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Carl Gustav Jacob JACOBI (1804 - 1851)  Auf Merkliste setzen

Canon arithmeticus, sive Tabulae quibus exhibentur pro singulis numeris primis vel primorum potestatibus infra 1000 numeri ad datos indices et indices ad datos numeros pertinentes. Berolini, typis academicis, 1839. 4to, XL, 248 pp.; sign.: a-e4, 1-314. Original bluette wrappers, Handwritten title-piece on spine. Well-preserved copy on large paper.

First, scarce edition of this important work on primitive roots. For each prime (p) and power of a prime less than 1.000 the Canon gives two companion tables showing the numbers with given indexes and the index of each given number. In other words, Jacobi’s tables give numbers (residues) x for given indices i, and vice versa, when x and i are connected by the binomial congruence gi – x ≡ 0 (mod p), for each of the odd primes p less than 1.000. Most of the research and accomplishments of Carl Jacobi - among the greatest mathematicians of the first half of the 19th century - are characterized by linkage of different mathematical disciplines. He introduced elliptic functions into both number theory and theory of integration, which in turn is connected with the theory of differential equations where, among other things, the principle of the last multiplier is due to him. Most of his investigations on first-order partial differential equations and analytical mechanics were published posthumously. Taking the research of William Rowan Hamilton (1805 - 1865) on the differential equations of motion (canonical equations) as a starting point, Jacobi also carried on the work of the French school. He sought the most general substitutions that would transform canonical differential equations into such equations. The transformations are to be such that a canonical differential equation (of motion) is transformed into another differential equation which is again canonical. He also developed a new theory for the integration of these equations, utilizing their relation to a special Hamiltonian differential equation. This method enabled him to solve several very important problems in mechanics and astronomy. In some special cases Alfred Clebsch (1833 - 1872), editor of his posthumous works, later improved Jacobi’s results, and decades later Hermann von Helmholtz (1821 - 1894) carried Jacobi’s mechanical principles over into physics in general. REF.: POGGENDORFF I, 1178; OCLC 457408764 (Seller ref. MC0221)

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Sachgebiete: Erstausgaben, Mathematik

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