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Sonja Brentjes

The cultural potpourri of visual knowledge in portolan charts of the fourteenth century

The analysis of important elements of the visual language of portolan charts produced in Genoa, Venice and at Majorca during the fourteenth century has been slowed down by privileging the study of coastal lines, methods of construction, toponymy, inscriptions and the questions of origin and priority. Other objects such as rivers, rulers or riders – to name only a few examples – were either ignored for a long time or downplayed as fantasies. Assumptions about the movement of people and knowledge along the shores and across the Mediterranean and the obstacles for such movements blinded researchers for seeing the obvious, namely that there did not exist two competing, geographically defined traditions of portolan chart making during the fourteenth century, one situated in the Italian towns of Genoa and Venice and the other at Majorca, but a shared pool of visual and non-visual sources from which all chart makers drew their knowledge about which rivers to represent and how to do it. The same applies to representations of human beings and animals.
    I will argue this thesis by showing that the visual language of individual fourteenth-century portolan charts consists of elements appropriated from Byzantine maps of Ptolemy’s Geography, medieval Latin world maps, regional or/and world maps from Islamic societies and art works from thirteenth-century Arabic and fourteenth-century Iranian provenance. I will point to changes between the source material and the images displayed on the portolan charts and reflect on possible causes for the transformations.


Charles Burnett

The multiple translations of Ptolemy in the Middle Ages

In terms of multiple translations of individual texts into Latin in the Middle Ages, Ptolemy scores higher than any other ancient or medieval author of mathematical texts: at least 3 translations of the Almagest (2 from Arabic, one from Greek), 7 translations of the Quadri-partitum (6 from Arabic, one from Greek), and 5 of the Centiloquium (commonly understood to be by Ptolemy). What accounts for this popularity of Ptolemy, and what why were so many Latin versions made (all within the 12th and 13th centuries)? This talk will address the origins of the different translations, the variety of styles that they manifest, the relative characteristics of the Arabic and Greek contributions, and the place that these works eventually establish for themselves in the Latin West.


Pieter De Leemans

The Paradox of the Fides Interpres. Remarks on the transformation of Aristotelian Thought in the Middle Ages

It is a well-known fact that translators who rendered Aristotle from Greek into Latin in the twelfth and thirteenth centuries adopted a very literal translation method. Undoubtedly one of the reasons to do so was the respect for Aristotle's authority, whose text should be rendered as faithful as possible in order to preserve its 'virginity'. Yet, by adopting this method, they produced texts that were almost Greek-in-Latin-words and that, as a consequence, were hard to read and to understand. It is thus not surprising that medieval users of these translations developed strategies to deal with them, strategies that were different according to the cultural and linguistic context. In this way the fidus interpres paradoxically contributed to the transformation of Aristotelian thought in the Middle Ages. In this paper, I will discuss some aspects of this transmission and transformation process.


Bruce Eastwood

Students and teachers of Latin astronomy from Roman schools to the Carolingian court and cloister into the eleventh century

Astronomical knowledge in the Western Empire was preserved in the early medieval West by royalty, aristocratic landlords, and literate monks desiring basic descriptions of the patterns of stars in the heavens for very practical needs. Travel, navigation, agriculture, nocturnal time-keeping, setting feast days, and establishing an annual calendar were the standard needs through the eighth century. The era of Charlemagne and his dynasty saw the extensive recovery of Roman texts, like Martianus Capella’s, for many disciplines, including astronomy, and their study and teaching ca. 800 – 1050. This new knowledge emerged through the tradition of literary, textual commentary; it included eccentrics and epicycles. Many Carolingian commentaries emphasized diagrams. At times, diagrams could be equivalent to commentary. The improvement and understanding of Roman astronomical texts was enhanced by the new attention to diagrams, with greater comprehension of geometrical techniques and precise data.


