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"OUT OF NOTHING I HAVE CREATED A STRANGE NEW UNIVERSE" BOLYAI S INVENTION OF NON-EUCLIDEAN GEOMETRY THE ONLY MAXIMALLY COMPLETE COPY IN PRIVATE HANDS. First edition, the finest and most complete copy ever likely to come to the market, of "the most extraordinary two dozen pages in the history of thought" (Halsted), containing the independent foundation (along with the work of Lobachevsky) of non-Euclidean geometry. This work is one of the few absolute rarities among the classics of science: in his recently published census, Lemley locates 25 surviving copies, including this one (no. 21 in the census). Our copy is in the most complete state (1H, 2C in Lemley s classification). Only two other copies in this state are known, both in institutional collections (Universitätsbibliothek Leipzig and the Bibliothčque universitaire des Sciences et Techniques in Bordeaux). There are only two copies in auctions records: the Norman copy (no. 2, Christie s NY, 1998, $98,000), in original binding but not the most complete state; and no. 5 (Sotheby s Paris, 2011, 120,750), in contemporary marbled boards, again not in the most complete state. "Despite its brevity and relative obscurity, János Bolyai s twenty-six-page Appendix was epoch-making in the history of mathematics. In it, Bolyai (1802 60) created a non-Euclidean system of geometry by challenging Euclid s fifth postulate, otherwise known as the axiom of parallelism. While its reception was initially muted, János s work would ultimately provide the mathematical basis for Einstein s special theory of relativity, developed be- tween 1905 and 1915" (Lemley, pp. 196-197). Nikolai Lobachevsky (1792-1856) and János Bolyai had independently created non-Euclidean systems by challenging the parallel postulate of Euclid. It has been a matter of debate for centuries whether this postulate that through any point not on a given straight line exactly one line can be drawn that does not intersect the given line can be deduced from the other postulates of Euclidean geometry. "János began work on his new geometry in 1820 at the age of eighteen, though his father, Farkas Bolyai, attempted to dissuade him from disproving Euclid s fifth postulate … After his son s unanticipated success, however, Farkas Bolyai published János s treatise as an appendix to the first volume of his mathematics textbook titled, Tentamen Juventutem Studiosam. Published in this form as a postscript to a small edition printed by an unknown Hungarian college in a provincial town in Transylvania the work was almost guaranteed obscurity" (Lemley, p. 197). A copy of the Appendix was sent to Gauss shorty after publication. Gauss was impressed, writing to Gerling on 14 February 1832 that "I consider this young geometer von Bolyai to be a genius of the first order" (Gray, p. 125). However, "Gauss responded in a letter [to Farkas] dated 6 March 1832: If I commenced by saying that I am unable to praise this work, you would certainly be surprised for a moment. But I cannot say otherwise. To praise it would be to praise myself. Gauss s dismissive assertion of priority disheartened János and effectively ended the young geometer s career in mathematics. And while Farkas viewed Gauss s letter as transparent praise from a master mathematician, János doubted Gauss s claim of priority and suspected his father of sharing his work prior to its publication. In the years following its publication, Bolyai s Appendix remained an obscure masterpiece. However, interest in non-Euclidean geometry was revived gradually in the decades before Einstein s theory of special relativity, and since then the Appendix has been rightly viewed as transformative in the history of mathematics" (Lemley, pp. 197-198). Farkas Bolyai was a close friend of Gauss and regarded by the latter as the only man who fully understood Gauss s metaphysics of mathematics. "He can be taken as a precursor of Gottlob Frege, Pasch, and Georg Cantor; but, as with many pioneers, he did. Seller Inventory # 4659
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