0410 Scales of Notation 



number with digits reversed, problem. Laisant, 

 C. A. Bordeaux S. Sc. Mm. 1 (1876) 403-. 



, theorem. Lemoine, E. As. Fr. 



C. E. (1884) (Pt. 2) 58-. 



recurring digits, theorem. Glaisher, 

 J. W. L. [1875] Mess. Mth. 5 (1876) 3-. 



whose powers terminate in same digits. 

 Tanner, H. W. L. [1877] Mess. Mth. 7 

 (1878) 63-. 



square ends in same digits as itself. 

 Pabnstrom, A. Christiania Skr. (Mth.-Nt. 

 Kl.) (1900) No. 3, 16 pp. 



12345679, properties. Plateau, J. A. F. 

 (vm) Brux. Ac. Bll. 16 (1863) 62-. 



, (Plateau). Hooton, J. J. Intell. 

 Obs. 4 (1864) 439. 



. , . Plateau, J. A. F. Brux. Ac. Bll. 



38 (1874) 469-. 

 , , and generalisation. Laisant, G. A, 



Lisb. J. Sc. Mth. 5 (1898) 203-. 

 octonary. Johnson, W. W. [1891] N. Y. 



Mth. S. Bll. 1 (1892) 1-. 

 , application to system of weights and 



measures. Taylor, A. B. Am. Ph. S. P. 



24 (1887) 296-. 

 powers of integers. Drot, . N. A. Mth. 4 



(1845) 637- ; 5 (1846) 25-. 

 . Schlomilch, 0. Z. Mth. Ps. 12 



(1867) 350. 

 . Andre, D. N. A. Mth. 16 (1877) 



370-. 

 problems. Berdelle, C. As. Fr. C. E. (1898) 



(Pt. 2) 139-. 

 quinary, denary, and vicenary. Marre, A. 



Liouv. J. Mth. 13 (1848) 233-. 

 sum of digits. Berton, . N. A. Mth. 18 



(1859) 209-. 

 of certain numbers. Sanctis, P. de. 



Em. N. Line. At. 46 (1893) 115-, 183- ; 47 



(1894) 53-; 50 (1897) 11-; 54 (1901) 18-. 

 numbers, last. Gelin, (I'Abbe) . 



Les Mondes 43 (1877) 430-. 

 sum of three consecutive numbers. 



Egidi, G. Em. N. Line. At. 46 (1893) 63-. 

 sums of digits, numbers. Terrot, C. H. [1843] 



Edinb. E. S. T. (1849) 87-. 

 theorem. Crelle, A. L. Crelle J. 30 (1846) 



215-. 

 theorems. Sanctis, P. de. Em. N. Line. 



Mm. 11 (1895) 145-. 

 "Tonal system." Nystrom, J. W. Franklin 



I. J. 46 (1863) 263-, 337-, 402-. 

 2n-ary. Studnicka, F. J. Prag Sb. (1896) 



(Mth.-Nt.) No,. 7, 10 pp. 

 with variable base. Sokolow, N. Fschr. Mth. 



(1896) 122. 

 weights problem. Sornin, J. Toul. Mm. Ac. 



6 (1856) 37-. 

 . Stahlberger, E. Carl Epm. 5 (1869) 



. F., E. R. Nt. 42 (1890) 568. 



. Willis, J. Nt. 43 (1891) 30-, 198. 



. Everett, J. D. Nt. 43 (1891) 104, 



199. 



. Macmahon, P. A. Nt. 43 (1891) 

 113-. 



. B., E. E. Nt. 43 (1891) 198-. 



Irrational Numbers 0420 



weights problem, analogues. Matter, H. F. 

 Z. Mth. Ps. 21 (1876) 227-. 



Square of large number. Pastorcek, J. M. 

 Casopis 6 (*1877) 277-; Fschr. Mth. (*1877) 

 808-. 



property of 48 ... 89, analogous numbers. 

 Laisant, C. A. Par. S. Phlm. Bll. 4 (1892) 

 77-. 



Sum or difference of products of factors. 

 Austin, J. [1815] Am. Ph. S. T. 1 (1818) 

 181-. 



Transformation of product of natural num- 

 bers. Frisiani, P. Mil. Effem. As. (1850) 

 44-. 



"Unitation," new arithmetical operation. 

 Walenn, W. H. Ph. Mg. 36 (1868) 346-; 

 46 (1873) 36-; 49 (1875) 346-; 50 (1875) 

 117-, 521- ; 1 (1876) 546-; 4 (1877) 375-; 

 5 (1878) 214- ; 9 (1880) 121-, 271-. 



0420 Existence of irrational and 

 transcendental numbers; infinite 

 processes adapted to rational 

 numbers. 



Agreement of two methods of approximation to 



a square root (Newton & Lagrange). Carrara, 



B. G. Mt. 28 (1890) 39-. 

 Algorithm for the calculation of the nth root 



of a. Schmidt, C. Mth. A. 45 (1894) 301-. 

 Approximate evolution, note. Tanner, H.W.L. 



L. Mth. S. P. 23 (1892) 295-. 



representation of irrationals by rational 

 fractions. Hurwitz, A. Mth. A. 39 (1891) 

 279-. 



roots of numbers. Philbrick, . Iowa Ac. 

 Sc. P. (* 1875-80) 24. 



and quotients, errors. Anon, (vi 546) 

 Gergonne A. Mth. 13 (1822-23) 175-. 



Approximation by rational fractions. Hurwitz, 



A. Mth. A. 44 (1894) 417-. 

 Archimedes and v '3. Thiele, T. N. Ts. Mth. 



2 (1884) 151- ; Fschr. Mth. (1884) 8. 

 Arithmetic, transcendental. Eisenstein, G. 



Crelle J. 29 (1845) 177-. 

 Arithmetical theorems, four. Strnad, A. Ca- 

 sopis 17 (1888) 204- ; Fschr. Mth. (1888) 



185. 

 Arithmetization of mathematics. Pierpont, J. 



N. Y. Am. Mth. S. Bll. 5 (1899) 394-. 

 Chuquet, N., extraction of square root, 1484. 



Tannery, P. Bb. Mth. (1887) 17-. 

 Chuquet's work, mean rule. Mansion, P. 



Bb. Mth. (1888) 36. 

 Comparison of magnitudes ; Brouncker's method 



extended. Sang, E. [1870-90] Edinb. E. 



S. T. 26 (1872) 59-; Edinb. E. S. P. 18 



(1892) 341-. 

 Continued radicals. Bouche,A. M.-et-L. Mm. 



S. Ac. 12 (1862) 81-. 

 Convergents to the roots of a number. Muir, T. 



Edinb. E. S. P. 19 (1893) 15-. 

 Cube, duplication with any approximation. 



Popov, A. T. (xii) Kazan Un. Mm. 6 (1871) 



233-. 



