège de Sorbonne. One element of particular interest in this concisely worded text is Jean's discussion of the length of the solar year, which was the first to take into consideration the consequences of the Alfonsine precession model for the length of the tropical year. Another is his approach to finding the time of true syzygy, which can be compared with some of his earlier writings on the same topic. Taken together, these writings reveal something about Jean's development as an astronomer over time, as he adjusted his preferred method of syzygy computation in reaction to empirical data. The article concludes with a look at the chapters devoted to the calculation of eclipse times and magnitudes, which turn out to be strongly influenced by John of Genoa's Canones eclipsium, written in 1332.

Jean des Murs's quadrivial pursuits: Introduction

January 2019

Journal article

Erudition and the Republic of Letters

© 2019 by Koninklijke Brill NV, Leiden, The Netherlands. This is article serves as the introduction to a special issue on the intellectual activities of Jean des Murs, a mathematician, astronomer-astrologer, and music theorist active in France in the first half of the fourteenth century.

Henry Bate's Tabule Machlinenses: the earliest astronomical tables by a Latin author.

October 2018

Journal article

Annals of science

The known works of the medieval astronomer/astrologer Henry Bate (1246-after 1310) include a set of planetary mean motion tables for the meridian of his Flemish hometown Mechelen. These tables survive in three manuscripts representing two significantly different recensions, but have never been examined for their principles of construction or underlying parameters. Such analysis reveals that Bate employed an unusual value for the length of the tropical year (c.365 1/4 - 1/112 days), which was probably derived by comparing ancient and contemporary observations of the vernal equinox. In addition, there are clear signs that Bate kept revising his parameters for the mean motions of Venus and the three superior planets, none of which can be traced back to earlier sources. Together with some of Bate's preserved statements, these findings support the conclusion that the Tabule Machlinenses were unique among the astronomical tables produced in medieval Latin Christendom for using independently derived parameters that were the result of new observations. Bate's achievement connects him to a wider milieu of astronomers operating in late-thirteenth-century Paris, who put an increased emphasis on observation and the critical examination of received data.

Astronomy, History, Medieval, Astrology, Belgium, Netherlands

Chronologically Confused: Claudius of Turin and the Date of Christ’s Passion

April 2018

Chapter

Late Antique Calendrical Thought and its Reception in the Early Middle Ages: Proceedings from the 3rd International Conference on the Science of Computus in Ireland and Europe, Galway, 16–18 July, 2010

Ptolemaic Orbs in Twelfth-Century England: A Study and Edition of the Anonymous 'Liber de motibus planetarum'

March 2018

Journal article

Mediterranea: International Journal on the Transfer of Knowledge

Scandalous Error

March 2018

Book

<p>The Gregorian calendar reform of 1582, which provides the basis for the present-day Western civil calendar, has often been portrayed as a triumph of early modern scientific culture and an expression of papal ambition in the wake of the Counter-Reformation. Much less attention has been paid to our calendar’s intellectual and material roots in the European Middle Ages, when the reckoning of time by means of calendrical cycles was a topic of central importance to education and learned culture. For centuries prior to the Gregorian reform, astronomers, mathematicians, theologians, and even Church councils had been debating the necessity of improving or emending the existing ecclesiastical calendar, which throughout the Middle Ages kept growing out of sync with the astronomical phenomena at an alarming pace. Scandalous Error uses a broad base of sources, many of them unpublished or previously unknown, to paint the first full-scale survey of the medieval debate surrounding the calendar and its astronomical underpinnings.</p>

John Holbroke, the Tables of Cambridge, and the "true length of the year": a forgotten episode in fifteenth-century astronomy

January 2018

Journal article

ARCHIVE FOR HISTORY OF EXACT SCIENCES

Zaccaria Lilio and the shape of the earth: A brief response to Allegro's "Flat earth science".

December 2017

Journal article

History of science

This is a response to James J. Allegro's article "The Bottom of the Universe: Flat Earth Science in the Age of Encounter," published in Volume 55, Number 1, of this journal. Against the solid consensus of modern scholars, Allegro contends that the decades around 1500 saw a resurgence of popular and learned doubts about the existence of a southern hemisphere and the concept of a spherical earth more generally. It can be shown that a substantial part of Allegro's argument rests on an erroneous reading of his main textual witness, Zaccaria Lilio's Contra Antipodes (1496), and on a failure adequately to place this source in the context of the cosmographical debate of the late fifteenth and early sixteenth centuries. Once this context is taken into account, the notion that Lilio was a flat-earther falls flat.