Dag Nikolaus Hasse

The Transformation of Arabic Astrology in Renaissance Humanism

Arabic astrology was available in the Latin West since the twelfth century (and, partially, already in the eleventh century), but the highpoint of its influence, at least in some of its branches, came as late as in the sixteenth century. This is particularly true of general astrology. In this paper, I discuss the Renaissance reception of two originally Persian doctrines that were later developed by the Arabs: revolutions of the years of the world and great conjunctions. In the Renaissance, these doctrines were criticized by Giovanni Pico della Mirandola and be¬came the object of much controversial discussion; they were amply used in annual predictions and apocalyptic prognostications; and they were employed to construct elaborate astrological histories. The question is: in what sense did these Renaissance trends lead to a transformation of the Arabic doctrines?


Jan P. Hogendijk

Parallel Transformations: Two rules of Brahmagupta in the Islamic world and the Dutch republic

This paper concerns Brahmagupta’s rule for the computation of the diagonals and area of a cyclic quadrilateral from its sides. The area rule was stated (in sutras) by Brahmagupta, who did not make clear that it is correct for cyclic quadrilaterals only. It was transmitted from India to the Islamic world. There, the rule was restated according to the rules of Greek geometry and provided with an elegant proof in Greek style, which was attributed to Abu Abdallah al-Shanni (ca. AD 990). The diagonal rule was stated by Brahmagupta but seems to have been unknown in Islamic geometry. It was discovered in Western Europe, possibly more than once. Ludolph van Ceulen (1540-1610) stated it in arithmetical form in the 1580s. The rule was turned into an incorrect geometrical construction in Greek style by Joseph Scaliger (1540-1609), and then into a correct construction (with proof) by Francois Vieta (1540-1603). The proof was misrepresented by Ludolph van Ceulen. Concyclic quadrilaterals provide an example in which the transmissions of mathematics between two cultures (from India to Islam) can be compared to the transmission of mathematics between two communities in one culture (arithmeticians-surveyors working in the vernacular, and scholars working in Latin).


David Juste

The transfer of Arabic and Hebrew onomancy into Latin: the case of the Alchandreana

The Alchandreana are of particular importance in the history of Western science, because they represent the earliest Latin translations and adaptations of Arabic sources (as well as Hebrew sources for that matter). They are made of seven main texts, all of which were produced in Catalonia around the middle or in the second half of the tenth century. Their subject matter is astrology, but astrology of a special kind, that requires very little astronomical expertise and where the fundamental elements of the ‘horoscope’ are not based on the date and time of birth of the individual, but on the numerical value of his/her name, that is onomancy.
    Onomancy supposes a system of letter-number equivalents. In Greek and in the Semitic languages, this system is provided by the ‘abjad’ alphabet, where the first nine letters correspond to the units, the nine following letters to the tens, and the remaining letters to the hundreds. Onomantic texts survive at least in Greek, Syriac, Ethiopic, Arabic and Hebrew, and, in all cases, these texts are accompanied by the ad hoc numerical alphabet. Of course, the transfer of onomantic techniques between these linguistic groups does not necessitate significant adaptation or ‘transformation’, since there is a general phonetic agreement between ‘abjad’ alphabets (most letters, i.e. sounds, have the same numerical value in all these languages, e.g. l=30, m=40, n=50). 
    The situation is different when the appropriating culture is Latin, because there is no system of letter-number equivalents in the Latin language. As is immediately obvious, the making of a Latin ‘abjad’ (i.e. by attributing numbers to letters following the order of the alphabet) is not a suitable solution, because such a system would bear no phonetic correspondence with the Arabic and Hebrew ‘abjad’ (results would be, e.g., l=20, m=30, n=40), with the result that Arabic and Latin astrologers would calculate different horoscopes for the same person. The translators and authors of the Alchandreana were of course aware of this problem. The aim of this talk is to review the various solutions they put forward to resolve it.


