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Vollständige Anleitung zur Algebra.St. Petersburg: Kaiserliche Academie der Wissenschaften, 1770.
First edition of Euler's great textbook of algebra in its language of composition, preceded only by an extremely rare Russian translation published in 1768-9 by two of his students. "Euler's Vollständige Anleitung zur Algebra is not only the most popular textbook on elementary algebra, with the exception of Euclid's Elements it is the most widely printed book on mathematics." (Truesdell). It "was translated into Russian (1768-9), Dutch (1773), French (1774), Latin (1790), English (1797, 1822) and Greek (1800). The popular German edition from Reclam Verlag sold no less than 108,000 copies between 1883 and 1943 (Reich, 1992). After 240 years this algebra textbook is still in print today, available in several languages and editions" (Heeffer).

"In 1770 Euler published his 'Vollständige Anleitung zur Algebra'... The first volume treats of determinate algebra. This contains one of the earliest attempts to place the fundamental processes on a scientific basis: the same subject had attracted D'Alembert's attention. This work also includes the proof of the binomial theorem for an unrestricted real index which is still known by Euler's name ... The second volume of the algebra treats of indeterminate or Diophantine algebra. This contains the solutions of some of the problems proposed by Fermat, and which had hitherto remained unsolved." (Ball).

"Euler proved the impossibility of solving x3+y3=z3 in which x, y, and z are integers, xyz ?0 (a particular case of Fermat's last theorem); his demonstration, based on the method of infinite descent and using complex numbers of the form a+b(-3)<½> , is thoroughly described in his Vollständige Anleitung zur Algebra, the second volume of which has a large section devoted to Diophantine analysis." (DSB).

Euler composed his famous 'Algebra' in German in 1765-6, soon after his return to St Petersburg from Berlin. He was by then partially blind, and dictated the work to a young valet. Publication of the original German version (as offered here) was, however, delayed until 1770 and thus came to be preceded by a Russian translation by his students Peter Inokhodtsev and Ivan Yudin which was issued in 1768-9. This Russian translation is practically unobtainable; OCLC locates just one copy worldwide. The offered original German edition is also very rare with just two copies being auctioned in the past fifty years (Norman 1998 & Honeyman 1979).

Norman 735; Honeyman 1075; Eneström 387 & 388; Truesdell, Leonard Euler: Supreme Geometer, 1972; Albrecht Heeffer, The Rhetoric of Problems in Algebra Textbooks from Pacioli to Euler, pp.4-5; Ball, A Short Account of the History of Mathematics, p.397. A very fine copy.. 2 volumes, 8vo (194 x 122 mm), bound in two, fine contemporary German calf with raised bands and spine labels (capital of second volume with a little shipping and upper part of front hinge slightly cracked, but still fine and completely unrepaired), pp. [16] [1-3] 4-356; [2] [1-3] 4-532 [2:errata]. Fine and clean, a very nice set

      [Bookseller: Sophia Rare Books]
Last Found On: 2013-12-05           Check availability:      Antikvariat    

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