0410 



Rational Numbers; Arithmetical Operations 



0410 



G. C. M., number of divisions. Lionnet, E. 



N. A. Mth. 4 (1845) 617- . 

 , . Dupre, A. Liouv. J. Mth. 



11 (1846) 41-. 

 , . Grunert, J. A. Grunert 



Arch. 8 (1846) 137-. 

 , . Schulten, N. G. af (fil.). 



Helsingf . Acta 2 (1847) (pte. 2) 745-. 

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



10 (1851) 85-. 

 , Poinsot's method. Grunert, J. A. 



Grunert Arch. 7 (1846) 153-. 

 of two numbers, expression for. 



Lerch, M. Prag Sb. (1885) (Mth.-Nt.) 414-. 



Harmonic series, property that (2m)! M?- 



is divisible by 2m + 1. Schiappa Monteiro, 



A. Lisb. J. Sc. Mth. 5 (1898) 224-. 

 Imaginary bases for arithmetical notation. 



Griimwald, V. Brescia At. Cm. (1886) 



43-. 

 Involution and evolution, improvements. 



Nicholson, P. Tilloch Ph. Mg. 52 (1818) 



341- ; 57 (1821) 33-. 

 --- by logarithms, general rule. Eiddell, 



J. L. Silliman J. 7 (1849) 232-. 

 Laisant's theorem on 1, 2, 3 ... (n- 1) in scale 



of notation n. Sokolow, N. Fschr. Mth. 



(1896) 141. 

 Mental arithmetic. Cuthbertson, C. Nt. 45 



(1892) 78-. 

 -- . Haas, K. Nt. 45 (1892) 198-. 



arithmetical feats by Inaudi, report on. 

 Darboux, J. G. C. E. 114 (1892) 1335-. 



multiplication. Oakes, (Lieut.-Col.) W. H. 

 Assur. Mg. 10 (*1863) 326-. 



, process. Saussure, H. de. Laus. Bll. 

 S. Vd. 3 (1849-53) 256-. 



Multiplication, abridged, proof. Pedersen, H.A. 

 Mth. Ts. 2 (I860) 50-. 



, , Thoyer's method. Cauchy, A. L. 

 C. E. 12 (1841) 242-, 941-. 



, , various means. Gergonne, J. D. Ger- 

 gonne A. Mth. 7 (1816-17) 157-. 



, arithmetical note. Scott, C. A. Science 

 12 (1900) 648-. 



, commutative law in. Poussou [non Possou], 

 . Mntp. Eec. Bll. 2 (1805) 252-. 



and division, numerical. Querret, . Ger- 

 gonne A. Mth. 13 (1822-23) 277-. 



games, Lucas's " Arithmetique amusante" 

 in particular. Studnicka, F. J. Casopis 25 

 (1896) 289-; Fschr. Mth. (1896) 122. 



of numbers, facts concerning. Azoulay, . 

 Par. S. Phlm. Bll. 4 (1892) 71-. 



--- , problem. Berg, F. J. van den. N. 

 Arch. Wisk. 5 (*1879) 47-; 10 (1884) 202. 



by quarter squares. Laundy, S. L. Assur. 

 Mg. 6 (*1857) 121-. 



rules, nature and teaching. Baron, R. 

 Ens. Mth. 1 (1899) 317-. 



simplified by negative digits. Cunningham, 

 A. Nt. 48 (1893) 316. 



, various kinds. Grassmann, H. Crelle J. 

 49 (1855) 123-. 



Negative figures, arithmetic with. Longchamps, 

 G. de. As. Fr. C. E. (1893) (Ft. 2) 200-. 



Nomography (helps in calculation) and need 

 for its introduction in teaching. Pasquier, E. 

 Ens. Mth. 1 (1899) 350-. 



Numbers, problems in theory. Gelin, E. Ma- 

 thesis 16 (1896) (Suppl.) 34 pp. 



, property depending on scale of their nota- 

 tion. Andreini,A. G. Mt. 26 (1888) 315- ; 

 28 (1890) 43. 



, . Gambioli, . 



G. Mt. 27 (1889) 334-. 



, . Maillet, E. As. Fr. 



C. E. (1894) (Pt. 2) 242-. 



, . Gambioli, D. 



G. Mt. 33 (1895) 157-. 



Powers, formation, and root extraction. 

 Querret, . Gergonne A. Mth. 12 (1821- 

 22) 359-; 13 (1822-23) 163-. 



of integers. Mariantoni, F. Mathesis 18 

 (1898) 244-. 



Proportion, problems. Lucchesini, . C. E. 



11 (1840) 476-. 

 Pseudo-symmetric numbers. Lemoine, E. Par. 



S. Mth. Bll. 12 (1884) 155-. 

 Pythagorean triangles. Safford, T. H. Wise. 



Ac. T. 12 (1900) 505-. 

 Eeciprocals of numbers, theorems. Caminati, 



. As. Fr. C. E. (1887) (Pt. 1) 173. 

 , table, construction. Lehmann, J. W. H, 



As. Nr. 52 (1860) 1-. 

 Eoot extraction, new method. Gy'dry, S. (xn) 



Mag. Ak. Ets. (1850) 260- ; (1851) 57-, 



173-. 



, . Vazquez Prada, M. C. E. 121 



(1895) 635-. 



Eule of double-false-position. Poussou [non 

 Possou], . Mntp. Eec. Bll. 3 (1809) 

 285-. 



Scales of Notation. 



Berndtson, B. Stockh. Ac. Hndl. 39 (1818) 



212-. 

 best number for radix. Thiele, T. N. Kjtfb. 



Ov. (1889) 25-. 

 binary and octonary. Berdelle, C. As. Fr. C. 



E. (1887) (Pt. 2) 206-. 

 , theorems. Simony, O. Mth. A. 31 (1888) 



549-. 

 denary. Oettinger, L. Grunert Arch. 26 



(1856) 445-. 

 , divisibility. Singer, E. Mil. G. I. Lomb. 



5 (1853) 141-. 

 , . Hann, J. [1876] Z. Mth. Ps. 22 



(1877) 54-. 

 , , criteria. Ziige, . Arch. Mth. Ps. 17 



(1900) 45-. 

 , , two rules. Vervaet, P. J. Casopis 5 



(*1876) 189- ; Fschr. Mth. (1876) 84. 

 division, arithmetical. Fontes, . As. Fr. 



C. E. (1892) (Pt. 2) 182- ; Toul. Ac. Sc. Mm. 



4 (1892) 289-. 

 method of transformation. Barlow, P. 



Nicholson J. 25 (1810) 181-. 

 with negative base. Grunwald, V. G. Mt. 23 



(1885) 203-, 367. 

 number with digits reversed. Lemoine, E. 



As. Fr. C. E. (1883) 113-. 



45 