From the true Birth Year of Christ

June 2017

Journal article

ISIS

Strategic Skepticism: A Reappraisal of Nicholas of Cusa’s Calendar Reform Treatise

June 2017

Chapter

Le temps des astronomes: l’astronomie et le décompte du temps de Pierre d’Ailly à Newton

Criticism of trepidation models and advocacy of uniform precession in medieval Latin astronomy

May 2017

Journal article

ARCHIVE FOR HISTORY OF EXACT SCIENCES

Walcher of Malvern: De lunationibus and De Dracone

April 2017

Book

A Reluctant Innovator: Graeco-Arabic Astronomy in the Computus of Magister Cunestabulus (1175)

January 2017

Journal article

EARLY SCIENCE AND MEDICINE

medieval astronomy, Graeco Arabic science, computus, calendars, Easter reckoning, twelfth-century Renaissance, medieval England, Magister Cunestabulus, Ptolemy

Astronomy and calendar reform at the curia of Pope Clement VI: a new source.

January 2017

Journal article

Annals of science

The article introduces a previously unknown fourteenth-century treatise on computus and calendrical astronomy entitled Expositio kalendarii novi, whose author proposed elaborate solutions to the technical flaws inherent in the calendar used by the Roman Church. An analysis of verbal parallels to other contemporary works on the same topic makes it possible to establish that the Expositio was produced in the context of a calendar reform initiative led by Pope Clement VI in 1344/45 and that this anonymous text is probably identical to a 'great and laborious work' on the calendar that the monk Johannes de Termis prepared for the pope around this time. Its author strove to make an original contribution by extracting new astronomical parameters from both ancient and contemporary data, which made him arrive at an estimate of the length of the tropical year that was independent of the then-current Alfonsine Tables. With its suggestion to remove eleven days from the Julian calendar and to correct the calendar through modified leap-year rhythms and periodically adjusted sequences of lunar epacts, the proposal enshrined in the Expositio exhibits some remarkable similarities to the Gregorian reform of the calendar promulgated in 1582. Although its influence on the latter must remain a matter of speculation, the newly discovered text sheds a revealing light on the history of medieval calendar reform debates and on the mathematical sciences practiced at the Avignon court of Clement VI.

Astronomy, Mathematics, History, Medieval, Europe, France, Manuscripts as Topic, Calendars as Topic

Josephus and New Testament Chronology in the Work of Joseph Scaliger

October 2016

Journal article

International Journal of the Classical Tradition

The Early History of Man and the Uses of Diodorus in Renaissance Scholarship: From Annius of Viterbo to Johannes Boemus

June 2016

Chapter

For the Sake of Learning (2 vols) Essays in Honor of Anthony Grafton

Bede and the Future

June 2016

Journal article

ENGLISH HISTORICAL REVIEW

Duking it Out in the Arena of Time: Chronology and the Christian–Jewish Encounter (1100–1600)

May 2016

Journal article

Medieval Encounters

This article surveys the historical points of intersection between the study of chronology and the polemical encounter with Judaism in medieval Latin Christendom. Particular attention will be paid to the work of Roger Bacon, who viewed chronology as a tool that could furnish proof for Christianity, e.g., by supporting a Christological interpretation of the prophecies in the book of Daniel. A second focus will be on the reception and study of the Jewish calendar among Christian scholars and how it both influenced exegetical thought about the chronology of the Last Supper and informed efforts to improve the ecclesiastical calendar. With regard to the latter, it will be argued that the competition with Judaism and the Jewish calendar was an important motivating factor in the debates that led to the Gregorian calendar reform of 1582.

