2410 



Algebraic Equations 



2410 Elements of the theory of 

 algebraic equations; existence 

 of roots, symmetric functions; 

 rational fractions; partial frac- 

 tions. 



Algebra, fundamental theorem, proof. Mertens, 



F. Wien Ak. Sb. 97 (1889) (Ab. 2 a) 1505-. 

 , , and solution of equations by square 



roots. Vahlen, K. T. Acta Mth. 21 (1897) 



287-. 

 Algebraic equation, roots of derivative. Berloty, 



. C. E. 99 (1884) 745-, 832. 

 , . Cayley,A. C. R. 110 (1890) 



174-, 215-. 



equations, a law of inertia for. Meyer, F. 

 Gott. Nr. (1891) 279-. 



Cauchy's theorem. Zbikovskij, A. K. Kazan 



S. Nt. (Ps.-Mth.) P. 6 (1888) 240-. 

 Coefficients in expansions invol /ing symmetric 



expressions. Anglin, A. H. Liouv. J. Mth. 



2 (1886) 139-. 

 expressed as functions of sums of like powers 



of roots. Janni, V. Nap. Ed. 18 (1879) 



199-. 



and sums of powers of roots, relations 

 between. Cauchy, A. L. C. E. 12 (1841) 

 698-, 813- . 



Decomposition of certain expressions into 2 

 squares. Realis, S. N. A. Mth. 4 (1865) 

 451-. 



Development of an algebraic fraction. Mac- 

 Mahon, P. A. Am. J. Mth. 6 (1884) 287-. 



Diaphoric functions. Tanner, H. W. L. Mth. 

 Gz. 1 (1900) 152- . 



(Tanner). Genese, E. W. Mth. Gz. 1 



(1900) 184. 



Differences of roots, analytic use. Minich, S. E. 

 [1875] Em. E. Ac. Line. At. 3 (1876) (Pt. 2) 

 303. 



Differential equations in theory of asym- 

 metric algebra. Forsyth, A. E. Camb. Ph. 

 S. T. 16 (1898) 291-. 



Discriminant of cubic equation and quadratic 

 expression Q 2 - 3PP', relation. Young, J. E. 

 [1876] Ir. Ac. P. 2 (1875-77) 744-. 



Equation of differences. Cayley, A, Tortolini 

 A. 2 (1859) 365-; Phil. Trans. (1860) 93-. 



7ith order, and system of n equations 



satisfied by roots. Antaev, S. N. [1897-1900] 

 Eec. Mth. (Moscou) 20 (1899) 33-; 21 (1901) 

 1-; Fschr. Mth. (1897) 92; (1900) 94. 



for product of differences of (all but one) 

 roots of an equation. Cayley, A. Phil. 

 Trans. (1861) 45-. 



of quotients of roots. Terquem, O. N. A. 

 Mth. 4 (1845) 516-. 



with roots in arithmetical progression. 

 Viaggi, F. G. Mt. 15 (1877) 376-. 



roots of which are diminished by p, re- 

 lations between coefficients. Lobatto, E. 

 Amst. Vs. Ak. 4 (1856) 208-. 



, similar functions of roots. Kronecker, L. 

 Liouv. J. Mth. 19 (1854) 279-. 



2410 



Equation of squares of differences. Desmarcst, 



E. N. A. Mth. 1 (1842) 169-. 

 . Tarnier, . N. A. Mth. 3 



(1844) 410-. 

 . Pegado, M. Lisb. A. 2 (1858) 



19-. 



, progressive development. 

 Minich, S. E. Yen. At. (1858-59) 343-. 



of roots, existence of relation 



among coefficients. Ellis, E. L. (\iAdds.) 

 Gamb. Mth. J. 1 (1839) 256-. 



, and geometrical applica- 

 tion to tangents to a curve from one point. 

 Joachimsthal, F. N. A. Mth. 9 (1850) 

 98-. 



sums of roots taken 2 together. Gerono, 



G. C. N. A. Mth. 2 (1843) 128-. 



with 2 roots rationally expressible in terms 

 of others (Brioschi). Genocchi, A. N. A. 

 Mth. 16 (1857) 95-. 



Equations with equal differences of roots. 



Gatti, S. [1876] G. Mt. 15 (1877) 28-. 

 . Viaggi, F. G. Mt. 15 



(1877) 376-. 

 , formulae in theory. Sharp, W. J. C. Mess. 



Mth. 9 (1880) 188-. 

 , irreducible, relations of roots. Schane- 



mann, T. [1852] Wien D. 5 (1853) 143-. 

 , , (Schonemann) . Ettingshausen, 



A. von. Wien SB. 8 (1852) 442-. 

 , proof that roots have form p + q>J-I. 



Crelle, A. L. Berl. Ab. (1829) 1-. 

 , resolvability into factors of 1st or 2nd 



degree, Laplace's proof, etc. Hube, K. (vi 



Adds.) Krk. Eoczn. Uniwers. 3 (1818) 92-. 



with roots expressible as linear functions of 

 one root. Pellet, A. E. Bll. Sc. Mth. As. 

 4 (1880) (Pt. 1) 262-. 



in geometrical progression. Terquem, 



O. N. A. Mth. 5 (1846) 210-. 

 progression. Guilmin, A. N. A. 



Mth. 8 (1849) 242-. 

 ; theorem that complex roots occur in pairs, 



Gauss's proof. Combette, E. (xn) Brest S. 



Ac. Bll. 7 (1871) 28 (bis)-. 

 , theory. Gauss, C. F. Gott. Ab. 4 (1848- 



50) 3-. 

 , , fundamental principle. Du Bourguet, 



. Gergonne A. Mth. 2 (1811-12) 338-. 

 , , . Bret, . Gergonne A. Mth. 



3 (1812-13) 31-. 

 , , . Du Bourguet, . Gergonne 



A. Mth. 3 (1812-13) 94-. 

 , , . Bret, -. Gergonne A. Mth. 



3 (1812-13) 369-. 



, , . Encontre, D. Gergonne A. Mth. 



4 (1813-14) 201-. 



, , . Liouville, J. Liouv. J. Mth. 4 



(1839) 501- ; 5 (1840)31-. 

 , , . Woodtouse, L. G. Teix. J. Sc. 



6 (1885) 177-. 

 , , theorem. Hocks, H. Z. Mth. Ps. 



28 (1883) 123-. 

 , , , Cauchy's. Eudio, F. Ziir. 



Vjschr. 39 (1894) 345-. 

 , , , Mourey's proof. Grunert, J. A. 



Grunert Arch. 1 (1841) 81-. 



158 



