MERAY, Leçons nouvelles sur l'analyse infinitésimal, 1894-1898
MERAY, Charles.
Nouveau précis d'analyse infinitésimale.
Paris, Savy, 1872.
Un volume in-8 (227x137 mm), xxii-310 pages. reliure : Broché sous couverture éditeur.
Edition originale.
Charles Meray (1835-1911), mathématicien français, est aujourd'hui reconnu pour avoir été le premier à publier (en 1869, dans la revue des sociétés savantes) une théorie cohérente et rigoureuse des nombres irrationnels, avant Cantor (1872).
Charles Meray reprends sa théorie des nombres irrationnels dans ce "Nouveau précis d'analyse infinitésimale (1872)".
"Pour Méray, la limite est la notion de base de l'analyse. On sent bien ici la nécessité qui poussait Méray à définir correctement les nombres irrationnels, car les théorèmes sur les limites des suites n'avaient plus de sens lorsque ces suites ne tendaient pas vers des nombres rationnels, ce que Méray dit expressément. Ayant donné une définition correcte des nombres irrationnels, on retrouve alors tous les théorèmes sur les limites des suites tendant vers un rationnel ou non, par exemple, les théorèmes sur la somme, le produit d'un nombre fini de suites convergentes, etc "(Dugac. Charles Méray (1835-1911) et la notion de limite.).
références: DSB [IX, 307 :"Merray, (1835-1911), is remembered for having anticipated, clearly and with only minor differences of style, Cantor's theory of irrational numbers, one of the main steps in the arithmetization of analysis. (...) Dedekind also seems to have developed his theory of irrationals at an earlier date, but he did not publish it until after the appearance of Cantor’s relevant paper in 1872. In that year Méray’s Nouveau précis d’analyse infinitésimale was published in Paris. In the first chapter the author sketches again his theory of irrationals and remarks that however peculiar it might appear to be, compared with the classical traditions, he considers it more in agreement with the nature of the problem than the physical examples required in other approaches. The Nouveau précis had as its principal aim the development of a theory of functions of complex variables based on the notion of a power series. Thus here again, Méray followed unconsciously in the footsteps of Weierstrass; consciously, he was developing the subject in the spirit of Lagrange but feltrightly—that he could firmly establish what Lagrange had only conjectured. The book is in fact written with far greater attention to rigor than was customary in Méray’s time.
Little regard was paid to Méray’s main achievement until long after it was first produced, partly because of the obscurity of the journal in which it was published. But even in his review (1873) of the Nouveau précis, H. Laurent pays no attention to the theory, while gently chiding the author for using too narrow a notion of a function and for being too rigorous in a supposed textbook. At that time there was not in France—as there was in Germany—a sufficient appreciation of the kind of problem considered by Méray, and not until much later was it realized that he had produced a theory of a kind that had added luster to the names of some of the greatest mathematicians of the period. Although Méray’s theory of irrationals stands out above the remainder of his work, his development of it may be regarded as more than an accident. For elsewhere he also showed the same critical spirit, the same regard to detail, and the same independence of thought that led him to his greatest discovery."].
provenance: Tampon de bibliothèque ancien.
Prix : 300 €