Thomas Strzempiński, Hermann Zoest, and the Initial Stages of the Calendar Reform Project Attempted at the Council of Basel (1434–1437)

February 2016

Journal article

Cahiers de l’Institut du Moyen-Âge Grec et Latin

Controversial Rimes: Calender Reforms in the Old Empire 1582-1700

January 2016

Journal article

GERMAN QUARTERLY

Magister Rheticus and his School Mates: The Struggle for Knowledge and Implementation of the heliocentric World System of Copernicus around 1540/50

January 2016

Journal article

GERMAN QUARTERLY

Vanitas vanitatum et super omnia vanitas: The Astronomer Heinrich Selder and A Newly Discovered Fourteenth-Century Critique of Astrology

January 2016

Journal article

Erudition and the Republic of Letters

© 2016 Koninklijke Brill NV incorporates the imprints Brill, Brill Hes & De Graaf, Brill Nijhoff, Brill Rodopi and Hotei Publishing. A previously unknown treatise on historical chronology (Tractatus de tempore dominice annunciationis, nativitatis et passionis), written by a southern German author between 1371 and 1378, preserves an unusually sophisticated and penetrating scholarly critique of astrology. The main purpose of this article is to introduce and analyze this important work, which is characterized by its close attention to technical astronomical detail and the use of empirical data to refute astrological doctrines. Comparison will be made to the contemporary anti-astrological works of Nicole Oresme and Heinrich of Langenstein, from which the newly discovered Tractatus differs in a number of significant aspects, underscoring its originality. It will be argued that this anonymously transmitted work was authored by the obscure Swabian astronomer Heinrich Selder, whose Canones tabularum Alphonsinarum (1365) are noteworthy for their critical remarks on the Alfonsine Tables.

Walter Odington's De etate mundi and the Pursuit of a Scientific Chronology in Medieval England.

January 2016

Journal article

J Hist Ideas

This article deals with a forgotten treatise on the age of the world, written between 1308 and 1316 by Walter Odington, a monk of Evesham Abbey, otherwise known for his writings on alchemy and music theory. By tracing the sources and rationale behind Odington's arguments and comparing them with those of other medieval authors, the article attempts to shed new light on the state of chronological scholarship in England in the eleventh to fourteenth centuries, when astronomical and astrological methods were freely used to supplement or replace scriptural interpretation, yielding creative and unexpected results.

Johannes Keck, das Konzil von Basel und der vergessene Osterstreit des Jahres 1444

November 2015

Journal article

Deutsches Archiv fur Erforschung des Mittelalters

Bede's horologium: Observational Astronomy and the Problem of the Equinoxes in Early Medieval Europe (c.700-1100)

October 2015

Journal article

English Historical Review

© 2015 Oxford University Press 2015. All rights reserved. This essay aims to establish the Venerable Bede's place in the history of medieval astronomy by examining certain frequently cited passages that suggest that he and other monks in early eighth-century Northumbria measured the date of the vernal equinox by means of a sundial or horologium. These references must be located in the context of ongoing controversies between the 'Roman' and 'Celtic' parties in the British Isles, who followed diverging conventions for calculating the time of Easter and located the vernal equinox on different dates. While it is indeed possible to identify instruments and methods that may have served Bede in supporting his case for the 'Roman' equinox on 21 March, the historical significance of his appeals to horologica consideratio lies primarily in their reception by subsequent authors, who took from Bede the notion that observation was a legitimate way of validating computistical doctrines. This line of influence culminated in the frequently overlooked work of William of Hirsau (before 1069), who employed innovative observational techniques to establish new conventions for the dates of the equinoxes and solstices, thus providing us with a crucial link between the early medieval computus tradition and the assimilation of Arabic astronomical knowledge during the eleventh and twelfth centuries.

Medieval Astronomy in Catalonia and the South of France: The ‘Improved’ Lunar Kalendarium of Friar Raymond (Ramon) Bancal (ca. 1311) and Its Predecessors

June 2015

Journal article

LLULL : boletin de la Sociedad Espanola de Historia de las Ciencias

Science at the Papal Palace: Clement VI and the Calendar Reform Project of 1344/45

May 2015

Journal article

Viator

The astronomical data in the très riches heures and their fourteenth-century source

