Ob izchezanij trigonometrisheskikh strok. [Russian - i.e. On the Convergence of Trigonometrical Series] [In: "Uchenye zapiski" ("Scientific Memoirs") of Kazan University]. - [THE GENERAL DEFINITION OF A FUNCTION]

1834. Kazan, 1834. 8vo. Contemporary blank, blue wrappers (original?). A closed tear and a bit of staining to back wrapper and some tears and scratches to spine. Internally very nice and clean. Presumably not an off-print, as there are stitching-holes to the margins, indicating that it has been removed from a volume, although the wrappers could look original, certainly contemporary. With the original title-page for Book 11 of the "Uchenye zapiski" + pp. (167)-226. Scarce first printing of Lobachavsky's main contribution to his second most important field (after non-Euclidean geometry), namely infinite series, more specifically trigonometric series. This constitutes one of Lobachevsky's earliest papers and the one in which he presents his new results in the theory of trigonometric series. It is here that he gives his definition of a function as a correspondence between two sets of real numbers, the same definition that Dirichlet some three years later discovers independently of Lobachevsky (and is given the general credit for). This important paper was published in the Scientific Memoirs of the Kazan University. "Some of Lobachevsky's early papers, too, were on such nongeometrical subjects as algebra and the theoretical aspects of infinite series. Thus, in 1834 he published his paper "Algebra ili ischislenie konechnykh" ("Algebra, or Calculus of Finites"), of which most had been composed as early as 1825. The first issue of the "Uchenye zapiski" ("Scientific Memoirs") of Kazan University, founded by Lobachevsky, likewise carried his article "Ob ischezanii trigonometricheskikh strok" ("On the Convergence of Trigonometrical Series"). The chief thrust of his scientific endeavor was, however, geometrical, and his later work was devoted exclusively to his new non-Euclidean geometry." (DSB)