Collection of 4 Memoirs: 1. De formatione et proprietatibus Determinantium. 2. De determinantibus functionalibus. 3. De functionibus alternantibus earumque divisione per productum e differentiis elementorum conflatum. - 4. Zum combinatorischen Analysis. - [INTRODUCING "DETERMINANTS" AND "JACOBIANS"]

1841. Berlin, G. Reimer, 1841. 4to. Without wrappers as Heft 4 in "Journal für die reine und angewandte Mathematik. Hrsg. von A.L. Crelle", Bd. 22, heft 4. Titlepage to Heft 4. and pp. 285-380 +(2) pp. and 1 engraved plate. Jacobis papers: 1. pp. 285-318, 2. pp. 319,359, 3. pp. 360-371 and 4. pp. 372-374. First printing of 2 importent and influential papers by Jacobi. In 1841 "Carl Jacobi (1804-1851) develops the theory of determinants, including mention of the "functional determinant" or "Jacobian" in his paper "De formatione et proprietatibus Determinantium" (the first paper offered here). Later in the same year hepublishes a further development specifically of the theory of acobians in the memoir "De determinantibus functionalibus" (the second paper offered here). He shows for instance,that the Jacobian of a set of n functions in n variables is identically zero if and only if the functions are mutually dependent. Although functional determinants had been used earlier, they are later named after Jacobi due to his extensive development of their properties." (Claire L. Parkinson in Breakthroughs).