Reading the Classics of Science

A conference
organised by Philip Beeley, Karine Chemla, Sally Humphreys, Agathe Keller, Yelda Nasifoglu and Benjamin Wardhaugh

SPHERE, Université Paris Diderot – Maison Française d’Oxford – University of Oxford

Reading the Classics of Science: historical and anthropological perspectives

June 3rd and 4th, 2019 – Oxford University

Rationale

Preclarissimus liber elementorum Euclidis perspicacissimi (Venice, 1482). Bodleian Library Auct. K 3.19. Courtesy of the Reading Euclid project.

Traditions in science throughout the ancient and the early modern world have regularly given specific texts the status of classics or canonical texts. In this respect, scientific disciplines embraced a practice that was more generally followed in all scholarly fields. However – paradoxically – while it has always been recognised that commentary served as a vehicle for innovative dialogue with the socially most authoritative texts (sacred writing, law), scholars have been much slower to appreciate that the same is true in other fields, and to focus attention on commentary as practice. This conference aims at deepening our understanding of how classics and canonical texts were perceived qua texts, by relying on scientific sources, and to study the forms and editions through which these specific types of text were presented to users. Our project further seeks to observe the various readings and interpretations that actors operating in different contexts made of these texts. For this, we will scrutinize several types of evidence, from marginalia left by readers to commentaries systematically composed on classics and canonical texts. In particular, we want to defamiliarize the concept of commentary, and anchor it in more specific social and cultural contexts. We welcome case studies dealing with sources written in any language of the ancient and early modern world. The conference will approach these questions from a multidisciplinary perspective, bringing various forms of approaches and competences to bear on these issues.

Euclidis Optica & Catoptrica (Paris, 1557). Bodleian Library Savile T 7. Courtesy of the Reading Euclid project.

The conference is rooted in three projects that have been and are still developed at Oxford and Paris. Oxford project “Reading Euclid” deals with early modern English modes of reading of a classical work of mathematics, Euclid’s Elements, in its early modern editions. Paris-based project “Mathematical canons and commentaries” has aimed at understanding why and how mathematical activity in the ancient world has taken the shape of writing commentaries on canonical texts and which approaches to these canonical texts the commentaries testified to. Finally, Sally Humphreys has long developed a comparative and anthropological approach to ancient Greek classics; and has organized two comparative projects: Cultures of scholarship (Univ. of Michigan Press 1997) and Modernity’s Classics (Springer 2013).

 

Programme

Monday, June 3rd, 2019
Chair/commentator: Christopher Minkowski (Faculty of Oriental Studies, University of Oxford)
9:00 – 10:15 Karine Chemla (SPHERE & CHSA, CNRS & Université Paris Diderot)
The history of reading and the interpretation of a classic: Reading a problem, reading a procedure, reading the organisation in The Nine Chapters
10:15 -10:30 – break
10:30 – 11:45 Benjamin Wardhaugh (Faculty of History, University of Oxford)
Defacing Euclid: Printing and annotating the Elements of Geometry in early modern Britain
11:45 – 13:00 – Philip Beeley (Faculty of History, University of Oxford)
‘But, ’tis Euclide still!’ John Wallis on the principles and practice of editing classical Greek mathematics
13:00 – 14:30 – lunch break
Chair / commentator: tba
14:30 – 15:45Agathe Keller (SPHERE & CHSA, CNRS & Université Paris-Diderot)
Treatises and commentaries of Sanskrit mathematical texts: What was the author trying to say? Who is the classic?
15:45 -16:00  – break
16:00 – 17:15Antoni Malet (Universitat Pompeu Fabra)
Conceptual Change in Seventeenth-Century Jesuit Editions of Euclid’s Elements
Dinner of the conference

Tuesday, June 4th, 2019

Claude Richard, S.J., Commentary of Euclid, Elements, Book I (c.1640).
Real Academia de la historia, Madrid, 9/2680 -568

