The articles collected in this volume have their origin in an international workshop dedicated to “Experience and Knowledge Structures in Arabic and Latin Sciences.” Specialists from Great Britain, France, Denmark, Spain, Morocco, the United States, and Germany gathered in Berlin in 1996 in the context of an interdisciplinary research project on the history of mechanical thinking at the Max Planck Institute for the History of Science. The workshop initiated a process of discussion focused on problems of the intercultural transmission and transformation of knowledge. The present double issue is an outcome of this ongoing discussion.

This article describes how the decimal place value system was transmitted from India via the Arabs to the West up to the end of the fifteenth century. The arithmetical work of al-Khwārizmī's, ca. 825, is the oldest Arabic work on Indian arithmetic of which we have detailed knowledge. There is no known Arabic manuscript of this work; our knowledge of it is based on an early reworking of a Latin translation. Until some years ago, only one fragmentary manuscript of this twelfth-century reworking was known (Cambridge, UL, Ii.6.5). Another manuscript that transmits the complete text (New York, Hispanic Society of America, HC 397/726) has made possible a more exact study of al-Khwārizmī's work. This article gives an outline of this manuscript's contents and discusses some characteristics of its presentation.

This paper investigates the affiliation of Book I of the Latin translation of Euclid's Elements attributed to Hermann of Carinthia with the Arabic transmission of the Greek mathematical work. It argues that it is a translation of a text of the Arabic secondary transmission, that is, of an Arabic edition mixed with comments. Two methodological claims are made in the paper. The first insists that the determination of a text whose transmission was as multifaceted and complex as the Euclidean Elements needs to be based on a systematic investigation of entire books rather than on selected theorems or diagrams of global, mostly structural relevance. The second claim starts from the experience that almost all results regarding the place of a particular document in a chain of transmission are conjectural. It acknowledges that individual results are more or less persuasive, depending upon the qualitative status of the argument. It suggests that the quantitative accumulation of similarities, differences, errors, regularities, or peculiarities allows one to recognize patterns and thus improves the reliability of judgment.

For more than a century, there has been some discussion about whether medieval Arabic al-jabr (and hence also later European algebra) has its roots in Indian or Greek mathematics. Since the 1930s, the possibility of Babylonian ultimate roots has entered the debate. This article presents a new approach to the problem, pointing to a set of quasi-algebraic riddles that appear to have circulated among Near Eastern practical geometers since c. 2000 BCE, and which inspired first the so-called “algebra” of the Old Babylonian scribal school and later the geometry of Elements II (where the techniques are submitted to theoretical investigation). The riddles also turn up in ancient Greek practical geometry and Jaina mathematics. Eventually they reached European (Latin and abbaco) mathematics via the Islamic world. However, no evidence supports a derivation of medieval Indian algebra or the original core of al-jabr from the riddles.

In two articles published in 1881 and 1884, the young academics, Martin Klamroth and Johan L. Heiberg, engaged in a brief debate on the textual choices that should govern the publication of a new critical edition of Euclid's Elements. This short debate seemed to settle the problem in Heiberg's favor as to what should be taken as the definitive text of Euclid's Elements. But the issue ought to be considered once again for there are good reasons for the claim that Klamroth was right, and that Heiberg was wrong. If so, we have been consulting, and continue to consult, the wrong text in our efforts to interpret the Euclidean tradition. In order to substantiate this claim, the textual issue debated by Klamroth and Heiberg is rehearsed again, and the principal reasons brought forth by Heiberg against Klamroth's position are reconstructed. Specimens from three broad areas of evidence – structural, linguistic, and technical – will be considered. They reveal how the medieval tradition of the text advocated by Klamroth displays textual superiority to the Greek tradition promoted by Heiberg. Such a reorientation of the texts has the potential to change significantly our understanding of ancient mathematics.

A passage in Copernicus's De Revolutionibus regarding the rotation of the Earth provides evidence that he was aware, whether directly or indirectly, of an Islamic tradition dealing with this problem that goes back to Na[sdotu]īr al-Dīn al-[Tdotu]ūsī (1201–1274). The most striking similarity is the use of comets by both astronomers to discredit Ptolemy's “proofs” in the Almagest that depended upon observational evidence. The manner in which this question was dealt with by Copernicus, as an astronomical rather than natural philosophical matter, also argues for his being within the tradition of late medieval Islamic astronomy, more so than that of medieval Latin scholasticism. This of course is bolstered by his use of non-Ptolemaic models, such as the [Tdotu]ūsī couple, that have a long history in Islam but virtually none in medieval Europe. Finally, al-Qūshjī, who was in Istanbul just before Copernicus was born, entertained the possibility of the Earth's rotation; this also opens up the possibility of non-textual transmission.

