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)
*Descartes’ early mathematical errors: Texts and Context.*

We put in context various mathematical errors in Descartes’ notes from 1619—21. We will start with AT X 234—240; as this fragment has published translations and discussions, we will consider pp. 246—248 (solid geometry) and p. 294—297 (Pythagorean triples).

The key background text on Descartes’ early notebook is Gouhier, "Les Premières Pensées de Descartes". For AT X 234—240, see Chapters 3 of Sasaki (2003) "Descartes’s Mathematical Thought", and Shea (1991) "The Magic of Numbers and Motion”.

Wednesday May 23, !!salle 371 Klein !!

- Glen Van Brummelen (Quest University)
**Bianchini and the Flores Almagesti: Ptolemaic Astronomy from Beginning to End**

Fifteenth-century Italian astronomer Giovanni Bianchini was the author of several related texts dealing with to Ptolemaic astronomy, including the /Flores Almagesti/. This work, used frequently as a textbook in European universities, opens literally at the beginning of the subject, with basic arithmetic. Bianchini then moves to algebra before turning to basic trigonometry, eventually covering topics from the first six books of the /Almagest/. Its role as a textbook obscures some of its major innovations, including a complete decimal system of numeration, and novel approaches to trigonometry and spherical astronomy that extend well beyond the scope of the /Almagest/ itself.

+ conférence exceptionnelle / 14h-16h

- Jacqueline Feke (Université de Waterloo, Canada)
**Ptolemy’s Harmonic Ethics**

Abstract: Why did Ptolemy devote his time to the mathematical sciences, especially astronomy? The answer lies in his brief ethical statement in the first chapter of the Almagest. Coopting virtue ethics for the mathematician, Ptolemy argues that the best life is the one devoted to mathematics, where the mathematician configures his soul in accordance with the good order in the heavens. In this paper, I analyze this ethical statement and argue that to understand why and how astronomical objects serve as ethical exemplars in Ptolemy’s philosophy we must look to his Harmonics. It is because musical pitches, heavenly bodies, and human souls are all characterized by harmonic ratios that the study of either harmonics or astronomy can lead to the good life.

Wednesday June 13

- Alexis Trouillot (Univ. Paris Diderot, SPHERE)
- Alexis Trouillot (Univ. Paris Diderot, SPHERE)
*Un manuel de géométrie du 20ème siècle en Mauritanie, Nouachkott 532*.

(La langue de travail sera l’anglais.)

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