0420 Irrational Numbers 



Cube, duplication, new geometrical relation 

 serving to solution of problem. Buonofalce, 

 G. Les Mondes 41 (1876) 338-. 



root of 2, computation. Martin, Art. [1877] 

 Mess. Mth. 7 (1878) 50-. 



, value to 28 places. Gray, P. 

 Mess. Mth. 5 (1876) 172-. 



, verification and extension of 

 value. Gray, P. [1877] Mess. Mth. 7 

 (1878) 51-. 



roots of binomials, extraction. Lockhart, J. 

 Thomson A. Ph. 6 (1815) 152-. 



(Lockhart). Horner, W. G. 



Thomson A. Ph. 8 (1816) 279-, 388-. 

 Decimals, non-terminating, property. Young, 



J. R. Ph. Mg. 36 (1850) 15-. 

 , periodicity. Looff, W. Grunert Arch. 16 



(1851) 54-. 

 , recurring. Adams, Jas. Thomson A. Ph. 



2 (1821) 16-. 

 , . Catalan, E. C. N. A. Mth. 1 (1842) 



457-. 

 , . Stammer, W. Grunert Arch. 27 (1856) 



123-. 

 , . Hansted, B. (xn) Ts. Mth. 2 (1878) 



180-. 

 , . Glaisher, J. W. L. B. A. Rp. (1878) 



471- ; Nt. 19 (1879) 208- . 

 , . Schlomilch, 0. X. Z. Mth. Ps. 25 



(1880) 416. 

 , , class. Bouniakowsky, V. St Pet. Ac. 



Sc. Bll. 27 (1881) 362-. 

 , , divisibility. Gamier, F. P. Moigno 



Cosmos 6 (1855) 238-. 

 , , for -A-, general case for any radix. 



Glaisher, J. W. L. Mess. Mth. 2 (1873) 



188. 

 , , and Henry Goodwyn's tables. Glaisher, 



J. W. L. [1878] Camb. Ph. S. P. 3 (1880 



185-. 

 , , mixed, theory. Broda, K. [1874] 



Arch. Mth. Ps. 57 (1875) 297-. 

 , , new properties. Coninck G. N. A. 



Mth. 13 (1874) 569-. 

 , , periods. Dienger, J. Crelle J. 39 



(1850) 67-. 

 , , property (Colling). Oliver, J. E. 



Camb. (M.) Mth. M. 1 (1859) 345-. 

 , , theory. Sturm, J. B. Grunert Arch. 



33 (1859) 94-. 

 , , . Broda, K. Arch. Mth. Ps. 56 



(1874) 85-. 

 , theorem. Hansted, B. G. Teix. J. Sc. 2 



(1880) 154- . 



Equation x m =a + b,J -1. Valat, . Bor- 

 deaux Act. Ac. Sc. (1844) 177-. 

 Euclid, Book X, summary. Peano, G. Ev. 



Mt. 2 (1892) 7-. 

 Fractions approximating to square root of a 



variable. Cebysev, P. St Pet. Ac. Sc. Mm. 



(Rs.) 61 (1890) (Suppl.) No. 1, 22 pp. ; Acta 



Mth. 18 (1894) 113-. 

 , periodic. Laisant, G. A. Bordeaux S. 



Sc. Mm. 3 (1880) 213-. 

 , , in given systems of numbers, law of 



formation. Broda, K. Arch. Mth. Ps. 68 



(1882) 85-. 



Irrational Numbers 0420 



Fractions, periodic, laws. Moret-Blanc, . 



N. A. Mth. 14 (1875) 229-. 

 , , means of finding period. Laisant, A. 



Les Mondes 19 (1869) 331-. , 

 , , properties. Beaujeux, E., <& Laisant, A. 



N. A. Mth. 7 (1868) 289-. 

 , , theorems. Thibault, . N. A. Mth. 2 



(1843) 80-. 



Incommensurability , general theorem. Maizwre, 



de. Gergonne A. Mth. 1 (1810-11) 



293-. 

 , and its treatment in certain books. 



Amicis, E. de. Rv. Mt. 5 (1895) 110-. 

 Incommensurable fraction, development. 



Young, J. R. Ph. Mg. 36 (1850) 128-. 



lines. Lebesgue, V. A. N. A. Mth. 3 



(1844) 436-. 



, \/3 : 1. Bretschneider, C. A. Grunert 

 Arch. 3 (1843) 440-. 



number, meaning to be attached to the term, 

 etc. Meray, C. Par. EC. Norm. A. 4 

 (1887) 341-. 



numbers. Wantzel, L. Par. EC. Pol. J. 15 

 (1837) (25 e cah.) 151-. 



. of algebraic origin. Wantzel, L. N. A. 

 Mth. 2 (1843) 117- ; Par S. Phlm. P.-V. (1843) 

 10-. 



, general remarks. Girault, . Rouen 



Tr. Ac. (1849-50) 96-. 

 1 geometrical proof of theorem. Sylvester, 



J. J. (xn) J. H. Un. Cir. [1] (1882) 179-, 



209. 



and limits. Jablonski, E. N. A. 

 Mth. 20 (1881) 241-. 



, property. Stephanos, G. Par. S. Mth. 



Bll. 7 (1879) 81-. v 



, theorem of Cebysev. Le Paige, C. 

 Brux. Ac. Bll. 25 (1893) 235-. 



quantities. Leger, E. Liouv. J. Mth. 1 

 (1836) 93-. 



, elementary theory. Egidi, G. Rm. N. 



Line. At. 46 (1893) 149-. 



, theorem. Lebesgue, V. A. Liouv. J. 

 Mth. 1 (1836) 266-. 



roots and logarithms, definitions. Guilmin, 



A. N. A. Mth. 6 (1847) 313-. 

 Irrational formulae, irreducible. Bouniakowsky, 



V. [1840] St Pet. Ac. Sc. Mm. 4 (1841) 



471-. 



. , reciprocals. Canter zani, S. Bologna 

 Mm. I. It. 1 (pte. 2) (1806) 301-. 



numbers. Minnigerode, B. Mth. A. 4 

 (1871) 497-. 



. Peano, G. Rv. Mth. 6 (1896-99) 126-. 



, arithmetical properties. Ghristoffel, 

 E. B. A. Mt. 15 (1887-88) 253-. 



, definition. Illigens, E. Mth. A. 35 



(1890) 451-. 



development in rational continued 

 fractions. Schulten, N. G. af (fil.) [1847] 

 Helsingf. Acta 3 (1852) 405- . 



, introduction. Pasch, M. Mth. A. 40 



(1892) 149-. 

 , , with method of contiguous classes. 



Capelli, A. G. Mt. 35 (1897) 209-. 

 , theorems. Ramsay, A. Stockh. 6fv. 



39 (1882) No. 9, 21-. 



47 



