Working on ancient mathematical sources: Textual environment and historiographic operations

Organised by the ERC project SAW (Research Group SPHERE), in the context of the seminar History of Science, History of Text

Venue: Université Paris Diderot , Condorcet Building, room 483A
4 rue Elsa Morante 75013 Paris or 10 rue Alice Domon et Léonie Duquet 75013 Paris – map

January 7th, 2016 – 9:30 am to 5:30 pm

Presentation
This session is devoted to examining key operations at play in the shaping of documents that constitute sources for historians of science and ways in which historians rely on these sources in their work.

Speakers
CHEN Zhihui
, On the Rediscovery of the Jade Mirror of the Four Origins, and its Interpretations by Luo Shilin and Shen Qinpei
Pierre Chaigneau, The use of algebraic formulas in the commentaries on mathematical cuneiform texts: the case of the tablet BM 85196
Matthieu Husson, Editing a Zij at the turn of the 20th century : the case of Carlo Alfonso Nallino (1872-1938)

Programme  pdf version

CHEN Zhihui (ERC Project SAW & SPHERE – CNRS & Université Paris Diderot)
On the Rediscovery of the Jade Mirror of the Four Origins, and its Interpretations by Luo Shilin and Shen Qinpei
Abstract –  The Jade Mirror of the Four Origins (Siyuan yujian ???? , hereafter SYYJ), which was completed by Zhu Shijie in 1303 and rediscovered in 1800s, is a mathematical monograph about the system of simultaneous equations of multi-unknowns (up to four). However, this treatise represents a form of “problem-answer-solution”, and Zhu Shijie just wrote a very concise solution for each problem. After its rediscovery, scholars made efforts to recover Zhu Shijie’s original intention in the solutions and to interpret the reason for the establishment of the method (????). This talk analyses Luo Shilin’s (??? 1789-1853) Detail Account and two manuscripts of Detail Account with different commentaries by Shen Qinpei (??? fl. 1820s), to examine the ways in which they interpret the SYYJ.

Pierre Chaigneau (ERC Project SAW & SPHERE – CNRS & Université Paris Diderot)
The use of algebraic formulas in the commentaries on mathematical cuneiform texts: the case of the tablet BM 85196
Abstract – In commenting mathematical cuneiform texts, Neugebauer and Thureau-Dangin used algebraic formulas. Clearly such formulas are absent from the sources. So what was at stake when these editors used them? The issue is raised here in the case of the commentaries on the tablet BM 85196. The point is less to discuss about the danger of anachronisms in historical approaches than to question the use of algebraic formulas as an editorial practice: why are they used? How? Are they merely used for the reader to understand or as a tool for the editor in further decipherments?

L’utilisation de formules algébriques dans les commentaires sur les textes mathématiques cunéiformes : le cas de la tablette BM 85196
Résumé – En commentant des textes mathématiques cunéiformes, Neugebauer et Thureau-Dangin utilisaient volontiers des formules algébriques. Il va de soi que de telles formules sont absentes des sources. Qu’est-ce qui est en jeu lorsque ces éditeurs les utilisent ? La question est posée ici dans le cas des commentaires à la tablette BM 85196. Il s’agit moins de discuter du danger des anachronismes dans les démarches en histoire que de mettre en question l’utilisation de formules algébriques en tant que pratique éditoriale : pourquoi en utiliser ? De quelle façon ? Sont elles simplement là pour aider le lecteur à comprendre ou bien sont elles utilisées par l’éditeur comme un outil pour les déchiffrements ultérieurs ?

Matthieu Husson (ERC Project SAW & SYRTE – CNRS & Observatoire)
Editing a Zij at the turn of the 20th century : the case of Carlo Alfonso Nallino (1872-1938)
Abstract – Nallino’s edition of al-Battani’s Sabi zij was elaborated over ten years between 1899 and 1909. It consists of three volumes: volume I presents a Latin translation of the text; a transcription and emendation of the tables are found in the second volume, whereas volume III gives an edition of the Arabic text. Nallino worked mainly from a single manuscript (Escorial ms. Arabe 908) which is up to now the only known complete manuscript of the work. He was associated to the famous Italian astronomer Giovanni Schiaparelli (1835-1910) for his technical work on the tables.
We will begin by a short presentation of these two scholars and the kind of interest they had in ancient sciences. This will give us the context in which the project of Nallino’s edition was formed, the types of motives and purposes it had. From this it will be possible to analyse the way Nallino and Schiaparelli worked with the tables in the Escorial manuscript, their treatment of scribal and computational errors, in order to assess how their methodological means relates to their project. We are in a favourable situation to do this because half of volume I and II of Nallino’s edition is taken up by his own comments on the documents and the way he worked with it. Moreover in 2008 Benno van Dalen and Fritz S. Pedersen published a technical survey of Nallino’s edition from which we will depend as well.