2440 



Numerical solution of equations 



Principle of proportional parts. Biffignandi, 

 A. Acireale Ac. At. 2 (1891) 62-. 



Quadrinomial equations, solution by series. 

 Amanzio, D. G. Mt. 14 (1876) 153-, 306-. 



equations, calculation of real roots. Wiener, 

 A. Z. Mth. Ps. 31 (1886) 65-, 192. 



Eational roots of numerical equations, new 



method of finding. Moon,E. [1849] Camb. 



Ph. S. P. 1 (1866) 79-. 

 Eeal and imaginary roots of numerical equa- 



tion of higher order. Spitzer, S. Haidinger 



Ab. 3 (1850) (Ab. 2) 109-. 



root of equation, series expressing. Bras- 

 sinne, E. Toul. Mm. Ac. 6 (1849) 10-. 



roots, calculation. Buchioaldt, F. Mth. Ts. 

 3 (1861) 185-. 



-- , . Margerie, C. N. A. Mth. 3 (1884) 



33-. 

 -- , by infinite series. Wallinowsky, . 



Crelle J. 33 (1846) 164-. 

 -- , development in series. Yvon-Villarceau, 



A. J. F. Liouv. J. Mth. 4 (1878) 119-. 

 -- of equation with real coefficients. Giu- 



dice, F. Palermo Cir. Mt. Ed. 1 (1887) 



69-. 



, Moth's determination. Stampfer, S. 

 Wien Sb. 1 (1848) 194-. 



-- , simplest method for obtaining. Bella- 



vitis, G. [1845] Ven. Mm. I. 3 (1847) 



109-. 

 Eecurring series, solution by. Perrin, E. C. 



E. 119 (1894) 990-, 1190-, 1257-. 

 -- , -- . Capelli, A. Nap. Ed. 34 (1895) 



194-. 

 -- , -- , extension of D. Bernoulli's theo- 



rem. Mainardi, G. A. Sc. Lomb. Ven. 9 



(1839) 273-; 10 (1840) 113-. 

 Eeversion of series, application. Hagen, J. G. 



Am. Ph. S. P. 21 (1884) 93-. 

 Eoots of equation, development in series. 



Cauchy, A. L. C. E. 38 (1854) 1105-. 

 --- , --- . Antanzio, D. Nap. Ed. 



16 (1877) 122-, 143-. 

 --- , --- . Eunge, C. Acta Mth. 6 



(1885) 305-. 

 --- , --- . Madsen, N. Ts. Mth. 



5 (1887) 129- ; Fschr. Mth. (1887) 74. 

 --- , --- . Fabre, A. As. Fr. C. E. 



(1894) (Pt. 2) 149-. 

 --- , --- of powers. Heine, H. E. 



Crelle J. 48 (1854) 267-. 

 --- x n + ax + b = Q, development in series. 



Madsen, N. Ts. Mth. 6 (1889) 33- ; Fschr. 



Mth. (1888) 86. 



e x * (g- 



0. Markoff, A . St. 



Pet. Ac. Sc. Bll. 9 (1898) 435-. 



equations, considered as functions of a 

 variable parameter. Puiseux, V. C. E. 

 30 (1850) 171. 



--- -, criteria for determination. Sylvester, 

 J. J. Ph. Mg. (1844) 442-. 



as determinants of coefficients. 

 Fiirstenau, E. Marb. Schr. 9 (1872) 19-. 



---- , Fiirstenau's method. 

 Nagelsbach, H. Arch. Mth. Ps. 59 (1876) 

 147- ; 61 (1877) 19-. 



2440 



Eoots of equations given by recurring expres- 

 sions. Cohn, F. Mth. A. 44 (1894) 473-. 



, method for simultaneous calculation. 



McClintock, E. [1894] Am. J. Mth. 17 

 (1895) 89-. 



, nature and approximate value. Mal- 



fatti, G. F. Verona S. It. Mm. 4 (1788) 

 206-. 



, expression by continued fractions. Cwojd- 

 zinski, K. Arch. Mth. Ps. 17 (1900) 29-. 



and powers of roots expressed as series. 

 Euler, L. [1778] St. Pet. Ac. Sc. N. Acta 

 12 (1801) 71-. 



Series and definite integrals, solution by. 



Lorenz, L. V. (xn) Ts. Mth. 3 (1867) 71-. 

 logarithms, solution by. Valz, B. C. E. 



49 (1859) 705-. 

 , solution by. Possou, . Mntp. Eec. Bll. 



2 (1805) 146-. 

 , . Fergola, E. Nap. Ac. Sc. Mm. 2 



(1855-57) 207- ; Tortolini A. 8 (1857) 204-. 

 Square and approximate rectangle, paradox 



concerning. Schlegel, S. F. V. [1878] 



Z. Mth. Ps. 24 (1879) 123-. 

 Successive substitutions, solution by. San- 

 eery, L. N. A. Mth. 1 (1862) 305-, 384-. 

 , . Laska, W. Arch. Mth. Ps. 5 



(1887) 199- ; 6 (1888) vi. 

 Superior limit to roots of numerical equations, 



Petersen's criterion proved erronecfus. Giu- 



dice, . Palermo Cir. Mt. Ed. 6 (1892) 157-. 

 " Ideologic " method. Dickstein, S. Krk. Ak. 



(Mt.-Prz.) Ez. 19 (1889) 167-; 20 (1890) 



287-; Crc. Ac. Sc. Bll. (1889) No. 5, xxix; 



(1890) 118-. 

 Transcendental functions, solution by. Linde- 



mann, F. Gott. Nr. (1884) 245- ; (1892) 292-. 

 Trinomial equations. Marrecas Ferreira, L. F. 



G. Teix. J. Sc. 5 (*1883) 50-. 

 , imaginary roots, approximation. Wed- 



dle, T. Mathematician 3 (1850) 285-. 

 , numerical solution. Piobert, . N. A. 



Mth. 10 (1851) 174-. 

 , . Astrand, J. J. Stockh. Ofv. 34 



(1877) No. 7, 49-; Arch. Mth. Ntvd. 6 (1882) 



448-. 

 , . Farkas, J. [1878] Arch. Mth. 



Ps. 64 (1879) 24-. 

 , . M'Laren (Lord). Edinb. E. S. 



P. 17 (1891) 270-. 



, real roots. Drobisch, M. W. Leip. 

 B. 8 (1856) 21-; 10 (1858) 82-. 



, . Geelmuyden, H. Christiania 

 F. 15 (1873) 481-. 



, series involving binomial coefficients 

 for solution of. Schroder, E. Z. Mth. Ps. 

 25 (1880) 196-. 



, solution by continued radicals. Astrand, 



J. J. As. Nr. 89 (1877) 347-. 

 , series. Fergola, E. Nap. Ed. 1 



(1862) 39-. 

 Weddle's method. Popper, J. Bohm. Gs. 



Ab. 11 (1861) 531-. 



Graphical methods. 



Geometric construction. Magistrini, G. B. 

 Bologna N. Cm. 1 (1834) 194-. 



177 



