2470 Transcendental equations 



System of equations, one quadratic, the rest 



linear, solution. Baur, C. W. [1868] Z. 



Mth. Ps. 14 (1869) 129-, 426-. 

 , , , . Versluys, J. 



Arch. Mth. Ps. 60 (1877) 128-. 

 , , , . Nanson, E. J. 



Mess. Mth. 28 (1899) 107-. 

 ,2 quadratic, the rest linear, solution. 



Gundelfinger, S. Z. Mth. Ps. 18 (1873) 



543-. 

 , solution. Sylvester, J. J. Ph. Mg. 



37 (1850) 370-. 

 , . Scheibner, W. Leip. B. 8 (1856) 



65-. 



n equations with n variables, number 

 of solutions. Fouret, G. Par. S. Mth. Bll. 

 2 (1874) 127-. 



linear equations, graphic solution. 

 Fouret, G. Par. S. Mth. Bll. 3 (1875) 93- ; 

 As. Fr. C. E. 4 (1875) 154-. 



with n variables. Valeriani, V. 



G. Mt. 9 (1871) 371-. 

 , theorem. Fontene, G. 



N. A. Mth. 14 (1875) 481-. 

 relations between 2 systems of n 



quantities. Fontene, G. N. A. Mth. 17 



(1898) 317-. 

 2n equations with 2n variables occurring 



in mechanics. Bonolis, A. G. Mt. 11 (1873) 



38-. 



3 equations, goniometric solution. 

 Grunert, J. A. Grunert Arch. 6 (1845) 

 370-. 



6 equations in 9 quantities, solution. 

 Frattini, G. [1879] G. Mt. 18 (1880) 174-. 



Systems of equations. Cayley, A. Ph. Mg. 



20 (1860) 341-; QJ. Mth. 11 (1871) 132- ; 



Mess. Mth. 7 (1878) 17-; 12 (1883) 191-. 

 , solution without using determinants. 



Cockle, Jas. Ph. Mg. 2 (1851) 289-. 

 , theory, with application to curves. 



Saltel, L. N. A. Mth. 20 (1881) 546-; 2 



(1883) 554-. 

 Transformation of equations with 3 variables. 



Genocchi, A. G. Mt. 5 (1867) 106-. 

 linear equations by change of independent 



variable. Duclos, L. Mntp. Mm. Ac. Sect. 



Sc. 6 (1864-66) 281-. 

 2 simultaneous equations. Walton, W. 



QJ. Mth. 11 (1871) 262-. 



. Cayley, A. QJ. Mth. 11 (1871) 



266. 



2470 Transcendental equations. 



Algebraic analysis, application. Fourier, J. B. J. 



[1829] Par. Mm. Ac. Sc. 10 (1831) 119-. 

 Analysis of some equations. Frisiani, P. Mil. 



Eifem. As. (1845) 3-. 

 Compound interest and annuities : to find p 



from relation E = A (1 + p) n + Q_l- . 



Simony, 0. Z. Mth. Ps. 22 (1877) 190-. 

 Elimination of intervals, solution of algebraic 

 and transcendental equations by. Hermann, 

 A. N. A. Mth. 9 (1870) 180-. 



Transcendental equations 2470 



Equal roots. Turquan, L. V. C. K. 59 (1864) 

 701-. 



Equation allied to J (z) = 0, least root. Free- 

 man, A. Camb. Ph. S. P. 3 (1880) 375-. 



a x =b, solution. Belli, S. Siena At. Ac. 9 

 (1808) 255-. 



xv = y x , solution in real quantities. Wittstein, 

 T. Grunert Arch. 6 (1845) 154-. 



u- tan u = f , imaginary roots. Serret, J. A . 

 C. E. 42 (1856) 1182-. 



, . Catalan, E. C. (vi Adds.). C. E. 



42 (1856) 1184-. 



a x + b x =c x , solution. Dubois, E. Les 

 Mondes 4 (1864) 735-. 



, . Qaher-Bey. N. A. Mth. 5 (1866) 



129-. 



tanx=Xa;, expression of roots in series. 

 Michaelis, J. P. Lux. S. Sc. Mm. 7 (1864) 

 167-. 



_ o = J - _- + ^T 1 * .. , roots (Bour- 



5 x + l (x + l)(x + 2) 

 guet). Catalan, E. C. N. A. Mth. 16 (1877) 

 416-. 



y x =xv. Schwering, K. Z. Mth. Ps. 23 

 (1878) 339-. 



xv=y x . Luxemberg, M. [1880] Arch. Mth. 

 Ps. 66 (1881) 332-. 



-. Marrecas Ferreira, L. F. G. Teix. J. 



Sc. 2 (1880) 165-. 



cos x = x, numerical value of roots. Miller, 

 T. H. Edinb. Mth. S. P. 9 (1891) 80-. 



Equations, 



and 



I cos (x cos u) du = 

 cos (x cos u) sin 2 udu = 0, 



roots. Baehr, G. F. W. Amst. Vs. Ak. 6 



(1872) 325-; Arch. Ne'er!. 7 (1872) 351-. 

 Number of solutions of transcendental equation. 



Bidone, G. Turin Mm. Ac. (1805-08) (pte. 2) 



35-. 



Numerical solution by successive approxima- 

 tions. Sommerfeld, A. Gott. Nr. (1898) 



360-. 

 Properties of algebraic equations applicable to 



transcendental equations. Laguerre, E. C. 



E. 94 (1882) 160-. 

 Eeal roots of algebraic or transcendental 



equations, calculation. Buchwaldt, F. Mth. 



Ts. 3 (1861) 185-. 

 , , practical method. 



Mehmke, E. Z. Mth. Ps. 36 (1891) 158-. 

 , determination. Cauchy, 



A.L. C. E. 5 (1837) 357-. 

 , exact separation. Siebel, 



A. Arch. Mth. Ps. 5 (1887) 279-; 6 (1888) 



VI. 



Eepeated functional operations, solution of 



algebraic or transcendental equations by. 



Isenkrahe, C. Mth. A. 31 (1888) 309-. 

 Boots. Poisson, S. D. Par. S. Phlm. N. Bll. 



(1826) 145- ; Par. Mm. Ac. Sc. 9 (1830) 



89-. 

 of certain equations. Hurwitz, A. Hamb. 



Mth. Gs. Mt. 2 (1890) (Festschr., Tl. 2) 25-. 



187 