Chair/commentator: Elisabeth Hsu (School of Anthropology and Museum Ethnography, University of Oxford)
9:00 –10:15 Vincenzo de Risi (SPHERE, CNRS & Université Paris Diderot)
Leibniz Reader of Euclid
10:15 – 10:30 – break
10:30 –11:15Yelda Nasifoglu (History Faculty, University of Oxford)
‘A very difficult but erudite Authour in the usefull & concrete Mathematiques’: Reading Vitruvius in Seventeenth-century Oxford
11:45 – 13:00Sarah C. (Sally) Humphreys (Professor Emerita of History, Anthropology, and Greek at the University of Michigan in Ann Arbor, Michigan)
Learning through reading:  the aims and readership of ‘technical’ works in premodern cultures
13:00 – 14:30 – lunch break
Chair/commentator: tba
14:30 – 15:45 Florence Bretelle-Establet (SPHERE & CHSA, CNRS & Université Paris Diderot)
Writing about the Treatise on cold damage disorder (Shanghan lun 傷寒論, 3rd century CE) in late imperial China
15:45 -16:00  –  break
16:00 – 17:15 – General discussion

Abstracts

Philip Beeley
‘But, ’tis Euclide still!’ John Wallis on the principles and practice of editing classical
Greek mathematics

Abstract – In later life, the Oxford mathematician John Wallis turned his attention increasingly to the production of scholarly editions of works by Archimedes, Aristarchus, Pappus, and other Greek authors. Part of his motivation for this came from John Fell’s auspicious programme to promote a learned press at Oxford which envisaged the publication of, among others, “The ancient Mathematicians Greek & Latin in one and twenty volumes”. Another part was his understanding of scientific tradition generally and that it was his task as mathematician “to understand the true ground of what hath delivered to us from the Antients and to make further improvements on it”. The paper will look at the principles Wallis employed in reading and editing ancient Greek texts and how he defended these principles in discussion with contemporaries such as Thomas Smith and Arthur Charlett.

Florence Bretelle-Establet
Writing about the Treatise on cold damage disorder (Shanghan lun 傷寒論, 3rd century CE) in late imperial China
Abstract – The Treatise on cold damage disorder (Shanghan [zabing] lun) was written by Zhang Zhongjing (also known as Zhang Ji, 150-219) in the beginning of the third century, after, he explained, the two-thirds of his numerous family died from “cold damage disorders”. This text certainly circulated in handwritten copies after Zhang Zhongjing’s death until the Imperial Bureau for Revising Medical books printed one edition in the eleventh century. This text was then included in the imperial medical curriculum until the end of the Qing dynasty (1644-1911), and became one of the classical texts that any imperial medical student should learn. Once printed, and widely known, this text became the object of commentaries until today as well as the basis for new writings. For instance, out of the 276 medical texts written during the Qing dynasty and recorded in historical sources of the provinces of Yunnan, Guangxi and Guangdong, twenty-four were specifically written in relation with either Zhang Zhongjing’s original text or with the category of diseases known as shanghan cold damage disorders. Relying on the three extant texts devoted to the Shanghan lun, written in this particular area, in 1827, 1849, and 1876, my contribution aims at giving an overview of what it meant for these particular actors to read a classic and to write about it.

Karine Chemla
The history of reading and the interpretation of a classic: Reading a problem, reading a procedure, reading the organisation in The Nine Chapters
Abstract – The Nine Chapters on Mathematical Procedures (九章算術, hereafter The Nine Chapters), whose completion I date to the first century CE, was handed down with ancient commentaries selected by the written tradition. These commentaries include Liu Hui’s 劉徽 commentary, completed in 263, and Li Chunfeng’s 李淳風 commentary, presented to the throne in 656. In the commentators’ eyes, The Nine Chapters was a “canon jing 經”, which is surprising for us, since it is essential composed of mathematical problems and procedures solving them. To understand what it meant for the commentators that the book was a “canon”, we need to observe how they interpreted its problems, its procedures and the way in which The Nine Chapters was organized. This is the task that this talk aims at fulfilling.

Sally Humphreys
Learning through reading:  the aims and readership of ‘technical’ works in premodern cultures
Abstract – Through looking at material from the Greco-Roman world (including periploi and cookbooks), the paper problematizes modern assumptions about its uses and readership.

Agathe Keller
Treatises and commentaries of Sanskrit mathematical texts: What was the author trying to say? Who is the classic?
Abstract – In what contexts were Sanskrit astral and mathematical texts used? What was the aim of these texts and the rules they contained? Here by studying Bhāskara’s (628) and Sūryadeva’s (12th century) commentary on Āryabhaṭa (b.476)’s Āryabhaṭīya, and the anonymous and undated commentary on Śrīdhara’s Pāṭigaṇita (ca. 850), we will see how commentators unravel for us what they thought the author of the treatise was aiming at. These commentators help us see that the rules of mathematical «classics» didn’t necessarily aim at stating a procedure to be executed, but could also be themselves commenting on the procedure, its important steps, or the reasons of its validity.
This point of view, important for historians, may also have been important within traditions of Sanskrit astral and mathematical lore as well. This case study will be followed by another in which we see commentarial texts being rephrased and re-used in later treatises: who then is the classic? Both case studies will show how commentaries and treatises were considered together in theses scholarly milieus.

