3230 Principles and Elements of the Differential Calculus 3230 



Expression (x* + ax+b)-(P +> ), higher deriva- 



tives. Bjorling, E. G. Grunert Arch. 9 



(1847) 233-. 

 Fluxional ratio, applications. Wright, E. 



Silliman J. 24 (1833) 298- ; 25 (1834) 93-. 

 Fluxions. Christison, (Prof.) A. Thomson 



A. Ph. 5 (1815) 327-; 6 (1815) 420- ; 10 



(1817) 417-. 



, invention. Weld, C. R. Ph. Mg. 31 

 (1847) 35-. 



method, principles. Stockier, F. de B. G. 

 Lisb. Mm. Ac. Sc. 1 (1797) 200-. 



, problems, solutions. Strong, T. Silliman 

 J. 16 (1829) 283- ; 17 (1830) 69-, 329- ; 18 

 (1830) 67-. 



, theory. Wright, E. Silliman J. 14 (1828) 

 330- ; 15 (1829) 196- ; 16 (J829) 53-. 



, two, proposed by Simpson. Andrew, J. 

 Tilloch Ph. Mg. 39 (1812) 383-. 



Functions possessing no differential coefficient. 

 Hertz, K. Par. T. Nauk Sc. Pam. 11 (*1879) 

 Art. 1, 24 pp. ; Fschr. Mth. (*1879) 275. 



, successive differentials of which are in 

 arithmetical progression. Weyr, E. A. Mt. 

 4 (1870-71) 212-. 



, variability. Marroquin y Rivera, M. Mex. 

 S. "Alzate" Mm. 1 (1887) 27-. 



Identity 



proof. Posse, K. A. Bee. Mth: (Moscou) 13 

 (1886) 489-; Fschr. Mth. (1887) 256. 



Implicit functions, determination. Cauchy, 

 A. L. C. E. 34 (1852) 265-. 



n independent variables, each expressed as 

 function of n others, theorem. Minchin, 

 G. M. [1871] QJ. Mth. 12 (1873) 172-. 



Indeterminate expressions. Seliwanow, D. F. 

 Fschr. Mth. (1892) 253. 



forms, values. Olivier, L. Crelle J. 1 

 (1826) 308-. 



ratios with several variables. Autonne, L. 

 N. A. Mth. 16 (1897) 420-. 



Infinite, employment of the. Transon,A. C.B. 

 73 (1871) 367-. 



quantities. Hoppe, E. Arch. Mth. Ps. 55 

 (1873) 49-. 



Infinitesimal analysis. Cauchy, A. L. C. B. 



17 (1843) 275-. 

 -- , fundamental questions. Casorati, F. 



Em. E. Ac. Line. T. 5 (1881) 216-. 



calculus. Franchini, P. Brugnatelli G. 

 10 (1827) 79-. 



-- . Cauchy, A. L. Bb. It. 61 (1831) 321-. 

 --- . Bergasse, . Eouen Ac. Tr. (1849-50) 



-- .' ^1, j, Nm Li ge Mm. S. Sc. 10 



(1855) 25-; 16 (1861) 73-, 410-. 

 -- . Mehay, A. Mon. Sc. 12 (1870) 148-. 



, applications. Bellavitis, G. A. Sc. 

 Lomb. Ven. 1 (1831) 347-. 



-- , elements. Spina, P. Me"x. S. "Alzate " 



Mm. 4 (1890) 293-. 



-- , extension of some conceptions. Viterbi, 

 A. Em. E. Ac. Line. Ed. 6 (1897) (Sem. 1) 



Infinitesimal calculus, formation of new al- 

 gorithms. Guldberg, A. S. [1868] Sk. Nf. 



F. 10 (1869) 165-. 



, invention. Bertrand, J. J. Sav. (1862) 



465-. 

 , . Enestrdm, G. Bb. Mth. (1898) 



50-. 



, metaphysics. Saporetti, A. Bologna 

 Ac. Sc. Mm. 5 (1895-96) 309-. 



, origin. Milhaud, G. [1900] N. Y. Am. 



Mth. S. Bll. 7 (1901) 157, 158. 

 , . Cantor, M. [1900] N. Y. Am. Mth. 



S. Bll. 7 (1901) 158, 159-. 

 , and principles. Gomes Teixeira, F. 



G. Teix. J. Sc. 3 (1881) 21-. 



, paradoxes. Du Bois-Reymond, P. Mth. 



A. 11 (1877) 149-. 

 , principles. Gomes Teixeira, F. [1879] 



Bordeaux S. Sc. Mm. 4 (1882) 41-. 

 , and difficulties. Hoppe, R. N. Mg. 



Ntvd. 18 (1871) 321-. 

 , problem. Gilbert, L. P. (xn) Mathesis 



2 (1882) 17-. 

 , problems. Domenico, D. Brugnatelli 



G. 3 (1820) 229-, 319-. 

 , questions. Strebor [Roberts, W.} N. A. 



Mth. 9 (1850) 181-. 

 , theory. Carnot, L. N. M. Tilloch Ph. 



Mg. 8 (1800) 222-, 335-; 9 (1801) 39-. 

 , conception, history. Vivanti, G. Bb. 



Mth. (1894) 1-. 

 , , logical analysis. Fischer, E. G. Berl. 



Ab. (1829) 29-. 

 , definition. Vivanti, G. Ev. Mt. 1 (1891) 



135-, 248-. 

 , . Bettazzi, R. Ev. Mt. 1 (1891) 174- ; 



2 (1892) 38-. 



method, independent of metaphysics and of 

 limits method. Manillas, J. A. Gen. Civ. 

 2 (1863) 251-. 



Infinitesimals. Debacq, C. Les Mondes 16 



(1868) 484-; 17 (1868) 238-. 

 . Hoiiel, J. Les Mondes 16 (1868) 567-; 



17 (1868) 287-. 

 . Debacq, C. Les Mondes 18 (1868) 608- ; 



19 (1869) 66-, 156-, 255-, 485-; 20 (1869) 



77-, 173-, 368-, 761-. 

 . Stolz,0. Innsb. Nt. Md. B. 14 (1884) 21-, 



37-. 

 , class considered by Newton. Vivanti, G. 



Bb. Mth. (1891) 97-. 

 , principle. Inghirami, G. Inghirami Opusc. 



2 (1821) 494-. 

 , principles, establishment. Marianini, P. D. 



[1858] (x) Mod. Ac. Sc. Mm. 3 (1861) 17-. 

 , ratio finite, geometrical illustration. Ter- 



quem, 0. N. A. Mth. 3 (1844) 580-. 

 , theory. Hoppe, R. Arch. Mth. Ps. 64 



(1879) 444-. 

 Inverse differentiation. Buquoy, G. von. Oken 



Isis (1825) 37-; 21 (1828) 1090-. 



processes of calculus, failures in. Gregory, 



D. F. Camb. Mth. J. 2 (1841) 73-. 



Inversion of variables in -^, Burmann's law. 



Sylvester, J. J. Ph. Mg. 8 (1854) 535. 

 Irrational functions, fluents. Bromhead, (Sir) 



E. F. Phil. Trans. (1816) 335-. 



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