May 2015

Journal article

Journal for the History of Astronomy

© 2015 The Author(s). In spite of the immense worldwide popularity of the calendar that opens the Très Riches Heures du Duc de Berry, its astronomical content remains underappreciated and its purpose ill-understood. This holds true in particular for the inclusion of a "new Golden Number" (Nombre d'or nouvel), which corrects the standard lunar computation used by the medieval Church. The source for this correction, as this article seeks to demonstrate, was a revised table of Golden Numbers drawn up in 1345 by John of Murs and Firmin of Beauval in the context of a calendar reform project initiated by Pope Clement VI. In a similar vein, the daytime lengths recorded in the Très Riches Heures most likely derive from John of Murs' astronomical tables known as Patefit (c. 1329/1332). These findings stand in opposition to a recent hypothesis put forward by Lebigue (2014), who instead links the Très Riches Heures to a calendar reform project pursued by Pierre d'Ailly in 1411-1417.

Alfred Lohr, Der Computus Gerlandi. Edition, Übersetzung und Erläuterungen. (Sudhoffs Archiv, Beihefte, H. 61.) Stuttgart, Steiner 2013

April 2015

Journal article

Historische Zeitschrift

Critical Analysis of The Alfonsine Tables in the Fourteenth Century: The Parisian Expositio Tabularum Alfonsii of 1347

January 2015

Journal article

Journal for the History of Astronomy

An important text to shed light on the reception of the Alfonsine Tables during the early-to-mid-fourteenth century is the Expositio tabularum Alfonsii, a trenchant critique of their parameters written in Paris in 1347 and variously attributed to Henri Bate, John of Murs, or Geoffrey of Meaux. The article provides the first in-depth analysis of this hitherto neglected text, showing how it can offer new insights into late medieval thought about the role and foundations of computational astronomy and the transmission of Alfonsine astronomy from Spain to France. It also addresses the question of authorship. © 2015, SAGE Publications. All rights reserved.

John of Murs and the Treatise Autores kalendarii (1317): A Problem of Authorship.

January 2015

Journal article

Sudhoffs Arch

José Chabás & Bernard R. Goldstein, A survey of European astronomical tables in the late middle ages and José Chabás & Bernard R. Goldstein, Essays on medieval computational astronomy

January 2015

Journal article

Peritia

Roman vs. Arabic Computistics in Twelfth-Century England: A Newly Discovered Source (Collatio Compoti Romani et Arabici).

January 2015

Journal article

Early Sci Med

A frequently overlooked aspect of the knowledge transfer from Arabic into Latin in the twelfth century is the introduction of the Islamo-Arabic calendar, which confronted Western computists with a radically different scheme of lunar reckoning that was in some ways superior to the 19-year lunar cycle of the Roman Church. One of the earliest sources to properly discuss this new system and compare it to the old one is the anonymous Collatio Compoti Romani et Arabici, found in a manuscript from Tewkesbury Abbey, Gloucestershire. This article contains the first edition and translation of this previously unknown text, preceded by an analysis of its content and sources. As will be argued, the text was written in the second quarter of the twelfth century as a reaction to the astronomical tables of al-Khwāizmī, recently translated by Adelard of Bath, as well as to eclipse observations that had exposed the flaws of the 'Roman' computation.

Arab World, Astronomical Phenomena, Astronomy, England, History, Medieval, Roman World, Time

A tool for many purposes: Hermann Zoest and the medieval Christian appropriation of the Jewish calendar

April 2014

Journal article

Journal of Jewish Studies

Calendars Beyond Borders: Exchange of Calendrical Knowledge Between Jews and Christians in Medieval Europe (12th-15th Century)

February 2014

Journal article

Medieval Encounters

Abstract During the Middle Ages, calendars played a significant role in both the Jewish and Christian communities as a means of reckoning time and structuring religious worship. Although calendars spawned a rich and extensive literature in both medieval Latin and Hebrew, it remains a little-known fact that Jews and Christians studied not only their own calendrical traditions, but also those of their respective rival group: Jewish scribes incorporated Christian material into Hebrew calendrical manuscripts, while some Christian scholars even dedicated entire treatises to the calendar used by Jews. The present article will examine these sources from a comparative perspective and use them to shed new light on the intellectual exchange that took place between Jews and Christians during the twelfth to fifteenth centuries. Particular attention will be paid to the role of oral vs. written transmission in the transfer of calendrical knowledge from one context to another.

