1610 Rational polynomials 



Multiplication and division, algebraic. Salim- 



beni, L. Verona Mm. S. It. 7 (1794) 482-. 

 Polynomial, complete, number of terms. Ger- 



gonne, J. I). Gergonne A. Mth. 13 (1822-23) 



282-. 

 , condition for factor of form x n - a n . Zeipel, 



E. V. von. Ups. N. Acta S. Sc. 4 (1863) 



24pp. 

 , . Bjarling, C. F. E. 



Arch. Mth. Ps. 55 (1873) 429-. 

 , determination by integrals of its partial 



differentials. Mossbrugger, L. GrunertArch. 



4 (1844) 210-. 

 , development, case. Weihrauch, K. Z. 



Mth. Ps. 26 (1881) 127-. 

 , without binomial theorem. Brassinne, E. 



Toul. Mm. Ac. 1 (1851) 184-. 



4th degree, values of x for which it is a 

 square. Calzolari, L. G. Mt. 7 (1869) 

 317-. 



, linear factorisation. Kiipper, K. Casopis 

 14 (1885) 28-; Fschr. Mth. (1886) 60. 



, nth power. Studnicka, F. J. Prag Sb. 

 (1879) 375-; Casopis 9 (*1880) 49-. 



(x 2 - 1)", property. Polignac, C. de. [1874] 

 Par. S. Mth. Bll. 3 (1875) 19-. 



Polynomials, class. Appell, P. Par. EC. Norm. 



A. 9 (1880) 119-. 

 , factorisable in linear factors. Moutard, 



. C. E. 119 (1894) 42-. 

 , division and extraction of roots. Gergonne, 



J. D. Gergonne A. Mth. 4 (1813-14) 297-. 

 , equal factors of . Ostrogradsky, M. A. C.E. 



42 (1856) 930-. 

 , geometrical application of theorem. Laisant, 



C. A. As. Fr. C. E. (1898) (Pt. 2) 73-. 

 , powers. Brianchon, C. J. Par. EC. Pol. 



J. 15 (1837) (25 cah.) 158-. 

 , . Casinelli, A. (s. L.) Bologna N. Cm. 



4 (1840) 453-. 

 , . Lewis, W. J. Franklin I. J. 3 (1842) 



44-. 

 , , divisibility. Crelle, A. L. Berl. Ab. 



(1839) 1-, 299-. 

 , product of two, (Gauss). Terquem, O. N. 



A. Mth. 3 (1844) 47-. 

 , properties. De Forest, E. L. Des Moines 



Anal. 7 (1880) 39-, 73-, 105-. 

 , , method of demonstrating. De Forest, 



E. L. Des Moines Anal. 10 (1883) 97-. 

 , rational factors. Gergonne, J. D. Gergonne 



A. Mth. 12 (1821-22) 309-. 

 , , geometric construction. Winckler, A. 



Wien Sb. 53 (1866) (Ab. 2) 326-. 

 , roots. Sebuev, G. N. Kazan S. Nt. (Ps.- 



Mth.} P. 7 (1889) 394-. 



of 3rd degree in one variable. Nordlund, 

 K. P. Ts. Mt. Fys. 4 (1871) 185-. 



Power of polynomial, expression by symmetric 

 functions. Piarron de MondSsir, E. S. As. 

 Fr. C. E. (1877) 154-. 



Powers of (a^ + a<& 2 + ) n , theorem. Tralles, 



J. G. Berl. Ab. (1816-17) 56-. 



Principle of greatest and least exponents. Ap- 

 plications in theory of algebraic functions. 

 Bugaev, N. V. [1889] Eec. Mth. (Moscou) 

 14 (1890) 553-. 



Algebraic inequalities 1615 



Quotient and product functions, certain. Guld- 



berg, A. S. Christiania F. (1884) No. 4, 



18pp. 

 remainder in (x - l)P/x m . Catalan, E. C. 



Liege S. Sc. Mm. 15 (1888) No. 1, 142-. 

 quadrics to sums of squares. Laurent, H. 



N. A. Mth. 19 (1880) 12-; 20 (1881) 38-. 

 Series. ~2A n <j>(n)x n . Grunert, J. A. Crelle 



J. 25 (1843) 240- . 

 Square root extraction, of 6-nomials, 5-nomials, 



etc. Eeade, J. Thomson A. Ph. 11 (1818) 



31-. 

 Sum of a series connected with transvectants. 



Gordan, P. Palermo Cir. Mt. Ed. 12 (1898) 



326-. 

 Sums of like powers of (linear) expressions. 



Bierens de Haan, D. N. Arch. Wisk. 5 



(*1879) 208-. 

 powers of first n numbers, geometrical 



illustrations. Bochow, K. Magdeb. Nt. Vr. 



Jbr. u. Ab. (1896-98) 165-. 

 Ternary forms, conditions for linear factors. 



Brill, A. [1896-98] Mth. A. 50 (1898) 157- ; 



D. Mth. Vr. Jbr. 5 (1901) (Heft 1) 52-. 

 Theorems of Bezout and Euler. Poussart, A. 



Ens. Mth. 2 (1900) 136-. 

 Transformation of expression 



(la - cy)* + (ex - az) 2 + (ay - bx)*. 



Smith, Arch. Camb. Mth. J. 1 (1839) 



155-. 

 (cy - bz) 2 + (az - ex) 2 + (bx - ay) 2 . 



N., M. N. Camb. Mth. J. 2 (1841) 9-. 



E. G. Grunert Arch. 27 (1856) 482-. 

 x n + y n expressed in terms of x + y and xy. 

 Valeriani, V. G. Mt. 12 (1874) 208-. 



1615 Algebraic inequalities. 



Inequalities, applications. Brashmann, N. D. 



(xn) Mosc. Un. Mm. 10 (1835) 381-. 

 , calculus. Fourier, J. B. J. Par. S. Phlm. 



N. Bll. (1826) 99-. 

 , . Gergonne, J. D. Gergonne A. Mth. 



17 (1826-27) 134-. 

 , extension of theorem in. Rogers, L. J. 



Mess. Mth. 17 (1888) 145-. 

 , generalisation of formula of Tschebyscheff 



(Cebysev). Jensen, . Bll. Sc. Mth. 12 



(1888) 134-. 

 , means, and imaginaries. Grunert, J. A. 



Grunert Arch. 1 (1841) 268-. 

 , note on some, and their application to in- 

 tegral calculus. La Vallee-Poussin, C. de. 



Brux. S. Sc. A. 16 (1892) (Pt. 1) 8-. 

 , notes. Face, F. C. Mess. Mth. 18 (1889) 



90-. 

 , number of conditions expressed by. Sludskil, 



T. A. (xn) [1873] Eec. Mth. (Moscou) 7 



(1874-75) (Pt. 1) 419-. 

 , problem. (x m + y m > or < z m when 



x y + y 2 = z' 2 ). Grunert, J. A. Grunert Arch. 



20 (1853) 356-. 



79 



