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Axe Histoire et philosophie des mathématiques

Lecture de textes mathématiques

Responsable : Agathe Keller - CNRS, REHSEIS–SPHERE

Comme tous les ans, nous lisons des sources originales et leurs traductions, présentées par leur traducteur.

PROGRAMME 2017-2018
Les mercredis, 10:00 – 13:00, en salle Gris, 734A, sauf exception. Université Paris Diderot, bâtiment Condorcet, 10 rue Alice Domon et Léonie Duquet, 75013 - Paris (plan).

mercredi 25/10 : 734A-Gris 10h-13h

  • Zhu Yiwen (Zongshan Univ.)
    Part of the first problem of the Mathematical Book in Nine Chapters.

 !! mardi 6/11, salle Alechinsky, 743A !!

  • AJ Misra (Tamas)
    The preambulatory text accompanying the astronomical tables of the Amṛtalaharī of Nityānanda.

 !! jeudi 30/11 9:30-13 ;00 !!

  • JU Shier
    lira avec nous des textes en chinois concernant des cartes d’étoiles
  • ZHANG Yijie (Guangzhou University)
    la nouvelle méthode de Hu Shi par Zhu Zaiyu.

 !! lundi 22/01, salle Klein, 371A

  • Jeff Jiang Ping (StCloud State University)
    Practices of Cossic Algebra in 18th- and 19th-century China.
    Cossic algebra, the algebraic methods with a symbol for the unknown, was introduced to the Chinese court by the Jesuits in the 1690s. The mathematical compendium Yuzhi Shuli jingyun, 御製數理精蘊 (the Essence of numbers and their principles imperially composed), commissioned by Kangxi Emperor (1654-1722) and published in 1722, contains sections discussing this topic, the expressions of “polynomials” in one unknown, their basic arithmetic operations, and the associated algorithms that solve polynomial equations up to the third degree, which were collectively known in Chinese as Jiegenfang suanfa 借根方算法 (Calculation by borrowed root and powers) at the time. Although the expressions are not fully “symbolic,” their manipulating are well-developed for performing the same operations on both sides of equations, including adding, subtracting, and divided by numbers, the “root” (the unknown), or the square of the root as well as taking square and cubic roots of both sides.
    In this presentation, we examine an example of complex maneuver of cossic algebraic expressions in an early 19th-century treatise. Although the processes of manipulation are not demonstrated in “polynomial” expressions, the steps are recorded explicitly in the main text. This textual description of the step-by-step maneuvers include expanding squares of the sum of three terms, squares of fractional expressions, and the cancellation of common factors of quantities on “both sides of the equality.” The jiegenfang methods played an important role in the development of trigonometry in China as they provide algorithms to find the sine values of one-third and one-fifth of an arc/angle when the sine value of the angle is known. Our hope is to provide a better understanding of the practice of cossic algebra in the 18th and 19th century.

mercredi 21/03

mercredi 11/04

  • Ken Manders (Univ. of Pittsburgh)

mercredi 23/05

  • (sous-reserve) Glen Van Brummellen (Quest University)

mercredi 13/06 : 734A-Gris 10h-13h

Accès : Métro ligne 14 / RER C / Station : Bibliothèque François Mitterrand
Métro ligne 6 / Station : Quai de la Gare
Bus 64 / Arrêt : Tolbiac-Bibliothèque François Mitterrand
Bus 62 & 89 / Arrêt : Avenue de France or Bibliothèque François Mitterrand (terminus)
Bus 325 / Arrêt : Watt