2880 Application of Trigonometry 



Begular polygons, 17 sides, construction (von 



Staudt). Schroter, H. [1872] Crelle J. 75 



(1873) 13-. 

 _ , _, . Richmond, H. W. QJ. Mth. 



26 (1893) 206-. 

 \ , _. Gerard, L. Mth. A. 48 



(1897) 390-. 

 , , _. Fontene, G. Mathesis 19 



(1899) 179-. 

 , 19 and 37 sides, construction. Amaldi, 



I. G. Mt. 30 (1892) 141-. 

 1 257 sides. Baden- Ghijben, J. Amst. 



Vs. Ak. 2 (1868) (Ntk.) 1-. 

 , . Pascal, E. Nap. Bd. 26 (1887) 



33-. 

 Boots of unity, equation of periods. Pellet, A. 



As. Fr. C. E. (1900) (Pt. 1) 125. 

 , equations of three and four periods. 



Sylvester, J. J. As. Fr. C. B. (1880) 96-. 

 . , multisection. Sylvester, J. J. [1881] 



(xn) J. H. Un. Cir. [1] (1882) 150-. 

 , new system. Hamilton, (Sir) W. R. 



(vi Adds.) Ph. Mg. 12 (1856) 446. 

 , and operations relative to radicals. 



Wantzel, L. Ferussac Bll. Sc. Mth. 16 



(1831) 166-. 

 , primitive. Mollame, V. Nap. Bd. 



31 (1892) 179-. 

 _ , proposition. Stewart, B. [1856] 



Edinb. B. S. T. 21 (1857) 407-. 

 , _ (Stewart). Todhunter, I. [1865] 



Edinb. B. S. P. 5 (1866) 517-. 

 , theorem. Schroder, E. Z. Mth. Ps. 



22 (1877) 183-. 



, and transformation of functions. 

 Jiirgensen, C. Crelle J. 6 (1830) 195-. 



f gth. Cayley, A. Mess. Mth. 20 



(1891) 63. 

 , nth, theorems. Glaisher, J. W. L. 



B. A. Bp. (1875) (Sect.) 13-. 

 Table of complex prime factors, formed from 



5th roots of unity of primes of form 5^ + 1. 



Reuschle, [C. G.] Berl. Mb. (1859) 488-. 

 , 7th, llth, 13th, 17th, 



19th, 23rd, and 29th roots of unity of primes 



<1000. Reuschle, [C. G.] Berl. Mb. (1859) 



694-; (1860) 190-, 194-, 714-, 719-, 725-, 



729-. 

 Trigonometric equations. Guilmin, A. N. A. 



Mth. 5 (1846) 49-. 



functions deduced from equation x n =l. 

 Svanberg, J. Stockh. Ak. Hndl. 33 (1812) 



series, a special. PreobraZenskij , P. V. 

 Kazan S. Nt. (Ps.-Mth.) P. 6 (1888) 10-; 

 Fschr. Mth. (1888) 172-. 



sin ~ , arithmetical role. Cesdro, E. A. Mt. 



13 (1885) 315-. 

 cos p= , quadratic radical expression for. Steg- 



gall, . Edinb. Mth. S. P. 7 (1889) 4-. 

 XP-A, irreducibility. Mertens, F. Mh. Mth. 



Ps. 2 (1891) 291-. 

 x n -l, irreducible divisors. Gravelaar, N. L. 



W. A. N. Arch. Wisk. 20 (1893) 7-; Fschr. 



Mth. (1893-94) 158-. 



Transcendental functions 2890 



2890 Application of other tran- 

 scendental functions to arith- 

 metic. 



Asymptotic formulae, note. Gegenbauer, L. 

 Wien Ak. Sb. 93 (1887) (^6. 2) 35-. 



laws. Lejeune-Dirichlet, C. Berl. B. (1838) 

 13-. 



. Gegenbauer, L. Wien Ak. D. 49 (1885) 



(Ab. 1) 37-. 



-value of series 2 -_-L_ 5 . Mertens, 



F. Wien Ak. Sb. 106 (1897) (Ab. 2o) 411-. 



values of some numerical functions. Her- 

 mite, C. Crelle J. Mth. 99 (1886) 324-. 



(Hermite). Gegenbauer, L. 



Wien Ak. Sb. 99 (1891) (Ab. la) 387-. 

 Combinations of special kind. Bumakovskij , 



V. Ja. [1871] St Pet. Ac. Sc. Mm. (Rs.) 



20 (*1872) (Suppl.) No. 2, 71pp. 

 Continuous variables in theory of numbers. 



Hermite, C. Crelle J. 41 (1851) 191-. 

 Decomposition of number into sum of squares. 



Lorenz, L. V. (xn) Ts. Mth. 1 (1871) 97-. 

 . Mathews, G. B. L. 



Mth. S. P. 27 (1896) 55-. 

 ; four squares. Pepin, T. 



Bm. N. Line. At. 38 (1885) 139-. 

 Discontinuous factor, case. Lorenz, L. N. 



Ts. Mth. 1 (B) (1890) 76-; Fschr. Mth. (1890) 



296-. 



Division, theorem on remainders. Lejeune- 

 Dirichlet, G. Berl. B. (1851) 20-. 

 , (Lejeune-Dirichlet). Terquem, 0. 



N. A. Mth. 13 (1854) 396-. 

 Divisors of a number, theorems. Cesdro, E. 



G. Teix. J. Sc. 7 (1886) 3-. 



Elliptic functions, application. Kronecker, L. 



Liouv. J. Mth. 3 (1858) 265-. 

 , . Hermite, C. C. B. 53 (1861) 214- ; 



55 (1862) 11-, 85- ; Liouv. J. Mth. 7 (1862) 



25-. 



, _. stieltjes, -. C. B. 98 (1884) 663-. 



, to quadratic forms, binary. Hermite. 



C. [1883] St Pet. Ac. Sc. Bll. 29 (1884) 325-, 

 , . with negative discriminant. 



Petr, K. Prag Ceske" Ak. Fr. Jos. Bz. 



(Tfida 2) 9 (1900) Art. 38, 17 pp. ; Fschr. 



Mth. (1900) 212-. 



, solution of equation x s + y 3 = l. 

 Cayley, A. [1881] Camb. Ph. S. P. 4 (1883) 

 106-. 



, theory of numbers. Nazimov, 

 P. S. Mosc. Un. Mm. (Ps.-Mth.) 5 (1885) 

 67-; Par. EC. Norm. A. 5 (1888) 23-, 147-. 



, . Weber, H. Gott. Nr. 



(1893) 46-, 138-, 245-. 

 , of transformation-theory to theory of 



numbers. Weber, H. Mth. A. 43 (1893) 185-. 



and other functional constants, numerical 

 laws depending on. Bmigaieff, H. B. Bll. 

 Sc. Mth. 9 (1885) 89-. 



Euler's product, and arithmetical results. 



Jacobi, C. G.J. Liouv. J. Mth. 7 (1842) 85-. 

 Fuchsian functions and arithmetic. Poincare", 



H. Liouv. J. Mth. 3 (1887) 405-. 



224 



