Lobatschewski, Nikolai Iwanowitsch. Sposob uviersit'sia v izchezanii bezkonechnykh strok i priblizhat'sia k znacheniiu funktsii ot ves'ma bol'shikh chisel.

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Erste selbständige Ausgabe dieses wichtigen Aufsatzes zu den Grundlagen der Analysis und des Kalküls, verfasst vom Entwickler der Nichteuklidischen Geometrie. "As early as 1835, Lobachevsky showed in [this] memoir the necessity of distinguishing between continuity and differentiability" (Cajori). "The mathematicians of the 18th century did not touch the question of the relation between continuity and differentiability, presuming silently that every continuous function is eo ipso a function having a derivative. Ampère tried to prove this position, but his proof lacked cogency. The question about the relation between continuity and differentiability awoke general attention between 1870 and 1880, when Weierstrass gave an example of a function continuous within a certain interval and at the same time having no definite derivative within this interval (non-differentiable). Meanwhile, Lobachevski already in the thirties showed the necessity of distinguishing the 'changing gradually' (in our terminology: continuity) of a function and its 'unbrokenness' (now: differentiability). With especial precision did he formulate this difference in his Russian Memoir of 1835: 'A method for ascertaining the convergence, etc.'. A function changes gradually when its increment diminishes to zero together with the increment of the independent variable. A function is unbroken if the ratio of these two increments, as they diminish, goes over insensibly into a new function, which consequently will be a differential-coefficient. Integrals must always be so divided into intervals that the elements under each integral sign always change gradually and remain unbroken" (Halsted, S. 242).

Broschur etwas knittrig mit kleinen Papierschäden am Hinterdeckel, Rücken und Ecken fachmännisch mit ähnlichem Papier ergänzt. Ecken des Titelblatts angerändert; innen leicht verknickt bzw. lappig mit gelegentlichen unbedeutenden Wasserrändern. Wie alle von Lobatschewskis Kasaner Drucken außerordentlich selten, sogar in russischen Sammlungen (OCLC verzeichnet lediglich das Exemplar in Harvard).