Voobrazhayemaya geometriya with Primenenie voobrazhaemoi geometrii k nekotorym integralam - photo 1
Voobrazhayemaya geometriya with Primenenie voobrazhaemoi geometrii k nekotorym integralam - photo 2
Voobrazhayemaya geometriya with Primenenie voobrazhaemoi geometrii k nekotorym integralam - photo 3
Voobrazhayemaya geometriya with Primenenie voobrazhaemoi geometrii k nekotorym integralam - photo 4

Voobrazhayemaya geometriya with Primenenie voobrazhaemoi geometrii k nekotorym integralam

Lot 111
16.10.2025 00:00UTC +01:00
Classic
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CHRISTIE'S
AuctioneerCHRISTIE'S
Event locationUnited Kingdom, London
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ID 1472034
Lot 111 | Voobrazhayemaya geometriya with Primenenie voobrazhaemoi geometrii k nekotorym integralam
Estimate value
$ 30 000 – 50 000
LOBACHEVSKY, Nikolai (1792–1856). Воображаемая геометрія (Voobrožajemaja geometrija) [Imaginary Geometry]. Kazan: at the University Press, 1835. [With:] LOBACHEVSKY, Nikolai (1792–1856). Примѣненіе воображаемой геометріи къ нѣкоторымъ интегралаъ (Primenenije voobrožajemoj geometrii k nekotorym integralam) [Application of Imaginary Geometry to Certain Integrals]. Kazan: at the University Press, 1836.

Rare first edition offprint issues of Lobachevsky's Imaginary Geometry and its sequel on the application to integers. "The researches that culminated in the discovery of non-Euclidean geometry arose from unsuccessful attempts to ‘prove’ the axiom of parallels in Euclidean geometry. […] In Lobatchewsky’s geometry an infinity of parallels can be drawn through a given point that never intersect a given straight line […] His fundamental paper was read to his colleagues in Kazan in 1826 but he did not publish the results until 1829–30 when a series of five papers appeared [in Russian] in the Kazan University Courier’ (PMM). Lobachevsky ‘built up the new geometry analytically, proceeding from its inherent trigonometrical formulas and considering the derivation of these formulas from spherical trigonometry to guarantee its internal consistency. […] If imaginary numbers are the most general numbers for which the laws of arithmetic of real numbers prove justifiable, then imaginary geometry is the most general geometrical system. It was Lobachevsky’s merit to refute the uniqueness of Euclid’s geometry, and to consider it as a special case of a more general system" (DSB). Lobachevsky produced a continuation to this article, which was published in the following issue of the Kazan University Proceedings: Primenenie voobrazhaemoi geometrii k nekotorym integralam [Application of Imaginary Geometry to Certain Integrals], Kazan, University Press, 1836. See PMM 293; see Norman I, 1379.

Octavo (220 × 135mm). Both works with their folding plates, original printed wrappers bound in (intermittent spotting predominately in the first and last leaves of each work, first work's wrappers with small tears and one repaired, second work's wrappers with stains). 19th-century quarter black cloth with marbled paper over paper boards (extremities rubbed, light scratches on covers). Provenance: titles transliterated in pencil – erased inscription along top of first work's upper wrapper – Dr. Martin Sändig, Wissensch.-techn. Antiquariat (Wiesbaden book label on upper pastedown) – F. Engel (Leipzig, inscription on flyleaf dated 30 April 1898) – Egon Ullrich (20th-century inscription on flyleaf).
Place of origin:Russia
Address of auction CHRISTIE'S
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02.10.2025 – 16.10.2025
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