Antoni Malet
Conceptual Change in Seventeenth-Century Jesuit Editions of Euclid’s Elements
Abstract – This paper focuses on some 17th-century Jesuit editions of the Elements, including André Tacquet’s and Milliet Dechales’s editions — which had an enormous influence throughout Europe from c. 1650 through the second half of the 1700s, and which shaped the edition of Jacob Kresa (1648–1715), who taught in Madrid (Colegio Imperial). While the outstanding role played by Christopher Clavius’s edition of the Elements (1574, with many editions and reprints) in early modern mathematical education has been well documented, Clavius’s edition was far from being the only Jesuit reading of the Elements. In the 17th century, many Jesuit editions were at least indirectly linked to the so-called Antwerp school, which had in Gregoire de Saint-Vincent a major source of inspiration (and through it became influential in the Castilian speaking early modern world). Yet Jesuit mathematicians did not slavishly follow Clavius’s or Saint-Vincent’s views. Interesting heterodox readings of Euclid were offered by I. Pardies (1636-1674) and J. Zaragozá (1627-1679), for instance. Our paper pays attention to the ways in which Jesuit mathematicians introduced fundamental conceptual changes in the Elements. Taking for granted that the Elements was a major source of authority about basic mathematical objects, we will focus on their Jesuit reconstructions, including the critiques of the notion of ratio and proportionality that appeared in many 17th-century Jesuit editions. We will show that deep similarities are to be found among Jesuit understandings of the Elements‘ basic mathematical concepts.

Yelda Nasifoglu
‘A very difficult but erudite Authour in the usefull & concrete Mathematiques’: Reading Vitruvius in Seventeenth-century Oxford
Abstract – Vitruvius’s De architectura, the only treatise on the subject to have survived intact from antiquity, is considered a canon of architectural theory. Yet, architecture as a profession making a late entry to the British Isles, prior to the publication of its first English translation in 1692, the text had a more wide-ranging reception among the learned circles. It served as a guide to ancient systems of measurement as well as a source of practical knowledge on various subjects, from medicine to mechanics, from pigments to fortifications. It also provided anecdotal evidence of architecture’s place as a unifier of scientiae. This paper will examine the reception of De architectura in the academic setting of seventeenth-century Oxford, presenting evidence from the archives of Savilian professor of astronomy, Edward Bernard (1638–1697), and the recently-rediscovered manuscript of the first full English translation of the treatise by Christopher Wase (1625–1690).

Vincenzo de Risi
Leibniz Reader of Euclid
Abstract – In the course of his life, Leibniz read a great number of editions and commentaries of Euclid’s Elements and commented himself on them in private notes, letters and sections of his published works. Leibniz never edited a commentary to the Elements, but among his papers in Hannover several sets of notes comment extensively on Euclid. Leibniz’s first commentaries on the Elements date from his early years (around 1679), while the last ones were written in the last years of his life (1714). In the talk, I present Leibniz’s activities as a commentator of Euclid, drawing from these manuscript sources, attempting to sketch a history of the development of Leibniz’s views on the subject, underlining the most important topics that he treated, and discussing the existing Euclidean commentaries that he read. I also deal with Leibniz’s personal and scientific relations with other geometers working on the Elements, and with his support to the publication of a German edition of Euclid. Leibniz’s outstanding geometrical and logical skills, together with his openness to different sources and mathematical traditions, make Leibniz’s remarks on Euclid one of the most interesting corpora on the foundations of geometry, and show a very peculiar approach to the classical texts.

Benjamin Wardhaugh
Defacing Euclid: Printing and annotating the Elements of Geometry in early modern Britain
Abstract – This talk will explore the rich evidence provided by surviving copies of Euclid’s Elements of Geometry from early modern Britain. On the one hand, decisions by editors and printers about the text: its language and notation, scope, layout, diagrams and the degree of editorial explanation. On the other hand, marks made by readers to record ownership and intellectual engagement, including the unique processes involved in learning mathematics in this period. Together these lines of evidence allow us to reconstruct a distinctive world of geometrical teaching and learning.