2460 Simultaneous equations 



Equations with 2 variables, systems of 2. 



Sivering, J. N. A. Mth. 2 (1863) 372-. 

 3 variables, 



x+y+z=A; axy + fixz + yyz = B ; xyz = C, 



solution. Tortolini,B. (vm) A. Mt. 4 (1861) 



202- . 

 , solution of 3, at least two being 



linear. Grunert, J. A. Grunert Arch. 37 



(1861) 422-. 



n variables, system. Mollame, V. 

 Catania Ac. Gioen. At. 18 (1885) 53-. 



, theorems. Pliicker, J. Crelle J. 



16 (1837) 47-. 

 several variables. Liouville, J. Liouv. 



J. Mth. 12 (1847) 68-. 

 . Betti, E. [1857] Tortolini A. 



1 (1858) 1-. 

 , solution. Laurent, H. C. B. 



67 (1868) 491-. 

 , . Enriques, F. Mth. A. 51 



(1899) 134-. 

 , of a class. Drot, . N. A. 



Mth. 5 (1846) 389-. 



ax + by + cz = 0, a^xy + b$z + c^zx = 0, 

 solution. Grunert, J. A. Grunert Arch. 

 28 (1857) 110-. 



x 3 + y' t = a, x*y+xy* = b, solution. Strehlke, 

 F. Arch. Mth. Ps. 48 (1868) 1-. 



Euler's equation, solution. Gylden, H. St 



Pet. Ac. Sc. Bll. 10 (1866) 59-. 

 Homogeneous equations with 2 variables. 



Kaiser, H. Grunert Arch. 25 (1855) 76-. 



linear equations, system important in differ- 

 ential equations. Heffter, L. Crelle J. Mth 

 111 (1893) 59-. 



simultaneous equations. Catalan, E. C. A. 

 Mt. 7 (1865) 66-. 



, Catalan's memoir. Tortolini, B. A. 



Mt. 7 (1865) 70-. 

 Implicit equations with 2 variables, x and y, to 



express y in terms of x. Schubert, F. T. 



[1823] St Pet. Ac. Sc. Mm. 11 (1830) 138-. 



functions denned by infinite number of 

 simultaneous equations. Koch, H. von. Par. 

 S. Mth. Bll. 27 (1899) 215-. 



Lagrange and Newton's method of greatest and 

 least coefficients extended to 2 equations. 

 Nasimow, P. S. Fschr. Mth. (1898) 365. 



Lagrange's method of multipliers. Rutherford, 

 W. Mathematician 1 (1845) 32-. 



Line construction for solution of system of 

 linear equations, regarded as a configuration. 

 Berg. F. J. van den. Amst. Ak. Vs. M. 5 

 (1889) 267- ; Fschr. Mth. (1888) 76. 



LINEAE EQUATIONS. 



Valat, . Bordeaux Act. Ac. Sc. (1846) 1-. 



Lebon, J. N. N. A. Mth. 8 (1849) 59-. 



Biehler, C. N. A. Mth. 19 (1880) 31 1-, 356-. 



Rouche', E. Par. EC. Pol. J. 29 (= Cah. 48) 

 (1880) 221-. 



Meyer, A. N. Ts. Mth. 5 (B) (1894) 4-; Fschr. 

 Mth. (1893-94) 163-. 



Bez's method. Jakimov, V. P. Kazan S. Nt. 

 (Ps.-Mth.) P. 5 (1887) 2-. 



. Poreckij, P. S. Kazan S. Nt. (Ps.- 

 Mth.) P. 5 (1887) 3-. 



Linear equations 2460 



class. Liouville, J. Liouv. J. Mth. 11 

 (1846) 466-. 



(Chelini). Terquem, 0. N. A. Mth. 6 (1847) 

 129-. 



, solution. Terquem, 0. N. A. Mth. 5 



(1846) 67-, 162-. 



compatibility of a system. Capelli, A. Kv. Mt. 



2 (1892) 54-. 



discussion. Rouche, E. C. E. 81 (1875) 1050-. 

 formula for values of variables. Molins, H. 



Liouv. J. Mth. 4 (1839) 508-. 

 . Chelini, D. G. Arcad. 85 



(1840) 3-. 

 graphic solution. Ise, E. G. Mt. 14 (1876) 



180-. 

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



Ak. Vs. M. 4 (1888) 196- ; Fschr. Mth. (1887) 



89-. 

 . Klingatsch, A. Mh. Mth. Ps. 3 



(1892) 169-. 



. Griend, J. van der (jun.). N. 

 Arch. Wisk. 4 (1899) 22-; Fschr. Mth. 

 (1899) 108. 



. Vaes, F. J. N. Arch. Wisk. 



4 (1899) 42-; N. A. Mth. 18 (1899) 74-. 

 of two. Crocchi, L. [1876] G. Mt. 



15 (1877) 86-. 

 when indeterminate. Suremain-de-Missery, A. 



Gergonne A. Mth. 1 (1810-11) 204-. 

 variables expressed as multiple integrals. 



Jacobi, C. G. J. Crelle J. 14 (1835) 51-. 

 peculiar set. Muir, T. [1900] Edinb. K. S. 



P. 23 (1902) 248-. 



, Muir's paper. Tweedie, C. [1900] 

 Edinb. B. S. P. 23 (1902) 261-. 



problem. Gauss, C. F. N, A. Mth. 10 (1851) 



359-. 

 with real coefficients. Gordan, P. Mth. A. 6 



(1873) 23-. 

 solution. Grunert, J. A. Grunert Arch. 10 



(1847) 284-. 



. Prediger, C. Arch. Mth. Ps. 70 (1884) 



319-. 

 . Veltmann, W. Z. Mth. Ps. 31 



257-, 384. 

 , method and application to determinants. 



Clasen, (I'abbe) B. I. Brux. S. Sc. A. 12 



(1888) (Pt. 2) 251-. 

 system. Painvin, L. Liouv. J. Mth. 3 (1858) 



. Versluys, J. Arch. Mth. Ps. 52 (1871) 



257-. 

 , general solution. Hansen, P. A. Leip. B. 



1 (1846-47) 333-; Leip. Ab. Mth. Ps. 1 (1852) 



83-. 



of infinite number, solution. Kotteritzsch, 

 T. Z. Mth. Ps. 15 (1870) 1-, 229-. 



, solution. Ettingshausen, A von. Baum- 



gartner Z. 5 (1829) 209-. 

 , . Farkas, J. C. B. 87 (1878) 523-. 

 , standard solutions. Cayley, A. QJ. Mth. 



19 (1883) 38-. 

 systems, a geometric interpretation. Nicoli, F. 



Mod. Ac. Sc. Mm. 16 (1875) 141-. 

 , solution by roots of unity. Cauchy, A. L. 



C. B. 25 (1847) 285-. 

 theory. Lichtenfels, V. (Frhr.) von. Wien 



SB. 12 (1854) (Ab. 2) 935-. 



185 



