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10 MEMOIRES ORIGINAUX ou TIRES A PART (OFFPRINT) de CHEBYCHEV reliés en un volume in 8 demi-basane marron : (voir détail ci-après)
1. Ob interpolirovanii [in Cyrillic]. (Sur l'interpolation). Saint-Petersbourg, 1864, (1), 23pp. -- 2. O razlozhenii funktsiy v ryady pri pomosshi nepreryvnykh drobei [in Cyrillic]. (Sur le développement des fonctions en séries au moyen des fractions continues). Saint-Petersbourg, 1866, (1), 26pp. -- 3. Ob interpolirovanii velitchin ravnootstoyasshikh [in Cyrillic]. (Sur l'interpolation des valeurs équidistantes). Saint-Petersbourg, 1875, (1), 30pp. -- 4. Ob otnoshenii dvukh integralov, rasprostranennikh na odne i te zhe velitchiny peremennoy [in Cyrillic]. (Sur le rapport de deux intégrales prises entre les mêmes limites d'intégration. Communication faite à l'Académie impériale des sciences). Saint-Petersbourg, 1883, (1), 33pp. -- 5. O priblizhennykh virazheniyakh odnikh integralov tcherez drugie, vsyatye v tekh zhe predelakh [in cyrillic]. (Sur les expressions approchées des intégrales au moyen d'autres intégrales prises entre les mêmes limites). Kharkov, 1883, 6pp. -- 6. O predstavlenii predelnykh velithcin integralov posredstvom integralnykh vytchetov [in Cyrillic]. (Sur la représentation des valeurs limites des intégrales par des résidus intégraux). Saint-Petersbourg, 1885, (1), 25pp. -- 7. Ob integralnykh vytchetakh dostavlyayusshikh priblizhennyya velitchiny integralov [in Cyrillic]. (Sur les résidus intégraux qui donnent des valeurs approchées des intégrales). Saint-Petersbourg, 1887, (1), 50pp. -- 8. O priblizhennykh vyrazheniyakh kvadratnogo kornya peremennoy tcherez prostyye drobi [in Cyrillic]. (Sur les expressions approchées d'une racine carrée de la variable au moyen des fractions simples). Saint-Petersbourg, 1889, (1), 22pp. -- 9. O summakh sostavlennikh iz znatcheniy prosteysshiskh odnotchlenov umnozhennykh na funktsiyu, kotoraya ostaetsya polozhitelnoy [in Cyrillic]. (Sur les sommes composées des valeurs de monômes les plus simples multipliés par une fonction qui reste positive). Saint-Petersbourg, 1891, (1), 67pp. -- 10. O polinomakh nailutshe predstavlayusshikh znatcheniya prosteysshikh drobnykh funktsiy pri velitchinakh peremennoy zaklyutchayusshikhsya mezhdu dvumya dannimy predelami [in Cyrillic]. (Sur les polynômes qui représentent le mieux les valeurs des fonctions fractionnaires les plus simples pour les valeurs de la variable, comprises entre deux valeurs données). Saint-Petersbourg, 1893, (1), 13pp.
---- TRES RARE REUNION DE MEMOIRES ORIGINAUX DE CHEBYCHEV PRESENTES A L'ACADEMIE DES SCIENCES DE SAINT-PETERSBOURG ---- These papers concern the doctrine of limiting value of integrale. "Tchebychev's importance in the history of science consists not only in his discoveries but also in his founding of a great scientific school. It is sometimes called the Tchebychev school, but more frequently the Petersburg school. The Petersburg mathematical school owes its existence partly to the activity of Tchebychev's elder contemporaries, such as Bunyakovski and Ostrograski ; nevertheless, it was Chebyschev who founded the school, directed and inspired it for many years and influenced the tend of mathematics teaching at Petersburg university. Tchebychev's general approach to mathematics quite naturally resulted in his aspiration toward the effective solution of problems and the discovery of algorithms giving either an exact numerical answer o, if this proved impossible, an approximation ready for scientific and practical applications. He interpreted the strictness of the theory in the event of approximate evaluations as a possibility of precise definition of limits not trespassed by the error of approximation.". (DSB III pp. 222/232). (N° 24)**4961/CART.RUSS
Sur deux théorèmes relatifs aux probabilités. - [THE FOUNDATION FOR THE APPLICATION OF PROBABILITY THEORY TO STATISTICS]
Berlin, Stockholm, Paris, Almqvist & Wiksell, 1890. 4to. As extracted from ""Acta Mathematica"", Vol, 14, 1890. No backstrip. A fine and clean copy. Pp. 305-15.
First translation of Chebyshev's landmark paper (first published in Journal of the The St. Petersburg Academy in 1887) in which he laid the foundation for the application of probability theory to statistics, generalizing the theorems of Moivre and Laplace. It also generalized the theory of integral beta function. This led him to find an algorithm for finding an optimal solution in a system of linear equations with an approximate solution is known.""In the 1860's Chebyshev returned to the theory of probability. One of the reasons for this new interest was, perhaps, his course of lectures on the subject started in 1860. He devoted only two articles to the theory of probability, but they are of great value and designate the beginning of a new period in the development of this field. In the article of 1866 Chebyshev suggested a very wide generalization of the law of large numbers. In 1887 he published (without extensive démonstration) a corresponding generalization of the central limit theorem of Moivre and Laplace."" (DSB).""Chebyshev and many of his students were often cold and skepticall towrads various important achievements in Western European mathematics. In the two-hundred-year development period in probability theory its main achievements were the limiting theorems: the law of large number and the de Moivre-Laplace theorem. But the confines of applicability of these theorems and their further refinements and generalizations were not satisfactory. The second basic problem that occupied Chebyshev's attention was the central limit theorem. However, only in 1887 in the Proceedings of the Academy of Sciences was Chebyshev's paper devoted to this subject published."" (Maistrov, Probability and Mathematical Statistics, P. 202).
