2440 



Equations, 3rd order, numerical solution. 



Lindman, C. F. Stockh. Ofv. 11 (1854) 333-; 



Grunert Arch. 25 (1855) 290-. 

 , , . Burnier, F. Laus. Bll. S. 



Vd. 10 (1868-70) 591-. 

 , , . Catania, S. Bv. Mt. 5 (1895) 



81-. 

 , , roots as continued fractions. Marcher, 



. Grunert Arch. 39 (1862) 39-. 

 , , x 3 - 2x - 5 = 0, solution to 153 figures. 



Hicks, J. P. [1850] Camb. Ph. S. T. 10 



(1864) 337. 

 below 4th order, numerical solution. Warner, 



J. D. Am. As. P. (1880) 267-. 

 , 4th order, numerical solution. Choquet, C. 



N. A. Mth. 3 (1844) 439. 

 , , . Vidal, V. N. A. Mth. 17 



(1878) 367-. 

 , 5th order, and some others, numerical 



solution. Montucci, H. C. B. 60 (1865) 



440- ; 61 (1865) 31-. 

 Form of roots. Hill, C. J. D. Ups. N. Acta 



S. Sc. 2 (1856) 221-. 

 Four roots of numerical equation, finding. 



Riedl von Leuenstern, J. Tortolini A. 6 



(1855) 481-. 



Graffe's solution. Hansen, H. J. Ts. Mth. 5 



(1887) 169-. 



Horner's method. De Morgan, A. Mathe- 

 matician 3 (1850) 289-. 

 . Matzka, W. [1871] Prag Ab. 5 (1872) 



47pp. 

 , proof. Jenkins, M. Mth. Gz. No. 6 



(1895) 55-. 

 Imaginary roots, determination. Poletti, G. 



[1823-28] Tor. Mm. Ac. 30 (1826) 49- ; 35 



(1831) 77-. 

 , . Bellavitis, G. [1845] Yen. Mm. I. 



3 (1847) 109-. 



, . Buchwaldt, F. Mth. Ts. 2 (1860) 177-. 



, . Bellavitis, G. [1864] (vn) Ven. 



Mm. I. 11 (1862) 461-. 

 , . Yvon-Villarceau, A. J. F. C. B. 



86 (1878) 1427-. 

 , . Farkas, J. C. E. 87 (1878) 791-, 



1027- ; 88 (1879) 273-, 565-. 

 , by recurring series. Frisiani, P. Mil. 



Effern. As. (1850) 3-. 

 Infinite series, solution by. Multedo, . 



Geneva Mm. Ac. 3 (1814) 108-. 

 , . Jacobi, C. G. J. Crelle J. 6 



(1830) 257-. 

 , .' Heegmann, A. [1861-64] (xn) 



Lille S. Mm. 8 (1862) 217- ; 2 (1866) 1-. 

 , . Dietrich, R. Arch. Mth. Ps. 69 



(1883) 337-. 



Integer roots of equation with integral co- 

 efficients. Gerono, G. C. N. A. Mth. 15 



(1856) 449-. 



Lagrange's treatise. Raabe, J. L. Crelle J. 17 



(1837) 94-; 20 (1840) 57-. 

 Logarithmic solution. Garnett, J. Am. Ph. 



S. T. 6 (1809) 391-. 

 . Zenger. C. V. As. Fr. C. E. (1885) 



(Pt. 2) 91-. 

 Method of differences. Matrot, A. [18751 (xn) 



Lille S. Mm. 2 (1876) 7-. 



Numerical solution of equations 2440 



Weddle, T. E. S. P. 4 (1841) 



Method, new. 

 300-. 



, . Lalanne, L. L. C. C. B. 81 (1875) 

 1186-, 1243- ; 82 (1876) 1487-. 



, . Eggers, H. Des Moines Anal. 3 (1876) 

 149-. ' 



Methods, two simple. Giesen, A. Z. Mth. Ps. 



23 (1878) 35-. 

 Newton's method of approximation. Gergonne, 



J. D. Gergonne A. Mth. 20 (1829-30) 196-. 

 ---- . Anne,L. N. A. Mth. 5 (1846) 116-. 

 ---- . Lemonnier, H. N. A. Mth. 1 



(1862) 188-, 243-. 



---- . Genocchi,A. G. Mt. 2 (1864) 27-. 

 ---- . Thomson, F. D. [1864] Mess. 



Mth. 3 (1866) 40-. 

 ---- . Piani, D. Bologna Ac. Sc. Mm. 



6 (1866) 69-. 

 ---- . Darboux, G. N. A. Mth. 8 (1869) 



-- ' -- . Franklin, F. Am. J. Mth. 4 



(1881) 275-. 

 ---- . Fouret, G. N. A. Mth. 9 (1890) 



567-. 



. Berg, F. J. van den. Amst. 

 Ak. Vs. M. 9 (1892) 53-; Fschr. Mth. (1892) 

 103-. 



---- . Malo, E. N. A. Mth. 11 (1892) 



169-. 

 ---- . Tauber, A. Mh. Mth. Ps. 6 



(1895) 291-. 



and that of proportional parts, 

 comparison. Maleyx, L. N. A. Mth. 18 

 (1879) 218-. 



- solution. Baltzer, R. Leip. B. 18 (1866) 358-. 

 Numerical and algebraic solution of equations. 



Anon, (vi 564) Gergonne A. Mth. 20 (1829- 



30) 352-. 



---- . Biasi, G. [1876] Epm. 



Mth. 1 (1877) 315-. 



equation, problem. Koralek, P. N. A. 

 Mth. 13 (1854) 36-. 



equations. Vallas, A. Camb. (M.) Mth. 

 M. 3 (1860) 10-. 



--- . Laguerre, E. C. E. 79 (1874) 996-. 

 -- and analytical geometry in space. Zmurko , 



L. [1869] Wien D. 30 (1870) (2te Ab.) 217-. 

 -- depending on expressions of 1st degree. 



Serdoblnskii, V. E. [1874] (xn) Eec. Mth. 



(Moscou) 7 (1874-75) (Pt. 1) 263-. 

 -- of even degree, analysis, improvement. 



Young, J. R. Ph. Mg. 34 (1849) 413-. 

 -- with given number of imaginary roots, 



determination. Laguerre, E. C. E. 90 (1880) 



180-. 

 . -- having integer roots. Talbot, W. H. F. 



[1875] Edinb. E. S. T. 27 (1876) 303-. 

 -- , higher order, one or more unknowns, 



theorems. Spitzer, S. [1849] Haidinger 



Ab. 3 (1850) (Ab. 2) 143-. 

 -- and quadratic factors. Finck, B. Liouv. 



J. Mth. 10 (1845) 171-. 

 -- , theory. Lepriol, C. J. Eouen Tr. Ac. 



(1812) 41-. 

 -- , . Laguerre, E. C. E. 78 (1874) 



278-; Liouv. J. Mth. 9 (1883) 99-; Acta 



Mth. 4 (1884) 97-. 



176 



