Date : 1997
Editeur / Publisher : [S.l.] : [s.n.] , 1997
Format : 2 vol., 485 p.
Type : Livre / Book
Type : Thèse / ThesisLangue / Language : français / French
Résumé / Abstract : DANS NOTRE THESE NOUS ETUDIONS LE DEVELOPPEMENT DES MODES DE DESCRIPTION ET DES PRATIQUES ALGORITHMIQUES DU CALCUL DES SERIES. NOTRE RECHERCHE DONNE D'UNE PART UN APERCU DE L'HISTOIRE DES SERIES FINIES DANS LES MATHEMATIQUES CHINOISES DITES ALGORITHMIQUES. ON ABORDE LA QUESTION SOUS UN ANGLE DIACHRONIQUE POUR APPREHENDER LA NOTION DE CONTINUITE HISTORIQUE ET DE TRADITION. NOUS ETUDIONS D'AUTRE PART, D'UN POINT DE VUE PLUS SEMIOTIQUE, LA FONCTION DES NOMS DANS LES ALGORITHMES ET LA RECURRENCE DES STRUCTURES (CON-) TEXTUELLES, POUR EN TIRER DES CONCLUSIONS SUR LES DIFFERENTES CONCEPTIONS DE L'OBJET "SERIE". NOUS NE NOUS LIMITONS PAS A UNE EPOQUE PARTICULIERE MAIS PRESENTONS DES ANALYSES DE TEXTES ET DE LEURS COMMENTAIRES APPARTENANT AUX EPOQUES MARQUANTES DES MATHEMATIQUES EN CHINE. LA PREMIERE PARTIE TRAITE UN PROBLEME DE POURSUITE DES NEUF CHAPITRES SUR LES PROCEDURES MATHEMATIQUES (JIU ZHANG SUAN SHU, ENV. IER SIECLE DE NOTRE ERE) ET DE SES COMMENTAIRES DU IIIE AU VIIE SIECLE. DANS LA PARTIE PRINCIPALE NOUS CONSIDERONS L'OEUVRE ET EN PARTICULIER LA TERMINOLOGIE DES DIFFERENTS TYPES DE SERIES DE ZHU SHIJIE (VERS 1300) QUI DATE DE LA DYNASTIE YUAN, L'UNE DES APOGEES DES MATHEMATIQUES CHINOISES, QUE NOUS COMPARONS AUX TRAITEMENTS DES SERIES PAR SES PREDECESSEURS SHEN GUA ET YANG HUI (XIE ET XIIIE SIECLE RESPECTIVEMENT) DE LA DYNASTIE SONG. UNE DERNIERE PARTIE OUVRE UNE PERSPECTIVE SUR L'ETUDE DE LA RENAISSANCE DES MATHEMATIQUES CLASSIQUES ET LA RENCONTRE DE TRADITIONS DIFFERENTES PENDANT L'EPOQUE QING. ELLE ANALYSE LES COMMENTAIRES ECRITS SUR LE MIROIR DE JADE DES QUATRE INCONNUES (SI YUAN YU JIAN, 1303) DE ZHU SHIJIE, ET UN TEXTE DU SAVANT LI SHANLAN (1811-1882), QUI A ETE EN CONTACT AVEC DES MATHEMATICIENS OCCIDENTAUX.
Résumé / Abstract : ZHU SHIJIE'S TREATMENT OF "SERIES" IN HIS JADE MIRROR OF FOUR UNKNOWNS (SI YUAN YU JIAN, FIRST PUBLISHED IN 1303) IS ONE OF THE MOST CELEBRATED CASES IN THE HISTORY OF CHINESE YUAN DYNASTY MATHEMATICS. IN AN ATTEMPT TO ANALYZE CHRONOLOGICALLY THE RELATION BETWEEN ZHU'S APPROACH TO "SERIES" AND HIS PREDECESSORS' WE DESCRIBED THE DIFFERENT MODES OF EXPRESSION OF "SERIES" IN THE FRAMEWORK OF BOTH, A TEXTUAL AND AN ALGORITHMIC TRADITION. IT PROVED FRUITFUL TO COMPARE FIRST HOW ZHU SHIJIE, YANG HUI (SOUTHERN SONG DYNASTY) AND SHEN GUA (NORTHERN SONG DYNASTY) READ THE ANCIENT WORKS OF THEIR CLASSICAL PRECURSORS, AND THEN, TO OBSERVE THE DIFFERENT WAYS HOW ZHU HIMSELF WAS READ BY LATER MATHEMATICIANS AND HISTORIANS OF MATHEMATICS, IN PARTICULAR DURING QING TIMES. INCLUDING ZHU'S INTRODUCTION TO MATHEMATICS (SUANXUE QIMENG, FIRST PUBLISHED IN 1299) IN OUR ANALYSIS THE FOLLOWING QUESTIONS WERE ADDRESSED: 1) THE PROBLEMS CONCERNING "SERIES" WERE CONSTANTLY GROUPED TOGETHER WITH OTHER GEOMETRICAL, ARITHMETICAL OR ASTRONOMICAL PROBLEMS. WHAT WERE THE CHANGING PATTERNS OF CLASSIFICATION AND WHAT INFORMATION ON THE DIFFERENT CONCEPTIONS OF "SERIES" (E.G. DISCRETE ACCUMULATIONS IN THE SHAPE OF A CONTINUOUS VOLUME OR PROGRESSIONS FOR ACCELERATED MOTION) CAN BE IMPLIED FROM THESE TAXONOMIES? 2) ZHU'S TREATMENT OF SERIES WAS CONDUCTED WITHIN THE CONTEXT OF THE ALGEBRAIC TIAN YUAN METHOD. WHAT EXACTLY WERE THE STRUCTURES (E.G. THE STATEMENT OF A PROBLEM) AND ALGORITHMIC PRACTICES (E.G. THE USE OF TABLES) THAT HE IDENTIFIED AND ADOPTED FROM FORMER TEXTS IN HIS MODE OF DESCRIPTION? AND 3) ZHU SHIJIE APPLIES A HIERARCHICAL TERMINOLOGY TO DESIGNATE DISPARATE TYPES OF PILES, WHOSE TOTAL OF DISCRETE ELEMENTS GIVES THE SUM OF AN "ARITHMETICAL SERIES" OF HIGHER ORDER. HOW DOES ZHU'S RELATIONAL SET OF NAMES AFFECT LATER INTERPRETATIONS AND RECONSTRUCTIONS OF THE MATHEMATICAL OBJECTS AND PROCEDURES INVOLVED, BUT NOT SPELLED OUT, IN ZHU'S TEXT?