The Persian tradition of Euclid's Elements is closely connected with the Arabic transmission of the work in Iran, Central Asia and India. This tradition has multiple starting points. Naīr al-Dīn ūsī's Arabic edition had a profound impact, but it was one of several Arabic versions that served as the basis for Persian translations. At the institutional level both the Arabic and the Persian traditions flourished in different spaces—at the courts, in the madrasa, and in the sphere of collectors. Emphasizing the continued importance of court patronage, this paper explores the specifics of spatial and temporal coordinates in the transmission and transformation of Euclid's Elements in Islamic Iran.

Addressing the Arabic and Persian scientific traditions in eastern Islamic lands, this study focuses on the nature and place of demonstrations in optics and mechanics, sub-disciplines of geometry. A focus on the comparative context of demonstrations facilitates clearer understanding of local coordinates that affected the development of these fields, which are shown to have had distinct, and sometimes opposite, cases of transmission and application in Islamic and European lands. Sample demonstrations are presented in an appendix to highlight the concept and terminology of “mithāl” to identify shifts from geometrical to experimental methods in the case of optics, and from physical productions to model duplications in the case of mechanics.

This article seeks to develop an interpretation of ornament as geometric pattern that embodies metaphysical intent in Iranian monuments of the fifth/eleventh century. The proposed argument elucidates cultural meaning relevant to a particular time and specific place, with implications for broader application.1 Reading geometric patterns as visual commentary, this approach relates the presence of patterns in art accompanied by a Qur'anic inscription to both the practice of pattern-making and the contemporary discourse concerning mathematics, philosophy, and the Islamic sciences in Iran. Particular emphasis is placed on the use of a passage from the Qur'an (59:21–24) inscribed on the tomb towers at Kharraqān, in which the Qur'anic term, amthāl, is taken literally to refer to the patterns executed on the monuments.

This article analyzes two-dimensional images documented in the work of fourth/tenth century mathematician Abu al-Wafā' Būzjānī, which appear in his treatise, On Those Parts of Geometry Needed by Craftsmen. These images record three-dimensional tessellations of the sphere, geometric constructions, which may have served as a basis for architectural monuments and the interior design of domes in Islamic Iran. Such designs were very likely the result of collaborations among mathematicians and artists. As explained here, the construction of the icosahedron on a sphere, as presented in Būzjānī's treatise, is not mathematically correct. But the construction of the spherical dodecahedron is precise. Būzjānī's studies of the sphere as a three-dimensional form deserve further consideration as an important component in the development of mathematical thinking.

The contributions of Shī‘a scholars and noblemen to the advancement of knowledge is well documented. These contributions culminated in the institution of dār al-‘ilm during the Buyids (334–447/945–1055). While the advent of the Saljūqs signaled the disappearance of the dār al-‘ilm, the Shī‘a minority continued to serve in the production of both religious and secular knowledge, despite the increasingly strict social policies under the Saljūqs. This article examines the remarkable role of Abu al-assan Muahhar, the naqīb of Ray Alids, who provided protection as well as immense support for scholars of his time. It further elucidates the sectarian tensions that affected the institutionalization of the sciences, hence a greater need for the opportune support afforded by the naqīb Muahhar.

The present article aims to shed light on the professional activities of the historian and mathematician Sharaf al-Dīn ‘Alī Yazdī and his afar-nāmah. In so doing, two questions are addressed: (1) Did Yazdī’s expertise in mathematics influence his historical narrative? (2) Did Yazdī simply expand on Niām al-Dīn Shāmī's afar-nāmah, composed some twenty years earlier? Comparing the frequency of quantitative and qualitative data in Yazdī's and Shāmī's afar-nāmahs, the article finds that although Yazdī made an effort to incorporate quantitative data in his history, his narrative is not particularly informed by his expertise in arithmetic. This seems, at first glance, a byproduct of a predominant tradition in the Islamic-Iranian historiography, which makes extensive use of literary techniques. The comparison between the two afar-nāmahs, however, suggests that both Yazdī and Shāmī subscribed to a notion of “accuracy” which bore little resemblance to its modern counterpart manifested in quantitative precision. Finally, the article concludes that the allegation of plagiarism against Yazdī is unfounded.

The production of the mechanical clock, the printing press, and firearms in Western Europe during the Middle Ages is considered the precursor to many subsequent technological advances. This paper briefly reviews the introduction of these inventions to Iran, and the pace of their adoption in that country. Firearms were more readily accepted, but clocks and printing took a longer time to become prevalent. This paper will also examine some of the possible explanations for the contrast between the rapid spread of clocks and printing in Western Europe and the lack of their widespread adoption in Iran. This phenomenon cannot simply be attributed to scientific and technological backwardness, nor can it have been due merely to geographic or cultural differences. This underscores the significance of the overall social and economic conditions, which are in turn explored.

The fate of secular sciences in Islamic civilization has been the object of intense historical investigation. Historians have long sought to explicate the seemingly mysterious reduction of knowledge production in late medieval Islam. The present article attempts to grapple with this phenomenon by focusing on the social elements of knowledge production at the local, rather than the global level. It argues that the transmission of ancient knowledge to medieval Islam depended largely on a close cooperation among historical agents, who sought to advance various interests. The ultimate reduction of knowledge production—commonly referred to as the “decline” of sciences—was brought about by intense rivalry and the increased tension between different forms of knowledge and their representatives, which in turn hampered patterns of cooperation. The article stresses the contingent nature of the social relations that gave rise to the “decline” of sciences: the configuration of social agents, their interactions, and the final outcomes were not bound to unfold the way they did, nor did they have to follow the same path that led to emergence of modern Western science.