3230 Principles and Elements of the Differential Calculus 3230 



Differential calculus, theorem. Genocchi, A. 



Tor. At. Ac. Sc. 4 (1868-69) 327-. 

 , theory. Schubert, F. T. St Pe"t. Ac. Sc. 



Mm. 6 (1818) 153-. 

 , use of new symbol. Lamarle, E. Liouv. 



J. Mth. 11 (1846) 254-. 



coefficient and continuity. Steinitz, E. 

 Mth. A. 52 (1899) 58-. 



of function of function, etc. Fields, J. C. 



Am. J. Mth. 11 (1889) 388-. 

 __ _ i n terms of differential coefficients 



of inverse function. Fergola, E. Nap. Ac. 



Sc. Mm. 2 (1855-57) 200-. 

 of two variables. Genocchi, A. 



Tor. At. Ac. Sc. 4 (1868-69) 323-. 

 , 1st order. Binet, J. P. M. Par. S. 



Phlm. Bll. 1 (1808) 275-. 



, nth order, f (sin x). Malmsten, C. J. 

 Stockh. Ofv. 3 (1846) 36-. 



, , of y = e mxZ , Spitzer, S. Grunert 



Arch. 30 (1858) 79-. 



coefficients. Cohen, A. Phil. Trans. (1862) 

 469-. 



of function of function. Meyer, U. H. 



Grunert Arch. 9 (1847) 96-. 

 one variable. Stieltjes, T. J. 



(jun.) N. Arch. Wisk. 9 (*1882) 106-. 

 two functions, remarkable relation 



between. Steen,A. (xn) Ts. Mth. 5 (1881) 101-. 

 with general index, and integration of 



differential equations. Most, E. Z. Mth. 



Ps. 16 (1871) 190-. 



, higher. Most, R. Mth. A. 4 (1871) 499-. 



, . Engel, F. Leip. Mth. Ps. B. 45 

 (1893) 468-. 



, , of composite functions. Tardy, P. 



G. Mt. 2 (1864) 73-. 

 , , functions of functions. Fais, A. 



G. Mt. 13 (1875) 47-. 

 , , some functions. Schlomilch, O. 



Grunert Arch. 4 (1844) 364-. 



, , , and definite integrals 

 connected with them. Lindman, C. F. [1865] 

 Stockh. Ak. Hndl. 5 (1866) No. 8, 29 pp. 



, , independent representation. Hoppe, 



B. Mth. A. 4 (1871) 85-. 

 , , . Jensen, J. L. W. V. (xn) 



Ts. Mth. 3 (1879) 90-. 



, , , and summation symbols. 



Hoppe, E. Crelle J. 33 (1846) 78-. 



, , of logarithmic functions. Schlomilch, 



0. Grunert Arch. 8 (1846) 427-. 



,, quotients. Meyer, F. Mh. Mth. 

 Ps. 1 (1890) 33-. 



, , tangent. Schlomilch, 0. Grunert 



Arch. 12 (1849) 297-. 



, , theory. Malmsten, C. J. Stockh. 



Ofv. 3 (1846) 324-. 



-, , . Schlomilch, 0. Grunert Arch. 



7 (1846) 204- ; Leip. B. 9 (1857) 163-. 



, , of 



p _ sin a; 



1 + 2y cos x + 7/ 2 ' 



y + coax 

 l + 2y cos x + y 2 ' 

 Grunert, J. A. Grunert Arch. 3 (1843) 41-. 



Differential coefficients, higher, of 



Schlomilch, 0. Grunert Arch. 8 (1846) 357-. 

 -- , , cos" 6. Schlomilch, 0. Grunert 

 Arch. 9 (1847) 313-. 



, any order, calculation. Laurent, H. 

 N. A. Mth. 3 (1884) 240-. 



-- of unknown functions, determination. 



Norrenberg, . Baumgartner Z. 6 (1829) 



437- 

 --- e ax ^ cos ( a + p x \ etc> Unferdinger, F. 



[1869] Wien Sb. 60 (1870) (Ab. 2) 605-. 



, to find, without use of infinitesimals or 

 limits. Ficklin, J. Des Moines Anal. 4 

 (1878) 177-. 



formulae, theory. Liouville, J. Liouv. J. 

 Mth. 17 (1852) 478-. 



of function of two variables. Johnson, 

 W. W. Mess. Mth. 4 (1875) 132-. 



, higher, of a power, base and exponent of 

 which are functions of same variable. 

 Studnicka, F. J. Prag Sb. (1877) 368-. 



of log x. Cerquero, J. S. Quetelet Cor. 

 Mth. 10 (1838) 31-. 



---- . VerhuUt, P. F. Brux. Ac. Bll. 7 



(1840) 53-. 

 -- nth order of implicit function y defined 



y/(*-2/) = 0. Preobrazhenskil, V. V. 



(xn) Kazan S. Nt. (Ps.-Mth.) P. 1 (1883) 



[(No. 9)] 1-. 



relations in finite terms. La Casa, V. de 

 [Casa, V. deUd]. A. Sc. Lomb. Yen. 7 

 (1837) 178-, 205- ; 10 (1840) 255-; 13 

 (1844) 117-. 



----- (de la Casa). Minich, S. E. 



A. Sc. Lomb. Yen. 9 (1839) 216- ; 11 (1841) 



63-. . 

 -- , identical. Glaisher, J. W. L. [1876] 



L. Mth. S. P. 8 (1876-77) 47-. 

 Differentials, common divisors and multiples. 



Heffter, L. D. Nf. Vh. (1895) (Th. 2, 



Halfte 1) 8-. 



containing quadratic surd, rationalisation. 

 Mertens, F. Mh. Mth. Ps. 2 (1891) 217-. 



, elimination of radicals. Schlomilch, O. 

 Leip. B. 20 (1868) 151-. 



employed as alternate numbers (clefs alge"- 

 briques). Cauchy, A. L. C. E. 37 (1853) 

 38-, 57-. 



, exact. Sarrus, F. C. B. 1 (1835) 115-. 



of exponentials with variable base, etc. 

 Oettinger, L. Grunert Arch. 22 (1854) 

 401-. 



-- a function of two variables. Falk, M. 

 (xn) Ts. Mth. 6 (1882) 164-. 



as functions of finite differences, and vice 

 versa. Lemonnier, H. N. A. Mth. 20 (1861) 

 197-. 



of functions, new method of obtaining, with 

 especial reference to Newtonian conception. 

 Johnson, W. W., & Eice, J. M. Am. Ac. P. 

 8 (1873) 488-. 



, higher, of fractional functions of one vari- 

 able, representation. Studnicka, F. J. Prag 

 Sb. (1874) 1-. 



, , a function of functions. Konigs- 

 berger, L. Mth. A. 27 (1886) 473-. 



255 