Kim Plofker

“Indian” and “Yavana”: foreign identity in the transmission of the exact sciences

The name “Indian” was attached to many mathematical concepts and techniques in West Asia/North Africa and Europe starting at the beginning of the medieval period, from the “Indian numbers” and “Indian calculation” adopted by Arab mathematicians to the “Hindoo method” for solving quadratic equations in nineteenth-century algebra texts.  Likewise, the Sanskrit term “Yavana”, originally a transliteration of “Ionian (Greek)” but later applied to other foreigners as well, was attached to various foreign importations in the exact sciences.  However, not all innovations adopted from or into the Indian tradition were labeled “Indian” or “Yavana” respectively. This paper examines the question of what characteristics marked some borrowed techniques and concepts as "foreign" and stamped them with their outlandish origin, while others were quietly assimilated into "indigenous" learning.


Peter E. Pormann

The Formation of the Arabic Pharmacology. Between Transmission and Innovation

Like Islamic medicine more generally, the pharmacological tradition in Arabic heavily relied on Greek models. But the medicinal plants and substances available, for instance, in tenth-century Baghdad differed considerably from those found in classical Athens or imperial Rome. Moreover, the physicians themselves innovated in a number of ways. Therefore, the story of Islamic pharmacology is paradoxically one of both tradition and innovation.
    The two foremost authorities on pharmacy in Greek were undoubtedly Dioscorides and Galen. Pedianus Dioscorides of Anazarbos (in modern Turkey), who lived in the middle of the first century AD, composed a work entitled On Medicinal Substances in five books. He organises his material according to the types, and attributed certain qualities to each substance. Galen wrote a substantial monograph on the same subject with the title On the Powers of Simple Drugs. He often takes his cue from Dioscorides, but introduces an important innovation: he classifies the qualities, already found in Dioscorides, according to their strength into degrees (e.g., ‘warming in the second degree’; ‘moistening in the first degree’). Both these works were transmitted into the Arabic-speaking world in the ninth century through translation, and formed the basis of Islamic pharmacology.
    We do find, however, also change and innovation is the pharmacological literature which developed in the lands of Islam. On the theoretical level, the ninth-century polymath al-Kindī, mostly known for his work in the area of philosophy, refined the classification system of Galen. Galen talked about qualities in the first, second, third, and fourth degree (one being the lowest), but did not specify how these qualities interact with each other in compound drugs. Al-Kindī devised a system in which the power of the qualities grows exponentially (1, 2, 4, 8) and theorised how these different degrees of quality interacted in specific compound drugs. On the level of practice, we see that many new ingredients entered the formularies written in Baghdad during the ninth and tenth centuries. Especially ingredients from India proved particularly popular. In this way, both new pharmacological ideas and new ingredients were incorporated into the Greek system, thus expanded and enhanced.


Stefan Schröder

The transfer and transformation of Arabic-Islamic knowledge in mediaeval European maps

Interdisciplinary research of the last decades has shown the strong influence of Arabic-Islamic knowledge on Christian Europe. Especially in the history of medicine, the history of philosophy, and the history of astronomy the impact of Arabic scholars is well documented. The interrelations between the Arabic-Islamic maps and their European counterparts are mentioned occasionally in the research on mediaeval cartography as well. However, the conditions, methods and contents of exchange of cartographical knowledge between the cultures are still to be studied in detail. Based on a case study of Christian-Latin maps from the 12th and the early 14th century, the first purpose of my paper is to analyze the different kinds of Arabic knowledge presented in maps. Secondly the functions of these elements within the maps and within the accompanying texts are to be questioned. Why was Arabic-Islamic knowledge used and attractive for a European mapmaker? In which ways were traditional Western spatial concepts challenged and changed?


Michael H. Shank

In the Wake of Bessarion's Greek Almagest: The Circulation of Ptolemy in the Fifteenth Century

This talk will survey the transformations of knowledge, meaning, and context that followed upon the arrival of Bessarion’s Greek Almagest mss. (and related works) in Italy. Landmarks include George of Trebizond’s 1451 Almagest translation and commentary; the Almagest controversy between George of Trebizond, Bessarion, and Regiomontanus (Epytoma Almagesti and Defensio Theonis contra Georgium Trapezuntium); and George of Trebizond’s astonishing attempts to dedicate his works to Mehmed II (1465-66) in Istanbul and Bessarion’s reaction to them.


