2430 



Equations of the lower orders, etc. 



2430 Equations of the second, 

 third and fourth orders : other 

 particular equations. 



Abelian cubics and symmetrical equations. 



Cockle, Jas. QJ. Mth. 5 (1862) 237-. 

 Algebraic equations. Jonquieres, E. de. C.E. 



99 (1884) 345-, 450, 469-, 483-, 546. 

 . Lalanne, L. C. E. 99 (1884) 463-. 



, especially irreducible case of Cardan's 

 formula. Gegenbauer, L. Liege S. Sc. Mm. 

 2 (1900) A r o. 10, 6 pp. 



, pair. Mansion, P. Mess. Mth. 7 (1878) 57-. 



, solution by radicals and by series. Favero, 



G. B. Em. E. Ac. Line. Mm. 6 (1889) 415-. 



whose first member satisfies a linear 

 differential equation of the 2nd order. 

 Laguerre, E. C. E. 90 (1880) 809- ; 94 (1882) 

 412-, 508- . 



resolution of equations, theory. Giudice, F. 

 Ev. Mt. 2 (1892) 193-. 



Anharmonic-ratio sextic. Cayley, A. QJ. 



Mth. 10 (1870) 56-. 

 Binary equations of 4th or 5th order, conditions 



for 3 equal roots, etc. Cayley, A. Phil. 



Trans. 158 (1868) 577-. 

 Continued roots. Dixon, T. S. E. Des Moines 



Anal. 5 (1878) 20-. 

 De Moivre, class of equations solved by, and 



their derivatives. Realis, S. N. A. Mth. 4 



(1865) 209-, 289-. 

 De Moivre' s formula. Barsotti, G. Lucca At. 



Ac. 17 (1860) 149-. 

 theorem and Cardan's formula applied to 



equations. Barsotti, G. Pisa A. Un. Tosc. 



Sc. Cosm. 5 (1858-61) 99-. 

 Equation, roots of which are products in pairs 



of roots of another equation. Malet, J. C. 



QJ. Mth. 13 (1875) 30-. 

 , 2 given equations. 



Malet, J. C. [1878] A. Mt. (1878-79) 306-. 



, (-); r=0, 1, 2...n. Siacci, 



F. G. Arcad. 18 (1860) 166-. 



for secular inequalities of planetary motion, 

 Cauchy's theorem that roots are essentially 

 real. Hermite, C. C. E. 41 (1855) 181-. 



with variable parameter, roots. Cauchy, 

 A. L. C. E. 12 (1841) 1133-. 



Equations, certain reducible types. Spitzer, S. 

 Wien SB. 8 (1852) 422- ; Grunert Arch. 22 

 (1854) 1-. 



depending on numerical functions. [Bou- 

 gaieff, N. F.] Bugaev, N. V. [1874] (xn) 

 Eec. Mth. (Moscou) 7 (1874-75) (Pt. 1) 424-; 

 (rx) Bll. Sc. Mth. As. 10 (1876) 102-. 



determining functions of double argument. 

 Hill, C. J. D. Crelle J. 11 (1834) 241-. 



, first 4 orders, solution. Eisenstein, G. 

 Crelle J. 27 (1844) 81-. 



of form x 3 -bx = l. Lockhart, J. Mathe- 

 matician 2 (1847) 253-, 319-. 



x* + ax 2 + bx + c = 0, solution. Leire, 

 P. (xn) Ts. Mth. 1 (1877) 117-. 



+ &c. = 0. Laguerre, E. 



C. E. 93 (1881) 890-. 



2430 



Equations of form (xP - a") \f/(x) = Q. Berloty 



. N. A. Mth. 1 (1882) 173-. 

 (a, b, c, d) = (a 2 , b 2 , c 2 , d*), solution. 



Cayley, A. Mess. Mth. 15 (1886) 59-. 

 (a, b, c - ) = (aP, IP, c" - ), solution. 



Vivanti, G. G. Mt. 27 (1889) 229-. 

 () = (), . Tanner, H. W. L. 



Mess. Mth. 19 (1890) 118-. 



_ <J(x-a)(x-b) + J(x-c)(x-d) = e, 



solution. Dickson, J. D. H. Edinb. Mth. 



S. P. 9 (1891) 13-. 

 , general theory and application to curves. 



Sdderblom, A. Ups. Arsk. (1879) 64 pp. 



OL.. 



, roots of which are of form cos or 



n 



O7._ 



sin . Johnson, W. W. Des Moines Anal. 



6 (1879) 17-. 



soluble by Cardan's method. Guldberg, 

 A. S. Ts. Mth. 3 (1885) 39-; Fschr. Mth. 

 (1885) 74. 



, solution of certain. Allardice,B.E. Edinb. 

 E. S. P. 17 (1891) 139-. 



Equations, 2nd order. 



Matthewson, R. E. Camb. (M.) Mth. M. 2 



(1860) 232-. 

 Marrecas Ferreira, L. F. G. Teix. J. Sc. 2 



(1880) 77-. 

 adfected, solution. - Seers, J. Ph. Mg. 4 (1828) 



125-. 

 , by goniometry. Mollweide, C. Zach 



M. Cor. 22 (1810) 43-. 

 depression. Noel, J. N. Liege Mm. S. Sc. 8 



(1853) 94-. 



general. De Morgan, A. Mathematician 3 



(1850) 154- ; Suppl. 4-. 

 , reduction. S., W. J. Camb. and Dubl. 



Mth. J. 5 (1850) 286-. 

 with imaginary coefficients, solution. Grunert, 



J. A. Grunert Arch. 8 (1846) 65-. 

 invariants. Routh, E. J. QJ. Mth. (v) 6 



(1864) 270-, (vra) 308-. 

 maxima and minima, process for determining. 



Shreve, S.H.V. Nost. Eng. Mg. 15 (1876) 530-. 

 numerical. Bugaev, N. V. (xn) Eec. Mth. 



(Moscou) 8 (1876) (Pt. 1) 239-. 

 paradox. Anon, (vi 556) Gergonne A. Mth. 



15 (1824-25) 118-. 

 rational solutions, expression. Tist, . Les 



Mondes 23 (1870) 770-. 

 reality of roots. Cayley, A. [1862] Crelle J. 



61 (1863) 367-. 

 relation between roots and coefficients. Baehr, 



G. F. W. [1869] Amst. Vs. Ak. 4 (1870) 



(Ntk.) 197-. 

 solution. Mathews,G.B. Nt. 57 (1897-98) 463-. 



by trigonometry. Grunert, J. A. Grunert 

 Arch. 1 (*1841) 12-. 



(Grunert). Mensing, . Grunert 

 Arch. 1 (1841) 189-. 



theorem. Lebesgue, V. A. N. A. Mth. 13 



(1854) 412-. 



theory. Gay, J. Laus. Bll. S. Vd. 1 (1842- 



45) 388-. 

 . Macfarlane, A. Am. As. P. (1897) 54. 



169 



