3230 Principles and Elements of the Differential Calculus 3230 



Law of mean, and limits - , . 



03 



Osgood,W.F. Limiting value of 



s/2 



A. Mth. 12 (1898-99) 65-. 

 Leibnitz's infinitesimal calculus, compensation 

 of error. Guldberg, A. S. N. Mg. Ntvd. 16 

 (1869) 46-. 



infinitesimals, and first principles of calculus. 

 Debacq, C. Les Mondes 29 (1872) 486-. 



theorem. Genocchi, A. Tor. At. Ac. Sc. 4 

 (1868-69) 263-. 



. Tardy, P. N. A. Mth. 8 (1869) 



69-. 



. Frobenius, G. [1879] Crelle J. Mth. 



. 89 (1880) 262-. 



. Mansion, P. Mathesis 13 (1893) 



36-. 



, generalisation. Hoiiel, J. Bordeaux 

 Mm. S. Sc. 5 (1867) 379-. 



, . Genocchi, A. Tor. Mm. Ac. Sc. 



26 (1871) 61-. 

 Limit of a function, definition. Peano, G. 



Ev. Mt. 2 (1892) 77-; Am. J. Mth. 17 (1895) 



37-. 

 x x is 1, when x = 0, Pfaff 's proof. Mobius, 



A. F. Crelle J. 12 (1834) 134-, 292-. 

 x - ijx- - 1 when x = oo . Grunert, J. A. 



Arch. Mth. Ps. 43 (1865) 116-. 

 x x when x approaches zero. Grunert, 



J. A. Arch. Mth. Ps. 53 (1871) 510-. 

 _ n = x (cos n x), Tait's problem. Muir, T. 



[1877] Edinb. E. S. P. 9 (1878) 359-. 



of -/()> extension of Cauchy's theorem. 



Jensen, J. L. W. C. E. 106 (1888) 833-. 

 ' ' Limited ' ' differentiation and its applications. 

 Griinwald, A. K. Z. Mth. Ps. 12 (1867) 

 441- . 



Limiting value of fraction . Bertrand, J". 



Liouv. -J. Mth. 6 (1841) 14-. 

 . Blanchet, P. H. Liouv. J. 



Mth. 6 (1841) 65-. 

 . Liouville, J. Liouv. J. Mth. 



7 (1842) 160-. 

 . Terquem, 0. N. A. Mth. 5 



(1846) 259-. 

 . Rouqet, V. N. A. Mth. 16 



(1877) 113-. 



- ? . Jerrard, G. B. Ph. Mg. 12 



(1838) 345-. 



(1853) 381-.' 



(1873) 479-. 



"Jr 



when 



Wiener, C. Grunert Arch. 21 

 Gaudard, J. A. Gen. Civ. 2 



0. Terquem, 0. N. A. Mth. 



6 (1847) 391-. 

 0. S. (vi Adds.) Crelle J. 11 



(1834) 272-. 

 . Johnson, W. W. Des Moines 



Anal. 3 (1876) 118-. 

 . Sprague, T. B. Edinb. Mth. S. 



P. 3 (1885) 70-. 



1 m i 2"t _L + g 1 



Schlomilch, O. 



s m+l m + l' 



Grunert Arch. 14 (1850) 452-. 



0. Grunert Arch. 14 



r=oo. Schlomilch, 

 (1850) 454-. 



--- n (a n - 1) when n = oo . Schlomilch, 0. 



Schlomilch Z. 3 (1858) 387-. 

 --- f( x >y) when x and y are zero. Du 



Bois-Reymond, P. Crelle J. 70 (1869) 10-. 



--- /' (x) =lim. -M , theorem. Du Bois- 



Reymond, P. Mth. A. 16 (1880) 550. 

 values, calculus. Thieme,F.E. Arch. Mth. 



Ps. 58 (1876) 185-. 

 -- of fractions. Mansfield, J. [1816] Am. 



Ph. S. T. 1 (1818) 200-. 

 ---- . Galbraith, W. Edinb. Ph. J. 3 



(1820) 69-. 

 ---- . Marianini, P. D. Mod. S. It. 



Mm. 25 (1855) (pte. 2) 347-. 

 ---- . Young, J. R. 



Ph. Mg. 32 (1866) 



121-. 

 , L'H6pital's formula for ^ . 



Forestier, C. Toul. Ac. Sc. Mm. 10 (1878) 



482-. 

 ---- , theory (Woolhouse). Young, J. R. 



Ph. Mg. 8 (1836) 295-, 515- ; 9 (1836) 92-. 

 -- . -- , (reply to Young). Woolhouse, 



W. S. B. Ph. Mg. 8 (1836) 393-; 9 (1836) 



18-, 209-. 



De Morgan, A. QJ. 



Mth. 1 (1857) 204-. 



Ntvd. 17 (1870) 1-. 

 ---- indeterminate forms. Johnson, W. W. 



Mess. Mth. 4 (1875) 132- ; Des Moines Anal. 



4 (1877) 177-. 

 ----- . Marianini, P. D. Mod. Ac. 



Sc. Mm. 4 (1886) 379-. 

 --- quotients. Stolz, 0. Mth. A. 14 



(1879) 231- ; 15 (1879) 556-. 

 -- , theory. Cesdro, E. Palermo Cir. Mt. 



Ed. 1 (1887) 224-. 

 Limits. Cockle, (Sir) J. [1867] Mess. Mth. 4 



(1868) 116-. 



Sexe, S. A. N. Mg. Ntvd. 18 (1871) 



(pt. 2) 81-. 



. Woocl,DeV. Des Moines Anal. 9 (1882) 79-. 



, Berkeley's Analyst and its critics. Gibson, 

 G. A. Bb. Mth. (1899) 65-. 



, calculation. Cesdro, E. Mathesis 17 (1897) 

 177-. 



, calculus. Kirov, N. (xn) Mosc. Un. Mm. 

 8 (1835) 151-. 



, , new. Cauchy,A.L. (vi Adds.) Opusc. 

 Mt. Fis. 2 (1834) 1-, 133-, 261-. 



, Cauchy's theorems, extension. Peano, G. 

 Tor. Ac. Sc. At. 30 (1895) 20-. 



and continuity, conceptions. Cesdro, E. 

 Em. E. Ac.' Line. Ed. 4 (1888) (San. 1) 12-, 



, doctrine. Ncwcomb, S. 

 9 (1882) 114-. 



Des Moines Anal. 



258 



