Geometrical Researches on the Theory of Parallels - photo 1
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Geometrical Researches on the Theory of Parallels

Lot 53
27.01.2023 10:00UTC +00:00
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$ 25 200
AuctioneerCHRISTIE'S
Event locationUnited Kingdom, London
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ID 887826
Lot 53 | Geometrical Researches on the Theory of Parallels
Estimate value
$ 25 000 – 35 000
LOBACHEVSKY, Nikolai Ivanovich (1792–1856). Geometrical Researches on the Theory of Parallels. Translated by George Bruce HALSTED. [Offprint from:] Scientiae Baccalaureus. Vol 1, No 3, February, 1891. Austin: [Printed at Rolla, Missouri: School of Mines Press,] 1891.

“What Vesalius was to Galen, what Copernicus was to Ptolemy, that was Lobatschewsky to Euclid" (W.K. Clifford, quoted in the Translator's Preface)

The extremely rare offprint issue of the true first edition in English of Lobachevsky’s discovery of non-Euclidean geometry.

This work, published in the short-lived and little-known journal Scientiae Baccalaureus, is a translation of Geometrische Untersuchungen zur Theorie der Parallellinien (Berlin, 1840), which was the first complete account of Lobachevsky’s work to be published in a Western European language. Lobachevsky sent Carl Gauss a copy of the 1840 work, and Gauss’s opinion of it is recorded in a letter, dated 28 November 1846, written to his colleague the astronomer H. C. Schumacher: “In developing the subject, the author followed a road different from the one I took myself; Lobachevsky carried out the task in a masterly fashion and in a truly geometric spirit. I consider it a duty to call your attention to this book, since I have no doubt that it will give you a tremendous pleasure.”

“The researches that culminated in the discovery of non–Euclidean geometry arose from unsuccessful attempts to ‘prove’ the axiom of parallels in Euclidean geometry. This postulate asserts that through any point there can be drawn one and only one straight line parallel to a given straight line. Although this statement was not regarded as self-evident and its derivation from the other axioms of geometry was repeatedly sought, no one openly challenged it as an accepted truth of the universe until Lobatchewsky published the first non-Euclidean geometry … In Lobatchewsky’s geometry an infinity of parallels can be drawn through a given point that never intersect a given straight line” (PMM).

The appearance of Lobachevsky’s work in the Scientiae Baccalaureus is little-known. The first English translation is often mistakenly given as that which appeared, under the same title and with the same translator, in the “Neomonic Series” of the Bulletin of the University of Texas at Austin a few months later. The main text is identical (in text, not in typography) to that of the Scientiae Baccalaureus version, but its preface, dated May, 1891, was extensively rewritten and enlarged. Scientiae Baccalaureus is extremely rare. The journal ran to only four issues in a single volume and is extant in about 10 public libraries. This offprint edition is recorded in just one copy, the one which belonged to the editor of the journal and is now at the University of Virginia. Sommerville p 100; see PMM 293 and Norman 1379; L. M. Hall, “A Forgotten Nineteenth Century Mathematics Journal,” Missouri Journal of Mathematical Sciences 16 (2004), pp 159-167.

Octavo (204 x 150 mm). Numerous diagrams in the text. Contemporary cloth-backed boards, with wrapper title “Theory of Parallels, Lobatschewsky, Translated by Dr. George Bruce Halsted, Austin, Tex.” laid down on upper cover (minor spotting to covers, erasure to inside front cover). Provenance: two early pencil mathematical notes on pp. 126 and 127.
Place of origin:Eastern Europe, USA
Auction house category:Printed books
Address of auction CHRISTIE'S
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