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Titel: Az arithmetica eleje. (Az elö-szóban írt ...
Verlag: Marosvásárhely, Reform Kollégyom, 1830
8vo (190 x 110 mm), pp xvi [xviii-xx] 162, with one folding lithographed plate; a few filled wormholes in blank margins, a very good copy in original blue paper boards. $20,000First edition, exceptionally rare and a fine association copy (see below), of Farkas Bolyai's first mathematical publication, and the precursor of his Tentamen, 1832-3. This work is on the foundations of arithmetic, algebra, and analysis, and includes a discussion of Euclid's parallel postulate, set theory, combinatorial analysis, calculus of variations, convergence of series, etc. It is in fact quite a mathematically advanced text, and was studied by Farkas's son Janos, whose heavily annotated copy is in the Reform Kollégyom library in Marosvásárhely. It was Farkas's son János who published, as an appendix to his father's Tentamen, the epochal Appendix. Scientiam Spatii Absolute Veram exhibens, a foundation text for non-Euclidean geometry.In June 1831 Gauss wrote that this work was considered mathematically incomprehensible by his colleagues, being written anonymously in Hungarian, but that the author, Bolyai, clearly understood and expressed many important concepts. Farkas Bolyai (1775-1856) was a close friend of Gauss and regarded by the latter as the only man who fully understood Gauss' metaphysics of mathematics. 'He can be taken as a precursor of Gottlob Frege, Pasch, and Georg Cantor; but, as with many pioneers, he did not enjoy the credit that accrued to those that followed him' (DSB). He had worked on the parallel postulate and the possibilities of a non-Euclidean geometry from his earliest days as a mathematician in Göttingen, and had corresponded with Gauss on the subject, even sending him a manuscript entitled Theoria parallelarum, but it was his son János who was to achieve the breakthrough.Provenance: Ferenc Musnai, professor at the Reform College, friend of Bolyai, and author of a book of poetry with a preface by Bolyai (Szive kiömlése, 1829), with a long passage and signature on front free endleafPoggendorf III 156; not in OCLC. Buchnummer des Verkäufers 3699
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