Organiser : Agathe Keller - CNRS, REHSEIS–SPHERE

We read original sources and their translations, presented by their translator.

PROGRAM 2017-2018

On Wednesdays, 10:00–13:00, Room Gris, 734A, University Paris Diderot, Building Condorcet, 10 rue Alice Domon et Léonie Duquet, 75013 - Paris

Map of campus with metro and buses stops.

Wednesday October 25, 2017

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

!! Tuesday November 6, Room Alechinsky, 743A !!

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

!! Thursday November 30, 9:30-13;00 !!

- JU Shier
*Chinese texts on the star maps.*

- ZHANG Yijie (Guangzhou University)
*The new method of Hu Shi by Zhu Zaiyu.*

!! Monday January 22, 2018, Room Klein, 371A !!

- Jeff Jiang Ping (St Cloud 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.

Wednesday March 21

- Dominique Tournès (Univ. de la Réunion) – tbc

Wednesday April 11

- Ken Manders (Univ. of Pittsburgh)

Wednesday May 23

- Glen Van Brummellen (Quest University) – tbc

Wednesday June 13

- Alexis Trouillot (Univ. Paris Diderot, SPHERE)

Access: Metro line 14 / RER C / Station: Bibliothèque François Mitterrand

Metro line 6 / Station: Quai de la Gare

Bus 64 / stop: Tolbiac-Bibliothèque François Mitterrand

Bus 62 & 89 / stop: Avenue de France or Bibliothèque François Mitterrand (terminus)

Bus 325 / stop: Watt