As noted in the editor’s introduction, this collaborative publication realizes an unfinished book project by Alpay Özdural, who had submitted a manuscript shortly before his death in 2003. The manuscript presented a study of Fī tadākhul al-ashkāl al-mutashābiha aw al-mutawāfiqa (Bibliothèque nationale de France, Ms. Persan 169, fols. 180r–199r), referred to as the Anonymous Compendium throughout the publication, a treatise in Persian on geometric forms. Özdural’s project was the first to propose a full transcription of the Persian text, English translation, and publication of the manuscript in facsimile. All this has now been realized at a very high level of quality, completing Özdural’s work as a collaboration of Gülru Necipoğlu, Jan P. Hogendijk, Elaheh Kheirandish, and Wheeler M. Thackston. The publication combines sections of Özdural’s manuscript with new essays. Issues examined throughout the book include the date and historical context of the Anonymous Compendium, possible authorship, its mathematical implications, along with, as Necipoğlu eloquently notes: “the unresolved implications concerning the intersection, or lack thereof, between mathematical knowledge and artisanal expertise” (pp. 6–7). This observation is a central point of departure for future research, based on the book under review and the foundational work Necipoğlu presented in The Topkapı Scroll—Geometry and Ornament in Islamic Architecture (Santa Monica, CA, 1995). In her detailed introduction, Necipoğlu presents the stakes of editing the Anonymous Compendium, reaching far beyond the manuscript itself into discussions of mathematics, geometry, ornament, and the relationship between architecture and theoretical mathematics. Crucially, the Anonymous Compendium sits at exactly that juncture, as Necipoğlu notes, with author Abu Bakr possibly in the late thirteenth or early fourteenth century working as a “scholar-practitioner” (p. 18) at the intersection of theory and practice, and working in both Persian and Arabic. Within the larger context of the history of science in the Islamic world, such work is also crucial in order to further investigate the combined workings of ʿilm and ʿamal (knowledge and action), a subject that, as Necipoğlu notes, has not yet been fully investigated. The Anonymous Compendium, for instance, presents different ways to construct a range of geometric patterns, a practice that is also present in Abu’l-Wafaʾ al-Buzjani’s tenth-century Geometrical Constructions, but takes center stage in the work of Abu Bakr. As Necipoğlu argues, these types of practices are closely connected to the increasing use of geometric ornaments in the art and architecture of the Islamic world, beginning in the late tenth century, even though the Geometrical Constructions do not yet discuss many of the patterns developed in Buyid Baghdad, the author’s own time. In the Anonymous Compendium, however, it is possible to identify specific patterns that were used in architecture, within the context of the Great Saljuqs and their successors in Anatolia and northern Mesopotamia in the eleventh to thirteenth centuries, but also elsewhere in the medieval Islamic world. In her analysis of the transmission of the kinds of knowledge reflected in the Anonymous Compendium, and in architectural ornament, Necipoğlu notes that it is often difficult to trace just how the various strands of transmission worked, particularly with regard to practical applications which “rarely leaves a paper trail” (p. 33), hindering historical investigation. In the Anonymous Compendium, more than half of the constructions that are explained result in ornamental patterns that require the use of repeat-units in specific ways that are often described in detailed instructions. Discussions of repeat-units (ʿaqd) involve issues of proportion and ratios within geometric constructions, and at times specific drafting tools are mentioned in some of the commentaries to figures. Moving towards the relationship between the types of geometry discussed in the Anonymous Compendium and the Topkapı Scroll, Necipoğlu explains that the concept of ʿaqd is connected to the term girih (knot in Persian), used frequently beginning in the sixteenth century in order to describe star-and-polygon patterns, in some cases associating these forms with Anatolia (Rūm), where they were common under Saljuq and Mongol rule. This discussion has larger implications for the historiography of ornament in Islamic art, a topic that is at the center of several chapters in Gülru Necipoğlu and Alina Payne, eds, Histories of Ornament: From Global to Local (Princeton, NJ, 2016), along with further studies on ornament as a fundamental, if often shunned, question within art history. At this point, and several others throughout the text, the larger scholarly implications of a publication on the so far unique manuscript of the Anonymous Compendium emerge. Commonalities between the Anonymous Compendium and the Topkapı Scroll suggest, beyond differences in date and format, that both works could have served practical application within workshop contexts, and reached from the realm of theory into that of architectural practice; the presence in both of uninked construction lines is especially important in this context: use as templates was possible.

