2450 General resolution 



Solution, transcendental and algebraic. 

 Cockle, Jas. Ph. Mg. 21 (1861) 379-; 23 

 (1862) 135-. 



by transcendents. Pievani, (Dr) A. (vni) 

 A. Mt. 5 (1863) 57[61]-. 



Symmetric products involving prime roots of 

 unity. Forsyth, A. E. Mess. Mth. 14 

 (1885) 40-. 



, method. Cockle, Jas. Ph. Mg. 4 (1852) 



492-; 5 (1853) 170- ; 7 (1854) 130-. 



, , application to algebraic solution. 

 Harley, R. Manch. Ph. S. Mm. 15 (1860) 

 172- ; Phil. Trans. (1861) 327-. 



Theory of Lagrange and Vandermonde. Minich, 

 S. E. Ven. At. (1858-59) 19-. 



Transformation, Bring-Tschirnhausen. Sylves- 

 ter, J. J. Crelle J. Mth. 100 (1887) 465-. 



of equations. Jerrard, G. B. Ph. Mg. 7 

 (1835) 478-. 



. Cockle, Jas. Ph. Mg. 26 (1845) 



383-; Mathematician 1 (1845) 82-, 113-, 



194-, 297- ; 3 (1850) 178-. 

 . Jerrard, G. B. Ph. Mg. 5 (1853) 



354-, 493-. 

 . Brioschi, F. Mil. At. I. Lomb. 1 



(1858) 231-. 

 . Bring, E. S. Arch. Mth. Ps. 41 



(1864) 105-. 

 . Biehler, C. N. A. Mth. 3 (1884) 



209-. 

 . Brioschi, F. Mil. I. Lomb. Bd. 20 



(1887) 364-; L. Mth. S. P. 20 (1889) 127- ; 



C. E. 124 (1897) 661-. 

 , limits of method. Cockle, Jas. Ph. 



Mg. 29 (1846) 181- ; 30 (1847) 29-. 

 , principles of theory. Brioschi, F. 



A. Mt. 16 (1888-89) 329-. 

 , theorem (Hermite). Combescure, E. 



C. E. 64 (1867) 174-. 



and finding roots, firing's method. Tegman, 

 P. Stockh. Ak. Hndl. 22 (1801) 228-. 



lowering. Prouhet, E. N. A. Mth. 



3 (1864) 122-, 433-, 508-. 

 Tschirnhausen's coefficients, property. Bour- 



ndz, J. Orv. Termt. Ets. (Termt. Szak) 



(1898) 167-. 



and Jerrard's transformations. Grunert, 

 J. A. Grunert Arch. 40 (1863) 214-. 



transformation. Cayley, A. [1861-65] 

 Phil. Trans. 152 (1862) 561- ; 156 (1866) 97-. 



, coefficients, extension to quintic. Lava- 



gna, G. M. Tortolini A. 1 (1858) 238-. 



, equations invariant under. La Motte, 



F. A. [1900] N. Y. Am. Mth. S. Bll. 7 

 (1901) 244, 250-. 



, J. Hammond's series of numbers con- 

 nected with. Sylvester, J. J C. E. 104 

 (1887) 1228-. 



Uni-serial Abelian equations. Young, G. P. 

 Am. J. Mth. 9 (1887) 225-. 



Wronski's formulae for general solution. 

 Tor-riant, J. E. Lisb. Ac. Sc. Mm. 6 (1819) 

 33. 



method for general solution. Gergonne, J. D. 

 Gergonne A. Mth. 3 (1812-13) 51-, 206- ; 

 9 (1818-19) 213-. 



. Euffini, P. [1816] Mod. S. 



It. Mm. 18 (1818) 56-. 



Simultaneous equations 2460 



2460 Simultaneous equations; 

 including linear equations. 



Algebraic systems and their relations to systems 



of partial differential equations. Delassus, 



E. C. E. 123 (1896) 546-. 

 Approximate determination of roots of several 



equations. Biermann, 0. Mh. Mth. Ps. 11 



(1900) 148-. 

 Common solutions of simultaneous equations, 



number. Mantel, W. N. Arch. Wisk. 16 



(1889)203-; Fschr. Mth. (1889) 132. 

 zero values of 2 algebraic equations, mode of 



representing. Zaiuski, J. Prace Mt.-Fiz. 



8 (1897) 129- ; Fschr. Mth. (1897) 118. 

 Conditions of co-existence of equations, order. 



Roberts, S. Crelle J. 67 (1867) 266-; L. 



Mth. S. P. 6 (1874-75) 101-. 

 Dependence of equations. Borden, J. Camb. 



(M.) Mth. M. 3 (1860) 7-. 

 Equation, 2nd order, general, with 2 variables. 



Eodrigues, A. N. A. Mth. 4 (1845) 24-. 

 , , , . Grunert, J. A. Gru- 

 nert Arch. 25 (1855) 146-. 

 , , numerical, with 2 variables, reduction. 



Lentheric, . Mntp. Ac. Sc. Mm. 4 (1858- 



60)46-. 

 , 4th order, with 2 variables, factorisation. 



Janni, V. G. Mt. 7 (1869) 28. 

 , , 4 variables, solution. Le Besgue, 



V.A. C. E. 59 (1864) 1067-. 

 , mth order, with n variables. Gergonne, 



J. D. Gergonne A. Mth. 4 (1813-14) 115-. 

 Equations, 2nd order, condition for a common 



root of 2. Gelin, E. Mathesis 13 (1893) 



265-. 

 , , numerical solution of 2. Transon, 



A. (Prof.) N. A. Mth. 19 (1860) 414-. 

 , , in x, y, z, solution of 3. Lemannier, 



H. [1878] Par. S. Mth. Bll. 7 (1879) 16-. 

 , with 2 variables. Bret, . Gergonne 



A. Mth. 2 (1811-12) 218-. 

 , , resolution into 2 linear factors. 



Albitzky, W. J. Fschr. Mth. (1890) 111. 

 , , solution. Anne, L. N. A. 



Mth. 2 (1843) 195-. 

 , , . Unferdinger, F. Arch. 



Mth. Ps. 49 (1869) 474-. 

 , or 3 variables. Lemonnier, H. 



N. A. Mth. 3 (1864) 518- ; 4 (1865) 5-. 

 , 3rd order, 2, question. Roberts, M. N. A. 



Mth. 15 (1856) 76-; 16 (1857) 366-. 

 , higher order, graphic solution. Spitzer, S. 



[1850] Haidinger Ab. 4 (1851) (Ab. 3) 1-. 

 with 2 variables. Piani, D. Bologna Ed. 



(1854-55) 33-. 

 < , approximate solution of 2. 



Grunert, J. A. Grunert Arch. 20 (1853) 337-. 

 , numerical solution of 2. Zimmer- 



mann, H. Z. Mth. Ps. 20 (1875) 71-. 

 , solution of 2. Lefebure de Fourcy, 



L. Par. EC. Pol. Cor. 2 (1809-13) 276-. 

 , . Bonnet, O. N. A. Mth. 



6 (1847) 54-, 135-, 243-, 375-. 

 , system of 2, theorems. Jacobi, 



C. G. J. Crelle J. 14 (1835) 281-. 



184 



