2430 Equations, 3rd and 4th orders Equations, 4th order 2430 



double system of values in solving. Valles, F. 



C. R. 47 (1858) 30-. 

 . Ollive-Meinadier, . Gard 



Mm. Ac. (1859) 171-. 

 equation of anharmonic ratios corresponding 



to roots. Painvin, L. N. A. Mth. 19 (I860) 



407-. 

 squares of differences of roots. Roberts, 



M. Tortolini A. 2 (1859) 330-. 

 . Casey, J. [1874] Ir. Ac. 



P. 2 (1877) 40-. 

 . Forestier, C. N. A. Mth. 



2 (1883) 209-. 

 factors. Elliott, E. B. Mess. Mth. 25 (1896) 



170-. 

 and of 5th. Autonne, L. Par. S. Mth. Bll. 28 



(1900) 90-. 

 when J 18 = 0, solution. Faa de Bruno, 



F. Am. J. Mth. 3 (1880) 154-. 

 and 6th, solution by trigonometric and 



hyperbolic functions. Heymann, W. Crelle 



J. Mth. 113 (1894) 267-. 



final formula for algebraic solution. Mem- 

 man, M. Am. J. Mth. 14 (1892) 237-; N. Y. 



Mth. S. Bll. 1 (1892) 202-, 236. 

 general. Boer, F. de. Amst. Ak. Vs. M. 20 



(1884) 413- ; Fschr. Mth. (1884) 79. 

 , root formula. Unferdinger, F. Wien Sb. 



50 (1865) (Ab. 2) 225-. 

 , solution. Pilatte, . Gergonne A. Mth. 



2 (1811-12) 152-. 



, . Gergonne, J. D. Gergonne A. Mth. 13 



(1822-23) 385-. 

 , . Grassmann, H. Arch. Mth. Ps. 51 



(1870) 93-. 

 , . Fitz, N. Des Moines Anal. 3 (1876) 



50-. 



_, _. Weichold, G. C. R. 82 (1876) 1093-. 

 , . Lodge, A. QJ. Mth. 19 (1883) 257-. 

 literal, case. Pagani, G. M. Quetelet Cor. 



Mth. 4 (1828) 291-. 

 nature of roots. Lucas, F. Par. S. Mth. Bll. 



18 (1890) 145-. 

 with no real root, calculation of roots. Kora- 



lek, P. N. A. Mth. 11 (1852) 117-. 

 reality of roots. Desboves, A. H. N. A. Mth. 



3 (1844) 387-. 



reduction. Schlamilch. 0. Schlomilch Z. 8 

 (1863) 223-. 



to equation of 3rd order. Hoppe, E. Arch. 

 Mth. Ps. 69 (1883) 111-. 



reciprocal equation. Brocard, H. P. P. B. 



(xn) Mathesis 2 (1882) 180-. 

 of same order. Alexandre, R. N. 



A. Mth. 5 (1866) 477-. 

 2nd order. Ligowski, W. [1879] 



Arch. Mth. Ps. 65 (1880) 426-. 

 root forms, domains of the 3. Hoppe, R. Arch. 



Mth. Ps. 14 (1896) 398-. 

 roots, Aronhold's formula. Janni, V. G. Mt. 



21 (1883) 213-. 



related to sides of cyclic quadrilateral. 

 Matthiessen, L. Z. Mth. Ps. 9 (1864) 453-; 

 10 (1865) 331-. 



and of 6th, in theory of conies and quadrics. 



Joachimsthal, F. Crelle J. 53 (1857) 149-. 

 solution. Berndtson, B. Stockh. Ac. Hndl. 



28 (1807) 173-. 



Sochocki, J. Prace Mt.-Fiz. 10 (1899-1900) 



135- ; Fschr. Mth. (1899) 102-. 

 limit of roots. Fournier-Vannson, . N. A. 



Mth. 11 (1852) 60-. 

 literal, solution. Jourdain, . Liouv. J. Mth. 



4 (1859) 205-. 

 , . Matthiessen, L. Arch. Mth. Ps. 45 



(1866) 415-. 

 problem, solution. Tortolini, B. Rm. At. N. 



Line. 22 (1869) 166-. 

 roots of which can be expressed without cubic 



radicals. Realis, S. N. A. Mth. 18 (1879) 



296-. 

 solution. Twining, A. C. Silliman J. 9 (1825) 



86-. 

 . Sturm, J. B. Grunert Arch. 24 (1855) 



112-. 



. Tortolini, B. Tortolini A. 1 (1858) 310-. 

 . Hilt, G. W. Des Moines Anal. 2 (1875) 



4-. 



by construction. Chasles, M. Liouv. J. 

 Mth. 20 (1855) 329-; C. R. 41 (1855) 

 677-. 



, Lagrange's method. Candioti, M. R. Arg. 

 S. Ci. A. 46 (1898) 223-. 



by linear substitution x = . Azza- 



relli, M. Rm. At. N. Line. 24 (1871) 83-. 

 same principle. Sommer, B. Grunert 



Arch. 27 (1856) 354-. 

 solutions of which by radicals are rational. 



Rummer, E. E. Berl. Ak. Mb. (1880) 



930-. 

 Sturmian constants. Cayley, A. QJ. Mth. 4 



(1861) 7-. 

 theorem. Desboves, A. C. R. 90 (1880) 



theory. Cockle, Jas. Camb. Mth. J. 3 (1843) 



104-. 

 , elementary. Pokrowsky, P. M. Fschr. 



Mth. (1893-94) 152-. 

 values of roots when coefficient of first term 



is zero. Faure, H. N. A. Mth. 14 (1855) 



194-. 



Equations, 4th order. 



Bret, . Par. EC. Pol. Cor. 2 (1809-13) 



217-. 

 Ampere, A. M. Quetelet Cor. Mth. 9 (1837) 



Roberts, M. N. A. Mth. 18 (1859) 87-. 

 Catalan, E. C. , N. A. Mth. 2 (1863) 341-. 

 Pokorny, M. Z. Mth. Ps. 10 (1865) 320-. 

 Ball, R. S. QJ. Mth. 7 (1866) 6-, 358-. 

 Enneper, A. Z. Mth. Ps. 18 (1873) 93-. 

 Rawson, R. Manch. Lt. Ph. S. P. 19 (1880) 



127-. 

 Oekinghaus, E. Arch. Mth. Ps. 6 



169-. 



Gordan, P. Mth. A. 29 (1887) 318-. 

 Darbi, G. G. Mt. 38 (1900) 153-. 

 analytical solution. Valeriani, V. G. Mt. ["13 



(1875)] 99-. 

 case of reduction to canonical form. Gru- 



zintsev, A. P. (xn) Kharkov Mth. S. Com. 



(1881) 116-. 

 class. Brioschi, F. C. R. 57 (1863) 106-. 



172 



