0410 



Rational Numbers; Arithmetical Operations 



Decimal point, determination of position in 



multiplication and division. Jelinek, V. 



Casopis 20 (1891) 35- ; Fschr. Mth. (1891) 



166. 

 Decimals; approximation. Amiot, B. Rouen 



Ac. Tr. (1841) 161- ; N. A. Mth. 10 (1851) 



238-. 

 , multiplication. Bernauggi, I. Verona Mm. 



S. It. 6 (1792) 1-. 

 , recurring, division by 11. Transon, A. 



N. A. Mth. 4 (1845) 227-. 

 , , formula for conversion. Trembloy, . 



N. A. Mth. 1 (1842) 522-. 

 , reduction to fractions. Ponte-Horta, F. da. 



Lisb. J. Sc. Mth. 1 (1868) 275-. 

 Discontinuous geometry. Bugaev, N. V. [1890] 



Bee. Mth. (Moscou) 15 (1891) 600- ; Fschr. 



Mth. (1891) 726. 

 Division, abridged. Finck, B. N. A. Mth. 4 



(1845) 328-, 658-; 5 (1846) 599-. 

 , . Crelle, A. L. Crelle J. 31 (1846) 167-. 

 , . Crosson,A. N. A. Mth. 5 (1846) 244-. 

 , . Guy, . N. A. Mth. 5 (1846) 460-. 

 , . Verhulst, P. F. N. A. Mth. 5 (1846) 



629-. 

 , . Spitzer, S. [1850] Haidinger B. 7 



(1851) 175-. 



0410 



Hummel, F. H. 



, . Lionnet,E. N. A. Mth. 11 



, . Hausel,. 

 , . Rouche,E. 

 , . Henry, C. 

 , long. 



N. A. Mth. 14 

 N. A. Mth. 16 

 N. A. Mth. 20 



1852 

 1855 

 1857 

 1881 



148-. 

 129-. 

 152-. 

 213-. 



Dodgson, G. L. Nt. 57 (1897-98) 

 Nt. 57 (1897- 

 N. A. 



, . Christie, R. W. D. 



98) 390-. 

 , and ordinary. Turquan, . 



Mth. 13 (1854) 170-. 



, singular case. Adville, . N. A. 

 Mth. 11 (1852) 100-. 



of approximate numbers, rule. Verhulst, 

 P. F. Brux. Ac. Bll. 13 (1846) 696-. 



, arithmetical, new rule. Peirce, C. 8. 



Science 2 (*1883) 788-. 

 , , theory. Faucheux, L. E. N. A. Mth. 



14 (1854) 51-. 

 , complementary. Ter quern, O. N. A. Mth. 



6 (1847) 425-. 

 , . Meech, L. W. Des Moines Anal. 9 



(1882) 97-. 



and evolution, rationale of processes. 

 Niederrist, . Grunert Arch. 35 (1860) 

 201-. 



, Fourier's, ^and application to square root. 

 Schaar, M. Brux. Ac. Bll. 18 (1851) (pte. 2) 



, Gerbert's rules. Friedlein, G. Z. Mth. 



Ps. 9 (1864) 145-. 

 , new method. Kostenec, A. Casopis 15 



(1886) 74-; Fschr. Mth. (1886) 127-. 

 , numerical, easy method. Crelle, A. L. 



Crelle J. 13 (1835) 209-. 

 , results in. Langley, E. M. Mth. Gz. 1 



(1900) 205-, 275-. 



and subtraction, extended. Callegari, P. 

 Bologna N. Cm. 6 (1844) 513- ; 7 (1844) 529-. 



Divisors, fractional, in arithmetic. Terquem, O. 

 N. A. Mth. 8 (1849) 246-. 



Evolution by subtraction. 



Ph. Mg. 10 (1880) 190-. 

 Factorisation and factorial calculation. Paci- 



notti, L. Pisa A. Un. Tosc. Sc. Cosm. 2 



(1851) 143-. 

 Fraction and quotient, fusion of notions. 



Bobynin, V. V. Bb. Mth. (1899) 81-. 

 Fractions, compound, simplification. Euler, L. 



[1779] St Pet. Ac. Sc. Mm. 1 (1803-6) 3-. 

 , elementary theory. Meray, C. , & Riquier, C. 



N. A. Mth. 8 (1889) 421-. 

 , estimation. Petrie, W. M. F. [1875] Nt. 



13 (1876) 127-. 



with numerator 1, theorems. Fuss, N. 

 [1809] St Pet. Ac. Sc. Mm. 10 (1826) 27-. 



of 1, conversion to decimals. De Morgan, 

 A. Assur. Mg. 11 (*1864) 53-. 



, theorem. Posnikov, M. V. Kazan S. Nt. 



(Ps.-Mth.) P. 4 (1886) 238. 

 , transformation. Lagrange, J. L. Par. EC. 



Pol. J. 2 (1798) (5 e cah.) 93-. 

 , . Penjon, . Gergonne A. Mth. 4 



(1813-14) 265-. 

 , into decimals. Arndt, J. A. Grunert 



Arch. 1 (1841) 101. 

 , . Dienger, J. Grunert Arch. 11 



(1848) 232. 



' ar, expansion in sorites. Sylvester, 



J. J.' Am. J. Mth. 3 (1880) 332-, 388-. 

 , , reduced to decimal, number of figures. 



Sornin, J. N. A. Mth. 8 (1849) 50-. 

 Frolov's groups of numbers. Studnicka, F. J. 



Casopis 19 (1890) 124- ; Fschr. Mth. (1890) 



196. 

 Functions obtained by combining the four 



fundamental operations. Bianchi, G. Pa- 



lomba Eac. 2 (1846) 326-. 

 Geometry, generalisation of arithmetical opera- 

 tions in reference to. Wiegand, A. Mathe- 

 matician 3 (1850) 60-. 

 G. C. M. Finck, B. N. A. Mth. 1 (1842) 



353-. 

 . Bertrand, J. N. A. Mth. 8 (1849) 



358-. 

 . Gordan, P. [1873] Mth. A. 7 (1874) 



433-. 



. Gegenbauer, L. Wien Ak. Sb. 91 



(1885) (Ab. 2) 333-. 



, abridged method of finding. Nieven- 



gloski, G. H. N. A. Mth. 8 (1849) 447-. 



, Lame's theorem. Finck, B. N. A. 



Mth. 4 (1845) 71-. 



and L. C. M. Gergmme, J. D. Ger- 

 gonne A. Mth. 21 (1830-31) 117-. 



. Barrieu, P. (xn) Ma- 

 thesis 3 (1883) 217- ; N. A. Mth. 14 (1895) 

 95-, 165-, 214-. 



, mean values. Cesaro, E. A. Mt. 13 



(1885) 235-. 



, new method. Binet, J. P. M. C. B. 



13 (1841) 349-. 



, number of divisions. Lame,G. C.B. 



19 (1844) 867-. 



, . Binet, J. P. M. C. B. 19 



(1844) 937-. 



, . Nievengloski, G. H. N. A. 



Mth. 4 (1845) 568-. 



44 



