Marosvasarhely: Kali Simon, 1843. First edition.
An exceptionally fine copy, in the original boards, of Bolyai’s work on the foundations of mathematics, and the last of the great works of Farkas Bolyai. It is in part based on 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, 1832-33, to which it frequently refers. This work enlarges and extends Bolyai’s investigations into the principles of mathematics. 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.
The text refers frequently to Gauss and Lagrange, along with other mathematicians such as Maclaurin and Taylor.
Bolyai began this work in 1829 but only a short introduction and an excerpt were printed (in 1830) because he was under pressure with preparing for publication the Tentamen. At the time when this work was published, Bolyai was in despair as neither his son Janos nor he himself had received any recognition. He desperately wrote to Gauss (January 18th, 1848): ‘Some years ago I have published another attempt [the present work] in Hungarian but without any results - Mathematics does not grow in this “China”.’ Only one more letter to Gauss followed (February 6th 1853) before Bolyai’s death in 1856.
8vo (207x123 mm), pp. xliv, 386, with two folding lithographed plates on blue paper, one with six folding slips with grey and pink wash colouring; some very occasional and light foxing, a very fine copy, entirely unrestored in original blue boards with paper label to spine. Very rare.