2410 



Factors, resolution of integral functions into. 

 Bretschtieider, C. A, Arch. Mth. Ps. 46 

 (1866) 422-. 



, ----- . Mandl, M. D. Nf. Vh. 

 (1894) (Th. 2, Hdlfte 1) 7. 



, resolvability into real simple and quadratic. 

 Gauss, C. F. Gott. Cm. 3 (1814-15) 107-, 

 135-. 



, ------ . Collins, E. St. Pet. Ac. 



Sc. Bll. 2 (1837) 377-; Crelle J. 18 (1838) 

 119-. 



, ------ . Perott, J. Crelle J. 



Mth. 99 (1886) 141-. 



Formula 



(x-a)(x-b)f l (x)=-F(x)+f(x) 



IF (a) x - b F(b)x-a\ 

 \f(a)a-b + f(b)b-a\- 



Lemonnier, H. Par. S. Phlm. Bll. 2 (1878) 97-. 

 Fractions, a theorem on. Catalan, E. Brux. 



Ac. Bll. 19 (1890) 742-. 

 Function aleph, its properties. Dickstein, S. 



Krk. Ak. (Mt.-Prz.) Pam. 12 (1886) (35)-; 



Fschr. Mth. (1886) 121. 

 -- , some theorems. Dickstein, S. Krk. Ak. 



(Mt.-Prz.) Pam. 16 (1889) 53-. 

 Functions of differences, fundamental fact as 



to. Elliott, E. B. Mess. Mth. 29 (1900) 



180-. 



--- of roots of given equation. Selivanov, 



D. T. Eec. Mth. (Moscou) 15 (1891) 581-. 



-- roots, and coefficients, relations. Dickson, 



J. D. H. Edinb. K. S. T. 29 (1880) 535-. 



of an equation, Newton's identities 

 concerning. Saalschvtz, . Konigsb. Schr. 

 36 (1895) [5]-. 



Generating function, Borchardt's. Faa de 



Bruno, F. [1875] Crelle J. Mth. 81 (1876) 



217-. 

 -- , . Kostka, C. [1876] Crelle J. Mth. 



82 (1877) 212-. 

 -- , . ReJwfovsky, V. Casopis 11 (* 1882) 



111-; Fschr. Mth. (*1882) 105-. 

 -- of symmetric functions. Meier, F. Brux. 



Ac. Bll. 10 (1860) 608-. 



, symmetric relations found by. Bor- 



chardt, C. W. [1855] Crelle J. 53 (1857) 



193-. 

 Homogeneous products, sums, and roots of 



equations, theorems. Horner, J. QJ. Mth. 



6 (1864) 360-. 

 Infinite partial fractions, reduction of ex- 



ponential fractions to. Cisa de Gresi, . 



Tor. Mm. Ac. 31 (1827) 225-. 

 Integral symmetric functions. Mertens, F. 



Krk. Ak. (Mt.-Prz.) Rz. 1 (1891) 333-; 



Fschr. Mth. (1891) 154-. 

 Irrational fractions, rationalisation of denomi- 



nator. Sommer, B. Grunert Arch. 18 (1852) 



Isobaric functions, use in recurring series. 



Pietrocola, C. Nap. Ac. At. 9 (1899) No. 8, 



23pp. 

 Jacob! , theorem, general analysis of formula 



Algebraic Equations 



2410 



*& Liouville, J. C. R. 13 (1841) 

 



Logarithmic derived function of an integral 



polynomial. Laisant, C. A. As. Fr. C. R. 



(1894) (Ft. 2) 208-. 

 MacMahon's generalisation of the Newton- 



Girard formulae. Gegenbauer, L. [1900] 



Amst. Ak. Vs. 9 (1901) 332-; Amst. Ak. 



P. 3 (1901) 347-. 

 Newton, a formula of. Cesdro, E. Mathesis 



6 (1886) 172-. 

 Number of roots, theorem of d'Alembert. 



Delbceuf, J. Rv. S. 42 (1888) 823-. 

 Numerical equations, theory. Anon, (xi 53) 



N. A. Mth. 17 (1878) 104-. 

 Partial fractions. Franchini, P. [1829] Lucca 



At. Ac. 6 (1830) 173-. 



. Eisenstein, G. Crelle J. 32 (1846) 71-. 



. Meyer, U. H. Grunert Arch. 7 (1846) 



316-, 386-. 

 , identities concerning. Schmidt, J. JR. 



Amst. Mengelwerk 2 (1816) 153-. 

 , reduction to. Serooskerken, R. C. van T. 



Utr. A. Ac. (1817-18) 67 pp. 

 , . De Wit, Ae. Utr. A. Ac. (1817- 



18) 54 pp. 

 , . Dirksen, E. H. Crelle J. 1 



(1826) 53-. 

 , . Crelle, A. L. Berl. Ab. (1831) 



, . Oettinger, L. Crelle J. 32 (1841) 



63-, 148-. 

 , . Amstein, H. Laus. S. Vd. B1L 



17 (1881) 145-. 

 , . Hoepflingen-Bergendorf, H. von. 



Arch. Mth. Ps. 66 (1881) 314-. 

 , . Steplmnos, C. [1883] Bll. Sc. 



Mth. As. 8 (1884) 120-. 

 , , with application to trigonometry. 



Saalschiitz, L. Mh. Mth. Ps. 9 (1898) 132-, 



268. 

 , , geometrical meaning of. Eeuschle, 



C. Z. Mth. Ps. 41 (1896) 103-. 

 , and their integration, theory. Sauvage,. 



L. Mars. Fac. Sc. A. 2 (1892) 3-. 

 , theorems. Mainardi, G. Tortolini A. 



1 (1850) 342- ; 2 (1851) 505-. 

 Polynomials approximating to fractional func- 

 tions. Cebysev, P. [1892] St. Pet. Ac. Sc. 



Mm. (Rs.) 72 (1893) (Suppl.) No. 7, 13 pp. 

 , Jacobi's. Stieltjes, . C. R. 100 (1885) 



620-. 

 Power of polynomial, formula for. Piarron de 



Mondesir, E. S. As. Fr. C. R. (1877) 154-. 

 Powers of roots, Newton's theorems combined 



in one formula. Torriani, J. E. Lisb. Ac. 



Sc. Mm. (Cor.) 3 (pte. 2) (1814) 1-. 



Rational fraction , \f o2in' decomposition. 



Gerono, G. C. N. A. Mth. 18 (1859) 346. 



, formula of Laplace's. 



Y 



467-. 



Jilrgensen, C. Crelle J. 11 (1834) 136-. 



160 



