Farkas Bolyai, 1843

[BOLYAI, Farkas (1775-1856)]. A’ Marosvasarhelyt 1829-be nyomtatott Arithemetika Elejének részint röviditett, reszint bovitett, általán jobbitott, ‘s tisztáltabb kiadása. Maros Vásárhely [present-day Târgu Mureș, Romania], Kali Simon, 1843.

First edition of Bolyai’s work on the foundations of mathematics. This work extends Bolyai’s investigations into the principles of mathematics, based on both the author’s Az arithmethica eleje published in 1830 and on the second volume (the first volume being on geometry) of his magnum opus, the Tentamen juventutem studiosam elementa matheseos purae, 1832-1833. Farkas Bolyai (1775-1856) was a close friend of Gauss and was 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. The first editions of the works of either father or son are both very rare. Nagy, Ferenc, Bolyai: biographia, biblioteka, bibliografia, p 355.

Octavo (200 x 117mm). With two folding lithographed plates on blue paper, one with 12 folding slips and with grey and pink wash coloring (some very occasional mild foxing, including to title; a little contemporary underlining and marginalia, mostly in pencil). Modern half calf over marbled boards.