2410 



Algebraic Equations 



2410 



Eational fractions. Stainville, de. Gergonne 



A. Mth. 3 (1812-13) 279-. 

 , algebraic integrals in. Bouniakmvsky, N. 



St Pet. Ac. Sc. Mm. 3 (1833) 205-. 



, approximation to functions of one 

 variable by. Laguerre, E. Par. S. Mth. 

 Bll. 5 (1877) 78-. 



, decomposition. Stainville, de. Par. 



EC. Pol. Cor. 3 (1814-16) 25-. 

 , . Crelle, A. L. Crelle J. 9 (1832) 



231- ; 10 (1833) 42-. 

 , . Finck, B. N. A. Mth. 4 (1845) 



295-. 



, . Rawson, R. Mathematician 1 



(1845) 265-; 2 (1847) 6-. 



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



(1846) 462-. 



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



, . Montojo, S. Cadiz Period. M. Ci. 



1 (1848) 54-. 

 , . Brioschi, F. Crelle J. 50 (1855) 



239-, 318-. 



, . Rouche, E. C. E. 46 (1858) 

 540-. 



, . Vieille, J. C. K. 49 (1859) 746-. 



, . Horner, J. [1860] QJ. Mth. 5 



(1862) 39-. 

 , . Moch, S. N. A. Mth. 1 (1862) 



339-. 

 , . Realis, S. N. A. Mth. 3 (1864) 



438-. 

 , . Trudi, N. G. Mi. 2 (1864) 225-, 



257-. 



, . St Germain, A. de. N. A. Mth. 8 



, . Hermite, C. (xn) Brux. S. Sc. A. 



2 (1878) (Pt. 2) 157-. 

 , . Gomes Teixeira, F. G. Teix. J. 



Sc. 1 (1878) 5-, 17-, 33-, 49-, 97-, 113- ; 2 



(1880) 33-. 

 , . Jamet, V. N. A. Mth. 8 (1889) 



228-. 

 , , and theory of residues. Rouche, E. 



C. E. 49 (1859) 863-. 



, transformation. Rangoni, L. 

 [1834] Mod. Mm. S. It. 21 (1836) 65-. 



, development in partial fractions. Anon. 



(vi_536) Gergonne A. Mth. 10 (1819-20) 



255. 

 , expansion. Trudi, N. (xi) Nap. Ac. 



At. 2 (1865) No. 17, 68 pp. ; (vm) Nap. Ed. 



5 (1866) 441-. 

 . Factorials, ratios of reciprocal. Cauchy, 



A. L. C. E. 17 (1843) 921-, 1159-. 

 . , , and transformation of 



logarithms into definite integrals. Cauchy, 



A. L. C. E. 17 (1843) 779-. 



, geometric properties. Lucas, F. C. E. 

 78 (1874) 140-, 180-, 271-. 



, index. Hermite, C. Par. S. Mth. Bll. 



7 (1879) 128- . 

 , theorems by Hermite. Laguerre, E. 



Crelle J. Mth. 89 (1880) 339-. 

 , theory. Picquet, H. Par. 6c. Pol. J. 



Cah. 53 (1883) 79-. 



functions of the cubic. Sawin, A. A. Mth. 

 9 (1894-95) 158-. 



VOL. I. 161 



Eational functions of roots, form. Realis. S. 



G. Mt. 9 (1871) 206-. 

 of integral equation. Blutel, . 



Par. S. Mth. Bll. 20 (1892) 92-. 

 Eationalisation of algebraic expressions, 



Scheibner, W. Leip. B. 15 (1863) 63-. 

 consisting of sums of square roots 



(Fermat's problem). Lehmann, J. W. H 



Grunert Arch. 35 (I860) 207-. 

 any binomial denominator. Decher, G. 



Grunert Arch. 20 (1853) 245-. 



fractions. Unferdinger, F. Grunert 

 Arch. 33 (1859) 104-. 



a sum of 2 th roots. Rychlicki, S. Arch. 



Mth. Ps. 68 (1882) 180-. 

 Eecurring functions of 3rd degree. Gohierre 



de Longcliamps, . As. Fr. C. E. 9 (1880) 



115-. 

 Eegular difference terms. Kempe, A. B. L. 



Mth. S. P. 25 (1894) 343-, 396. 

 Eoots of equations, dimensions. De Morgan, A . 



QJ. Mth. 1 (1857) 1-, 80, 232-. 

 , expression by transcendental functions 



impossible. Wantzel, L. Par. S. Phlm. PV. 



(1845) 114-. 

 , form of. Olivier, L. Crelle J. 1 



(1826) 97-. 



, forms of. Casinelli, A. (s. L.) 

 Bologna N. Cm. 8 (1846) 317 



, geometrical representation. Goodwin, 



H. [1846] Camb. Ph. S. T. 8 (1849) 342-. 



, properties. Cockle, Jos. QJ. Mth. 5 



(1862) 291-. 



, property. Brioschi, F. N. A. Mth. 



15(1856)366-. 



, , with geometrical applications. 

 Laisant, C. A. As. Fr. C. E. (1888) (Pt. 2) 



, square roots of. Terquem, 0. N. A. 



Mth. 6 (1847) 456-. 



, transformation. Gelder, J. de. 

 Amst. Mengelwerk 1 (1816) 46-. 



quadratic with complex coefficients. 

 Johnson, . N. Y. Mth. S. Bll. 2 (1893) 

 171. 



Successive powers of root, Anglin's formula. 



Cayley, A. QJ. Mth. 19 (1883) 223-. 

 Sum of like powers of roots. Faure, H. N. 



A. Mth. 14 (1855) 94-. 

 , as function of coefficients. 



Pellet, A. E. N. A. Mth. 14 (1875) 259-. 

 , and vice-versa. 



Farkas, J. Arch. Mth. Ps. 65 (1880) 433-. 

 Sums of like powers of roots of equations, and 



Brioschi's theorem. Genocchi, A. N. A. 



Mth. 12 (1853) 260- ; 14 (1855) 246-. 

 powers of roots of general quadratic. 



Kapteyn, W. N. Arch. Wisk. 3 <*1877) 



203-. 

 , Newton's formula, generalisation. 



Lachlan, R. Mess. Mth. 13 (1884) 155-. 

 , theorem. Collins, E. [1837] 



St Pet. Ac. Sc. Bll. 3 (1838) 52-. 



, , and application to 

 infinite products. Stockier, F. de B. G. 

 Lisb. Mm. Ac. Sc. 2 (1799) 1-. 



, , proof. Schubert, F. T. 



[1808] St Pet. Ac. Sc. Mm. 2 (1810) 124-. 



