Beschreibung:

BOLYAI, Jnos (1802-1860). "Appendix. Scientiam spatii absolute veram exhibens: a veritate aut falsitate Axiomatis XI Euclidei (a priori haud unquam decidenda) independentem," in: Farkas BOLYAI (1775-1856), Tentamen juventutem studiosam in elementa matheseos purae. elementaris ac sublimioris, methodo intuitiva, evidentiaque huic propria, introducendi. Cum appendice triplici . Maros Vsrhelyini [Neumarkt]: Joseph and Simeon Kali at the Reform College Press, 1832-3. 2 volumes, 8 o (219 x 137 mm [Vol. 1]; 225 x 143 [Vol. 2]). Collation of Vol. I: s2, I-VI 4, VII 2; A-X 4, Z 4, J 4, V 4, AA-XX 4, ZZ 4, JJ 4, VV 4, AAa-PPp 4 (PPp4 divisional title for Appendix ); 2A- 2C 4, 2D 2 (Janos' Appendix , 2D2r-v errata); s8 (r-v list of subscribers). 302 (of 325 leaves; without the 23 leaves of errata and corrigenda after quire VII, which were apparently added to a second issue), paginated [iv], LII (without LIII-XCVIII), 502, [ii], 26, [2], XVI. Large folding letterpress table and 4 folding engraved plates containing numerous diagrams (one with overslips). Collation of Vol. II: s2 ( + 1), I 8; 1-8 8, 9 8 (+-9/3-4), 10-11 8, 12 8 (+-3), 13-14 8, 15 8 (+-15/2-3), 16 8 (+-4), 17-22 8, 23 2, 24 8, 26 8(-7). 204 leaves (without additional quire 27 8 (8+1) containing errata for Vol. 2), paginated [vi], XVI; 384. 10 folding engraved plates containing numerous diagrams (4 with overslips). (Horblit calls for one slip on plate 6, but it is not present here and may not be required). Original paper wrappers, rough trimmed and unopened (Vol. 1); original boards, unopened and untrimmed (Vol. 2). Morocco-backed folding case. Provenance : Prof. Jnos Bethlen, ORIGINAL SUBSCRIBER (signature on front pastedown in Vol. 2). FIRST EDITION OF BOLYAI'S SYSTEM OF NON-EUCLIDEAN GEOMETRY, which he invented independenly of Lobachevskii's slightly earlier discoveries (see lot 1174). Farkas Bolyai spent his life in close correspondence with Gauss, reconsidering the foundations of mathematics and proving Euclidean axioms. He published the Tentamen at his own expense at the press of the College where he taught in Transylvania. As an appendix to his work he published the short essay written by his son Jnos Bolyai, which was recognized by Gauss and Lobachevskii as one of the great original contributions to mathematics. "In the 26-page appendix to the mathematic work of his father, the young Bolyai established a generalised system of geometry free of Euclidian premises of the parallel-axiom, attempted earlier but neglected by Gauss. In the geometry of 'absolute space' an infinite number of lines can be drawn in a plane through a point, yet none of these will cut a given line in the same plane, thereby proving Euclid's eleventh axiom unnecessary. Thus three bodies of geometrical doctrine, elliptic, parabolic (Euclidian) and hyperbolic are formed, involving a new theory of surfaces" (Dibner). OF THE UTMOST RARITY. The list of subscribers lists 70 names, subscribing 128 copies, and it is doubtful if many more were printed. According to ABPC only two copies have appeared at auction in the past twenty-five years and only a few institutional copies are known: the Dibner copy at the Smithsonian, the Barchas copy at Stanford University, the Burndy Library copy (which was loaned to the Grolier exhibition), a copy at Japan's Kanzawa Institute of Technology, and the Cushing copy of the Appendix only at Yale. A VERY FINE COPY IN ORIGINAL CONDITION. "The Tentamen is crudely printed, and exhibits the ear marks of non-professional or inexperienced publishing, particularly in the numerous additional errata and corrigenda leaves present in the Dibner and Barchas copies ... These leaves were printed on different paper stocks and were obviously added after the original printing; their presence most probably constitutes a second issue" (Norman). Dibner, Heralds of Science 116; Grolier/Horblit 69b; Norman 259. (2)