2420 



Reality, multiplicity, separation, of roots 



Separation of roots by method of differences. 



Desboves, A. H. N. A. Mth. 13 (1854) 



60-. 

 . Capelli, A. Nap. Ed. 



33 (1894) 191-, 214-. 



, method, and Lagrange's formula. 

 Pellet, A. E. Bll. Sc. Mth. As. 5 (1881) 

 (Pt. 1) 393-. 



of numerical equations. Zinna, A. 



G. Mt. 6 (1868) 344-. 

 . Laguerre, E. C. E. 89 



(1879) 635- ; 92 (1881) 1146-. 

 some equations. Markov, A. A. 



Kharkov Mth. S. Com. (1885) 89- ; Fschr. 



Mth. (1886) 161. 

 , and superior limit. Laguerre, E. 



N. A. Mth. 19 (1880) 49-, 97-. 

 Signs and nature of roots. Anon, (vi 537) 



Gergonne A. Mth. 10 (1819-20) 341-. 

 Sturmians, class of. Chrystal, G. [1881] 



Edinb. E. S. T. 30 (1883) 161-. 

 Sturm's functions. Cayley, A. Liouv. J. 



Mth. 11 (1846) 297- ; 13 (1848) 269-. 



. Brioschi, F. N. A. Mth, 13 (1854) 71-. 



. Gilbert, P. Liouv. J. Mth. 12 (1867) 



-87-. 



. Brioschi, F. C. E. 68 (1869) 1318-. 



-T- . Kronecker, L. Berl. Ak. Mb. (1878) 



95-. 

 , auxiliary, relation to roots of an equation. 



Sylvester, J.J. B. A. Ep. (1841) (pt. 2) 23-. 



, calculation by determinants. Lemonnier, 

 H. C. E. 80 (1875) 252-. 



, coefficients expressed as determinants. 



Heal, W. E. A. Mth. 2 (1885-86) 85-. 

 , determination of a series from a single 



determinant. Vleck, E. B. van. [1899] 



A. Mth. 1 (1900) 1-. 



, formulae for equations of 2nd, 3rd, 

 and 4th orders. Koralek, P. N. A. Mth. 

 11 (1852) 333-. 



, functions analagous to. Lemonnier, H. 



Par. S. Mth. Bll. 6 (1878) 149-. 

 , . Miasojedov, A. N. 



Eec. Mth. (Moscou) 12 (1885) 461- ; 



Mth. (1885) 63-. 

 and their reciprocal relations. Kronecker, 



L. Berl. Mb. (1873) 117-. 

 of 2nd species. Wendlandt, H. Arch. 



Mth. Ps. 62 (1878) 1-. 

 , series of. Gegenbauer, L. Amst. Ak. 



Vs. 5 (1897) 185-. 

 , . Vries, J. de. N. Arch. Wisk. 



3 (1898) 40-. ' 

 , substitutes for. Mollanie, V. Nap. Ed. 



22 (1883) 256-. 

 , Sylvester's theorem on. Sturm, J. C. F. 



Liouv. J. Mth. 7 (1842) 356-. 

 , . Turazza, D. Yen. At. 11 



(1865-66) 419-. 

 and syzygies between rational integral 



functions. Sylvester, J. J. Phil. Trans. 



(1853) 407-. 

 , tables for equations of 2nd, 3rd, 4th, and 



5th orders. Cayley, A. Phil. Trans. (1857) 



733-. 

 , theorem of Cayley's, proof. Zeipel, E. 



V. von. QJ. Mth. 3 (1860) 108-. 



2420 



N. 



Sturm's method, application. Biehler, C. 

 A. Mth. 19 (1880) 76- ; 6 (1887) 421-. 



of finding real roots, expressions for 



?uotients in. Sylvester, J. J. B. A. Ep. 

 L853) (pt. 2) 1-. 



separation of roots, modification. 

 Nazimov, P. [1885] Eec. Mth. (Moscou) 

 13 (1886) 119- ; Fschr. Mth. (1886) 71-. 



quotients, explicit values. Sylvester, J. J. 

 Ph. Mg. 6 (1853) 293-. 



remainders. Heilermann, . Crelle J. 43 

 (1852) 43- ; 48 (1854) 190-. 



. Faa de Bruno, F. Tortolini A. 7 



(1856) 313-. 



series. Gegenbauer, L. Wien Ak. Sb. 81 



(1880) (Ab. 2) 576-. 



theorem. Terquem, 0. N. A. Mth. 2 

 (1843) 97-. 



. Badon-Ghijben, J. (vn) Amst. N. 

 Ws. Ntk. Vh. 1 (1844) 89-. 



. Mourgues, . N. A. Mth. 9 (1850) 



278-. 

 . Borchardt, C. W. N. A. Mth. 11 



(1852) 403-. 



. Hermite, C. C. E. 36 (1853) 294-. 



. Bertrand, J. C. E. 43 (1856) 1108-. 



. Kronecker, L. C. E. 68 (1869) 1078-. 



. Hattendorff, K. Gott. Nr. (1873) 779-. 



. Darboux, G. Bll. Sc. Mth. As. 8 



(1875) 56-, 92-. 

 . Janni, V. G. Mt. 20 (1882) 166-. 



. Nieivenglowski, B. N. A. Mth. 9 



(1890) 181-. 



. Willotte, H. Toul. Ac. Sc. Mm. 3 



(1891) 44-. 



, application. Spiller, . Mth. Misc. 2 



(1839) 133-. 

 , . Candioti, M. R. Arg. S. Ci. A. 27 



(1889) 201- . 



, to transformations of binomial 

 equations. Sturm, J. C. F. Liouv. J. Mth. 

 7 (1842) 132-. 



, determination of X n . Young, J. R. Ph. 



Mg. 7 (1835) 454-. 

 , extension. Phragmgn, E. C. E. 114 



(1892) 205-, 440. 



, to system of equations. Bendixson, I. 



[1892] Stockh. Ak. Hndl. Bh. 18 (Afd. 1) 



(1893) No. 2, 18 pp. 



and limits of roots of equation. Sylvester, 



J. J. Ph. Mg. 5 (1853) 446- ; 6 (1853) 14-, 



138-, 210-. 

 , Ostrogradski's. Desboves, A. H. N. 



A. Mth. 6 (1867) 348-. 

 , proof. Ettingshausen, A. von. Baum- 



gartner Z. 7 (1830) 444-. 



, . Trudi , N. G. Mt. 1 (1863) 59-. 



, remarks. Candeze, G. N. A. Mth. 20 



(1881) 193-. 



, simplification of calculations. Housel, 



. N. A. Mth. 6 (1867) 351-. 



theorems of comparison. BocJier, M. N. 

 Y. Am. Mth. S. T. 1 (1900) 414-. 



Variations, number gained or lost in multiplica- 

 tion of f(x) by x n a. Andre, D. C. E. 99 

 (1884) 182-. 



, in multiplication by x - a. Andrt, D. 



C. B. 98 (1884) 292-. 



168 