Climate, astrology and the age of the world in thirteenth-century thought: Giles of Lessines and roger bacon on the precession of the solar apogee

January 2014

Journal article

Journal of the Warburg and Courtauld Institutes

John of Pulchro Rivo and John of Saxony: A mise au point

January 2014

Journal article

Journal for the History of Astronomy

Me pudet audire Iudeum talia scire: A late medieval Latin school text on the Jewish calendar

January 2014

Journal article

Time, Astronomy, and Calendars

Medieval Latin Christian texts on the Jewish calendar a study with five editions and translations

January 2014

Journal article

Time, Astronomy, and Calendars

Origen, Climate Change, and the Erosion of Mountains in Giles of Lessines’s Discussion of the Eternity of the World (c. 1260)

January 2014

Journal article

The Mediaeval Journal

The reception and application of Arabic science in twelfth-century computistics: New evidence from Bavaria

January 2014

Journal article

Journal for the History of Astronomy

An Eleventh-Century Chronologer at Work: Marianus Scottus and the Quest for the Missing Twenty-Two Years

April 2013

Journal article

Speculum

A Sixteenth-Century Debate on the Jewish Calendar: Jacob Christmann and Joseph Justus Scaliger

January 2013

Journal article

Jewish Quarterly Review

Early Christian chronology and the origins of the Christmas date: In defense of the "calculation theory"

January 2013

Journal article

Questions Liturgiques

While the view that the celebration of Christmas on 25 December came about as the product of pagan influence continues to enjoy unbounded popularity, the rivaling "calculation theory" seems to have lost ground, owing in part to the recent criticism leveled against it by Hans Förster. The present article adduces Christian chronological sources from the third century in a fresh defense of the view that the choice of 25 December as the birthday of Christ was originally the result of chronological speculation. As will be demonstrated, Christian scholars from this period had the kind of arguments at their disposal that would have supported such a conclusion independently of inter-religious influence. Moreover, there is evidence to suggest that Julius Africanus already reckoned with this date at the beginning of the third century. As a result, the "calculation theory" is still deserving of serious consideration from scholars investigating the origins of Christmas. © 2013, all rights reserved.

The Meaning of Judaeus and the Myth of Jewish Male Menses in a Late Medieval Astronomical School Text

January 2013

Journal article

European Journal of Jewish Studies

Abstract The article introduces and explores a new source on Christian hostility towards Jews during the late Middle Ages. It comes in the shape of a commentary on a Computus Judaicus, which was used as a quadrivial school text in Central and Eastern Europe during the fourteenth and fifteenth centuries. Based on an examination of the rich manuscript tradition, it will be demonstrated how the text contributed to the evolution of the trope of Jewish male menstruation, which is here tied, in a unique manner, to an exposition of the Jewish calendar as a method of lunar reckoning.

The Origins of the Christmas Date: Some Recent Trends in Historical Research

December 2012

Journal article

Church History

The article reviews recent and current developments in research on the origins of Christmas, which has traditionally crystallized around two competing approaches, known as the "History of Religions Theory" and the "Calculation Theory." This essay shall look at the history of these approaches and discuss their rationale and limitations, before turning to the challenges that have been brought against them by the recent work of Steven Hijmans and Hans Förster. It will be argued that their studies reveal the need for a more nuanced approach to the history of Christmas, which retains the aspect of inter-religious influence, but also pays some overdue attention to the importance of chronological thought in early Christian scholarship.

Nicholas Trevet and the Chronology of the Crucifixion

July 2012

Journal article

The Mediaeval Journal

Augustine and the Shape of the Earth

December 2011

Journal article

Augustinian Studies

Noah's calendar: The chronology of the flood narrative and the history of astronomy in sixteenth and seventeenth-century scholarship

December 2011

Journal article

Journal of the Warburg and Courtauld Institutes

From Sukkot to Saturnalia: The Attack on Christmas in Sixteenth-Century Chronological Scholarship

January 2011

Journal article

Journal of the History of Ideas

Alden A. Mosshammer, The Easter Computus and the Origins of the Christian Era

January 2009

Journal article

Byzantinische Zeitschrift

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