2420 



Reality, multiplicity, separation, of roots 



commensurable roots. 

 N. A. Mth. 18 (1859) 



Limit, superior, of 



Montebello, G. de. 



356-. 

 , , negative roots deduced from Newton's 



formula. Vitasse, . N. A. Mth. 18 (1859) 



213-. 

 , , positive roots. Mourgues, . N. A. 



Mth. 9 (1850) 108-. 

 , , . Gisclard, L. N. A. Mth. 11 



(1852) 107-. 

 , , . Gohierre de Longchamps, . 



N. A. Mth. 19 (1880) 71-. 

 , , in numerical equations. Len- 



theric, . Gergonne A. Mth. 20 (1829-30) 



297-. 

 , , roots, determination. Candeze, G. 



N. A. Mth. 20 (1881) 49-. 

 , , , Laguerre's rule. Candeze, G. 



N. A. Mth. 19 (1880) 307-. 

 , , of numerical equations, Petersen's 



criterion proved erroneous. Giudice, . 



Palermo Cir. Mt. Bd. 6 (1892) 157-. 

 Limits of equations. Piani, D. Bologna N. 



Cm. 3 (1839) 237-. 



to moduli of roots. Dim, U. A. Mt. 1 



(1898) 77-. 



. Petrovitch, M. C. B. 129 



(1899) 583-, 873-. 



of roots. Vene, A. A. Bouen Tr . Ac. (1821) 

 97-; Ferussac Bll. Sc. Mth. 4 (1825) 206-. 



. Tillot, J. N. A. Mth. 4 (1845) 



224-. 

 . Toussaint, . N. A. Mth. 18 (1859) 



310-. 

 . Realis, S. N. A. Mth. 3 (1864) 



477-. 

 . Gyory, S. (xn) Mag. Tud. Ak. 



Ets. 1 (No. 6) (1867) 125-. 

 . Tranton,A. N. A. Mth. 11 (1872) 



254-. 

 . Fouret, . Par. S. Mth. Bll. 20 



(1892) 35-. 

 , Descartes' s theorem applied. Fourier, 



J. B. J. Par. S. Phlm. Bll. (1820) 156-, 181-. 



, and determination of commen- 

 surable roots. Thibault, . N. A. Mth. 

 2 (1843) 517-. 



of equation with only real roots. 



Pleskot, A. Prag Sb. (1897) (Mth.-Nt.) 



No. 37, 9 pp. ; N. A. Mth. 18 (1899) 301- ; 



19 (1900) 144. 

 literal equations. Bouvier, L. C. 



Gergonne A. Mth. 16 (1825-26) 54-. 



numerical equations. Bret, . 



Gergonne A. Mth. 6 (1815-16) 112-. 

 , approximate. Maiziere, 



de. Gergonne A. Mth. 3 (1812-13) 41-. 



of higher order. Row- 

 botham, J. Tilloch Ph. Mg. 63 (1824) 369-. 



, superior, of roots. Rachmanov, P. N. 



Kharkov Mth. S. Com. 4 (1895) 141- ; Fschr. 



Mth. (1893-94) 140. 

 , variation, in algebraic equations. Chevil- 



lard, A. J. N. A. Mth. 2 (1843) 343-. 

 Multiple roots of algebraic equations. Brioschi, 



. C. B. 121 (1895) 582-. 

 , theorem. Sondat, P. N. A. 



Mth. 19 (1900) 25-. 



2420 



Ph. 



N. A. 



Multiple roots, theory. Sylvester, J. J. 



Mg. 18 (1841) 249-. 

 Multiplicity of roots. Beynac, F. A. 



Mth. 9 (1850) 317-. 

 , amount and distribution. Sylvester, 



J. J. Ph. Mg. 18 (1841) 136-. 



in the octavic equation. Alagna, R. 

 Palermo Cir. Mt. Bd. 4 (1890) 287-. 



Nature of roots, Borchardt's proposition. 

 Studnicka, F. J. Casopis 27 (1898) 237-; 

 Fschr. Mth. (1898) 73. 



Newton and Descartes, rule of signs. Orzabal, 

 A. Arg. S. Ci. A. 22 (1886) 39-, 97-. 



Newton-Fourier imaginary problem. Cay ley, 

 A. [1879] Camb. Ph. S. P. 3 (1880) 231-. 



method applied to imaginary roots. Cay- 

 ley, A. QJ. Mth. 16 (1879) 179-. 



Newton's and Laguerre's criteria for positive 

 roots. Venard, C. N. A. Mth. 19 (1880) 



Number of different roots of an algebraic equa- 

 tion. Baur,L. Mth. A. 50 (1898) 241- ; 52 



(1899) 113-. 

 positive and negative roots. Gauss, C. F. 



Crelle J. 3 (1828) 1-. 

 roots between limits. Moigno, F. Liouv. 



J. Mth. 5 (1840) 75-. 

 . Grunert, J. A. Grunert Arch. 



1 (1841) 19-, 126-. 

 . Hermite, C. Crelle J. 52 



(1856) 39-. 

 , logarithmic criteria. Laguerre, 



E. C. B. 93 (1881) 1061-. 

 , theorem. Myasoyedov, A. N. [1882] 



(xn) Bee. Mth. (Moscou) 10 (1882-83) (Pt. 1) 



56. 

 Beal and imaginary roots of equations of 5th 



order, theory. Sylvester, J. J. C. B. 59 



(1864) 749-, 944-; 60 (1865) 759-. 



roots. Bolzano, B. Prag Ab. 5 (1818) 

 60 pp. 



. Terquem, 0. N. A. Mth. 10 (1851) 



180-. 



, absence of. Bellavitis, G. Crelle J. 

 50 (1855) 263-. 



, geometrical investigation of number. 

 Pincherle, S. Bv. Mt. 3 (1893) 54-. 



between given limits. Realis, S. G. Mt. 



9 (1871) 355-. 



, limit. Gohierre de LongcJiamps, . 

 N. A. Mth 18 (1879) 49-. 



, , superior. Paque, A. Liege Mm. S. 



Sc. 10 (1855) 199-. 

 , of number. Olivier, L. Crelle J. 



1 (1826) 223-. 

 , . Sylvester, J. J. C. B. 60 



(1865) 1261-. 



, in a class of equations. Syl- 

 vester, J. J. C. B. 58 (1864) 494-. 



, limits, method of finding. Sylvester, 



J. J. N. A. Mth. 12 (1853) 329-. 



, , theorem. Sylvester, J. J. N. A. 



Mth. 12 (1853) 286-. 



, number. Cauchy, A. L. [1813] Par. 



S. Phlm. Bll. (1814) 95- ; Par. EC. Pol. J. 10 

 (1815) (17 e cah.) 457-. 



, between limits. Bonnet, 0. N. A. 



Mth. 6 (1847) 464-. 



166 