After Necipoğlu’s erudite introduction, chapters by Elaheh Kheirandish, Jan P. Hogendijk, and the late Alpay Özdural examine specific aspects of the manuscript and its wider context. In her chapter, Kheirandish examines in detail the Book of Geometrical Constructions, a treatise by Abu’l-Wafaʾ al-Buzjani (d. ca. 998), and its transmission in both Arabic and Persian. Several texts Kheirandish examines are bound together with the Anonymous Compendium in Ms. Persan 169. Kheirandish discusses the life of Abu’l-Wafaʾ al-Buzjani in Iraq and Iran under Buyid rule and his larger work in order to situate the Geometrical Constructions within a broader context. Notably, the treatise’s full title “On What Is Needed by the Craftsman from Geometrical Construction” (Fī mā yaḥtāju ilyahi al-ṣāniʿ min aʿmāl al-handasa) gives options to present geometrical figures in a way useful to practitioners. In an extensive discussion of the manuscript tradition, separating Arabic and Persian for clarity, Kheirandish notes that the formulation at the beginning of the Geometrical Constructions is not explicit in addressing craftsmen, but that it is the earliest known work to address the question of use by practitioners. Thus, the two works to some extent converge methodologically although, as Hogendijk shows in his chapter, intent differs. Further, the larger contexts of the Geometrical Constructions and the Anonymous Compendium provide Kheirandish with an opportunity to address the use of geometry in other areas, particularly land surveying and optics. In terms of tracing knowledge production, the figure of Abu Ishaq ibn ʿAbdallah Kubanani Yazdi (fl. ca. 1442–post 1483) emerges as crucial because he signed the postface to the Persian translation of Abu’l-Wafaʾ’s Geometrical Constructions, and may have transcribed the texts contained in the Paris Codex. Kheirandish’s study results in an updated catalog of Kubanani Yazdi’s works, which also includes a compilation of “letters and fragmented works” (p. 112). Kheirandish concludes that while it is not certain whether Kubanani Yazdi was indeed involved in the fifteenth-century compilation of the Anonymous Compendium, mostly likely based on an earlier version of ca. 1300, the work certainly fits someone with his knowledge and experience.

The following chapter by historian of mathematics Jan P. Hogendijk focuses on mathematics in the Anonymous Compendium as a way to better contextualize the manuscript. Hogendijk notes that, for the most part, scholars in the Islamic world trained in Euclidean geometry within their studies of astronomy and astrology were rarely concerned with geometrical patterns in their works. By contrast, Abu’l-Wafāʾ al-Buzjāni’s Geometrical Constructions aim at providing geometrically exact constructions for such patterns, with the hope of getting craftsmen to use them. In the Anonymous Compendium, Hogendijk notes: “Mathematically exact and approximate constructions occur next to one another, and are presented without proofs” (p. 145). Overall, the Anonymous Compendium contains numerous approximate constructions, and mathematical precision clearly was not the aim of the work, according to Hogendijk’s analysis in comparison to works of theoretical geometry. The author also argues that perhaps the Anonymous Compendium was copied and transmitted by scholars who were interested in the more practically oriented constructions included in it, but lack of knowledge about the exact ways in which craftsmen used mathematics precludes full conclusions at this stage. In the remainder of his chapter, Hogendijk provides a classification of the sixty-one patterns of the Anonymous Compendium into seven mathematically based categories. This classification is explicitly written to complement Necipoğlu’s and Özdural’s chapters in the volume, and folio numbers facilitate locating the figures throughout. Hogendijk makes several central points, moving along with the discussion of examples. First, many figures assume the presence of a teacher to explain the drawings. Second, some of the figures may have served as challenging riddles for practitioners, and more straightforward solutions could have been applied in practical work. Third, the Anonymous Compendium “was clearly part of an oral tradition of instruction” (p. 152), and thus more similar manuscripts may await discovery, if they have been preserved.

The final chapter is Alpay Özdural’s introduction to his planned edition of and commentary on the manuscript, which also lists the intended chapters of the work. Özdural provides a bibliographic discussion of work on the Anonymous Compendium up to 2002, and a detailed description of the manuscript. While he does not speculate on the identity of an author (or authors), Özdural suggests a date of around 1300 for the Anonymous Compendium, and Tabriz as a place of production. (Both questions are discussed in Necipoğlu’s introduction, which also addresses the fifteenth-century context of the Paris copy.)

A full transcription of the Persian text by Wheeler M. Thackston and with Özdural’s English translation of the full manuscript and commentaries by Necipoğlu follows (pp. 180–334). Each page is paired with Özdural’s drawings of the geometrical figures described in the text. The last section of the volume (pp. 335–74) is occupied by a high-quality, reduced-size facsimile of the original manuscript in color, with each manuscript page given a full page in the facsimile in order to ensure legibility. The facsimile provides specialist readers with an opportunity to compare the manuscript with the transcriptions and translations, and to understand the ways in which the figures are drawn, along with a page layout that is often difficult to describe since some text passages are placed at various angles to the edge of the page in order to better follow along with the figures they describe.

For those interested in exploring further the starting point for the project, Özdural’s unpublished manuscript is made available in full online: https://doi.org/10.1163/9789004315204_007

The volume is the highly sophisticated result of a close collaboration of scholars whose expertise encompasses medieval and early modern Islamic manuscripts, the history of Islamic art, the history of mathematics, the history of science within the Islamic world, and Arabic and Persian language. The primary material made available along with the analyses provided in the four chapters of the volume is an invaluable resource for further research by scholars working in these fields, and opens avenues to investigate questions of ʿilm and ʿamal with regard to architecture, the relationship between theoretical and practical applications of mathematics, and more broadly further studies on ornament and aesthetics for which Necipoğlu’s Topkapı Scroll is also fundamental. This reviewer will be interested to see how the edition of the Anonymous Compendium will influence recent discussions on aesthetics and poetics, both in art history and literary studies.Footnote ¹