0810 Calculus of Operations 



Operation, laws. Ellis, A. J. E. S. P. 10 



(1859-60) 85-. 

 Operations equivalent to their adjuncts. Bor- 



tolotti, E. Em. E. Ac. Line. Ed. 7 (1898) 



(Sem. 2) 74-. 



in general. Bourlet, C. C. E. 124 (1897) 

 348-. 



, remarkable sequence. Brunei, G. Bordeaux 



S. Sc. P.-V. (1896-97) 86-. 

 , theorems. Grolous, J. Par. S. Phlm. Bll. 



12 (1875) 81-. 

 Periodicity, generalisation of notion. Brunei, . 



Bordeaux S. Sc. Mm. 4 (1888) xxvi-. 

 Quotient- and product-calculation. Guldberg, 



A. S. Ts. Mth. 2 (1884) 84-, 161- ; Fschr. 



Mth. (1884) 342. 

 Eeduction of Cayley 's operation to polar 



operations. Capelli, A. Mth. A. 29 (1887) 



331-. 

 Signs + and , nature in symbolical algebra. 



Gregory, D. F. Camb. Mth. J. 3 (1843) 153-. 

 Symbolic calculus, principles. Cesdro, E. (xn) 



Mathesis 3 (1883) 10-. 



equation, Tr m ir n u + qpu = 0, where symbols 

 ""m' ""n) P combine according to the laws 



"K-mP = pTT m +l ' ' Jr m' n 'n = lr n' lr m, + a ( n ~ m ) P' 



Boole, G. Camb. and Dubl. Mth. J. 2 

 (1847) 7-. 



equations, certain. Piiicherle, S. Bologna 

 Ac. Sc. Mm. 5 (1895-96) 663-. 



, employment. Cauchy, A. L. C. E. 

 17 (1843) 449-. 



, interchange of symbols. Graves, C. 

 Ir. Ac. P. 6 (1853-54) 144-. 



, resolution of non-linear. Cauchy, A. L. 



C. E. 22 (1846) 235-. 

 , theorems and formulae deduced from. 



Cauchy, A. L. C. E. 17 (1843) 377-. 



expansions. Russell, W. H. L. E. S. P. 

 14 (1865) 329-. 



methods, proofs of (1) formula for nth 

 differential coefficient, (2) Euler's theorems 

 on quantics, (3) Staudt's theorem on Ber- 

 noulli's numbers. BuchJieim, A. Mess. 

 Mth. 11 (1882) 143-. 



relations 



&c. Johnson, W. W. Mess. Mth. 11 (1882) 

 191-. 



theorem involving repeated differentiations. 

 Glaisher, J. W. L. [1879] Camb. Ph. S. P. 

 3 (1880) 269-. 



theorems, Crofton. Glaisher, J. W. L. 

 QJ. Mth. 16 (1879) 257-. 



variability of several dimensions. Formenti, 

 C. Mil. I. Lomb. Ed. 16 (1883) 288-, 351-. 



versus operative expansion. Hathaway, 

 A. S. Des Moines Anal. 5 (1878) 38-. 



Symbolical expression, properties and applica- 

 tion to attraction of ellipsoid. Cayley, A. 

 Camb. Mth. J. 3 (1843) 62-. 



Symbols of operation. Crofton, M. W. Am. 

 J. Mth. 4 (1881) 269-. 



Complex Numbers 0820 



Symbols, relation of certain. Cockle, (Sir) J. 



[1879] QJ. Mth. 17 (1881) 20-, 208-. 

 Ternary quadric operators on products of forms 



of any orders. Walker, J. J. L. Mth. S. P. 



20 (1889) 110-. 

 Transmutations. Bourlet, C. Par. S. Mth. 



Bll. 25 (1897) 132-. 

 Uniform substitutions and Babbage's problem. 



Iaggi,E. N. A. Mth. 19 (1900) 483-. 

 , convergence. Lemeray, E. M. N. A. 



Mth. 16 (1897) 306- ; 17 (1898) 75-. 



regarded as function of n. Krug, A. 



Wien. Ak. D. 57 (1890) 151-. 



0820 General theory of complex 

 numbers. (See also 2870.) 



d'Alembert's equation 



(1 + W^T) m = (1 - h x/^T)" 1 . 



Cossali, P. [1783] Mod. Mm. S. It. 9 (1802) 



231-. 

 Algebraic couples. Hamilton, (Sir) W. R. 



[1835] Ir. Ac. T. 17 (1837) 293-. 



. Cayley, A. Ph. Mg. 27 (1845) 38-. 



. Hargreave, C. J. B. A. Ep. (1857) 



184-. 



equations, theory. Gegenbauer, L. Mh. 

 Mth. Ps. 6 (1895) 12-. 



integers. Landsberg, G. D. Mth. Vr. Jbr. 

 4 (1897) 111-. 



numbers, new foundation for theory. 

 Hensel, K. D. Mth. Vr. Jbr. 6 (1899) 

 (Heft 1) 83-. 



and transcendent equations, complex num- 

 bers derived from. Hug, J. C. Zur. Vjschr. 

 7 (1862) 270-. 



triplets. Graves, C. Ir. Ac. P. 3 (1847) 

 51-, 57-, 80-, 105-. 



Calculation with p + qj-l. Ohm, M. D. 



Nf. Vsm. B. (1845) 73-. 

 Chessboard, mathematical theory. Problem of 



n queens on board of n 2 spaces. Giinther, S. 



Arch. Mth. Ps. 56 (1874) 281-. 

 Complex and bicomplex numbers, theory. 



Benthem, A. Arch. N6erl. 12 (1877) 



113-. 



coordinates in plane geometry. Berlin, M. 

 Lund. Acta Un. 9 (1872) (Mth.) No. 4, 

 45 pp. 



elements in analytical geometry, significance. 

 Stolz, 0. Mth. A. 4 (1871) 416-. 



factors. Cauchy, A. L. C. E. 24 (1847) 

 347-. 



forms, real representations. Segre, C. 

 Mth. A. 40 (1892) 413- . 



geometry, contribution. Sforza, G. Q. Mt. 

 30 (1892) 159-. 



integers. Lanavicensis (Sylvester, J. J.). 

 QJ. Mth. 4 (1861) 94-, 124-. 



magnitudes, addition-logarithms for. 

 Mehmke, R. Z. Mth. Ps. 40 (1895) 15-. 



number, cosine, significance in plane geo- 

 metry. Thiele, T. N. (xn) Ts. Mth. & 

 (1876) 177-. 



53 