Renate Smithuis

Transmission Strategies in Medieval Science: the case of Abraham ibn Ezra (1089/92-1164/67)

Abraham ibn Ezra published influential scientific works in two languages—Latin and Hebrew—in which he transmitted his first-hand knowledge of Arabic science, especially mathematics, astronomy and astrology. This fact offers us the opportunity to compare and contrast the strategies he used to impart his knowledge to the different audiences. Can we detect different transmission techniques? What levels of scientific knowledge did he pre-suppose the educated Jews and Christians had whom he tried to teach? Did Ibn Ezra possibly follow different agendas in his attempt to educate both groups?


John Steele

From numerical schemes to mechanical gears: a new form of the transmission of Babylonian astronomy to Greece

Abstract: The Antikythera Mechanism, a geared astronomical calculator dating to the first century BC, contains on the lower back side a dial that tracks the months of lunar and solar eclipse possibilities. In this talk I will present recent research on the dial and explore the relationship between the scheme used to generate the eclipse possibilities and similar schemes from Babylonia. The transformation of a Babylonian numerical scheme into a mechanical model provides a new perspective on our understanding of the transmission and adaptation of Babylonian astronomy within the Greek world.


Hidemi Takahashi

What Remains of the Mathematical Sciences in Syriac – From Sergius of Resh‘aina and Severus Sebokt to Barhebraeus and Patriarch Ni‘matallah

It is known that Syriac translations and Syriac scholars played an important role in the transmission of the sciences from the Greek to the Arabic world. Relatively little, unfortu-nately, remains of the translations and original works of earlier Syriac scholars, but some materials have survived, and further glimpses of what did exist may be gained from works of later authors. The paper will provide a brief survey of the earlier materials that have survived. This will be followed by examples illustrating how further materials can be recovered from the writings of later authors, and a mention, by way of epilogue, of an instance where the Syriac scientific tradition influenced a major scientific event in the West, namely the reform of the calendar by Gregory XIII.


Anne Tihon

Success and failure of foreign astronomical tables in Byzantium

Tables of Islamic origin - Arabic or Persian -  appear in two periods in the Byzantine world: initially in the 11th and 12th centuries, then in the 13th and 14th centuries, although there is no link between the two periods. Each time one can distinguish two categories:

  1. Tables that were the object of isolated notice or adaptation. These met with only limited success, and were confined to a few individuals, scholars or astrologers, who clearly knew the languages and the treatises, and made private use of them. The Greek translations are rudimentary, rather unclear, and often incomprehensible to the ordinary reader.
  2. Tables that knew a wider success, and which were spread mainly among devotees of astronomy, astrology, or scholars. There were carefully adapted, and available to everyone.

Αt the end of the 14th and in the 15th century the horizons of the Byzantine world were considerably enlarged. Latin tables make their appearance (Alfonsine Tables), and a great number of Jewish tables were introduced, which replaced the Persian Tables.
    During all these periods the tables of Ptolemy never ceased to be used, and the Almagest  was more and more studied and commented. In the manuscripts one sees a mélange of tables, tables adapted for specific places, and new tables created by George Gemistos Plethon.
    In this account we try to outline the reasons for these tendencies, and the changes due to the adaptations.


Warren Van Egmond

The Transformation of Algebra from Arabic to Latin to Italian

The means by which the art of algebra was transmitted from Orient to Occident through the translation and dissemination of several key texts has long been established through the publication and editing of these seminal works, but little attention has so far been given to the transformation that algebraic concepts and methods underwent during this process of transmission.  Through an analysis of the key words, concepts, procedures, and problems of algebra as it passed from Arabic to Latin and then to Italian, I will show that during this process algebra was in fact transformed from an early practical and quite ancient method of problem solving, thoroughly embedded in its limited cultural context, to an incipient theory of equations that would prove to be capable of universal application to all of mathematics.


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