An Andalusian tradition of zījes seems to have been predominant in the Maghrib due to the popularity of the zīj of Ibn Is[hdotu]āq al-Tūnisī (fl. Tunis and Marrakesh ca. 1193–1222) and derived texts compiled in the fourteenth century. This tradition computed sidereal planetary longitudes and allowed the calculation of tropical longitudes by using trepidation tables based on models designed in al-Andalus by Abū Is[hdotu]āq ibn al-Zarqālluh (d. 1100). This tradition also used Ibn al-Zarqālluh's model to calculate the obliquity of the ecliptic, which implied that this angle had a cyclical period of oscillation between a maximum of 23;53° and a minimum of 23;33°: after reaching this minimum value the obliquity of the ecliptic was bound to increase. This paper argues that some new Maghribi sources give information on observations made in the Maghrib in the fourteenth and beginning of the fifteenth centuries that imply that precession had increased beyond the limits allowed by the Zarqāllian trepidation theory, while the obliquity of the ecliptic had diminished below the level accepted by astronomers who followed Ibn al-Zarqālluh. This explains the introduction in the Maghrib of Eastern zījes, which computed directly tropical longitudes and did not accept the cyclical variation of the obliquity. Information about observations of dawn and twilight made both in Egypt and in the Maghrib in the fourteenth and fifteenth centuries is also presented.

Assuming the crucial interest of Arabic material for the recovery of the textual tradition of some Greek texts of mechanics, the following article aims at presenting a partial survey of the Graeco-Arabic transmission in the field of mechanics. Based on new manuscript material dating from the ninth to the twelfth century, it investigates the textual and theoretical traditions of two writings ascribed to Aristotle and Euclid respectively and transmitted to Arabo-Islamic culture in fragmentary form. The reception and the impact of the Peripatetic Mechanics are analyzed on the basis of texts edited by al-Khāzinī as well as by the comparative study of the proof of the law of the lever in three authors: Pseudo-Aristotle, Thābit ibn Qurra, and al-Isfizārī. The codicological analysis of the extant manuscripts of Maqāla fī ‘l-mīzān – a rather systematic treatise on the balance ascribed to Euclid – leads to the assumption that it is a Greek fragment edited in Arabic. This reconstruction of the Arabic tradition of Euclidean mechanics is further elaborated by an annotated synopsis of al-Isfizārī's systematic recension of the text.

This article reassesses the reasons why Toledo achieved prominence as a center for Arabic-Latin translation in the second half of the twelfth century, and suggests that the two principal translators, Gerard of Cremona and Dominicus Gundissalinus, concentrated on different areas of knowledge. Moreover, Gerard appears to have followed a clear program in the works that he translated. This is revealed especially in the Vita and the “commemoration of his books” drawn up by his students after his death. A new edition of the Vita, Commemoratio librorum and Eulogium, based on all the manuscripts, concludes the article.

The article argues that Frederick II of Hohenstaufen and his court played a unique role in the transfer and diffusion of Arabic science (with its Greek, Hebrew and Christian elements). Scientists at the court translated and elaborated upon it. Moreover, there existed a two-way traffic of scientific knowledge between Frederick and his court scholars, on the one hand, and several oriental courts and their scientists on the other hand. Thus the reader gains a view of Frederick's scientific activities from the Arab perspective, too.

Frederick's contribution to the existing biological sciences of his time was his “Book of Falconry”, which was exceptional in the then contemporary approach and methods employed in those fields. Even in this treatise on falconry, Frederick drew upon the fund of knowledge of Arab practitioners. This chain of arguments concerning Arabic science is situated within the setup of Frederick's oriental political practice and sumptuous court life.

During the Middle Ages many Greek mathematical and astronomical texts were translated from Greek into Arabic (ca. ninth century) and from Arabic into Latin (ca. twelfth century). There were many factors complicating the study of them, such as translation from or into other languages, redactions, multiple translations, and independently transmitted scholia. A literal translation risks less in loss of meaning, but can be clumsy. This article includes lists of translations and a large bibliography, divided into sections.