1620 Binomial Coefficients 



sum of squares. Szily, K. Mth. Termt. Ets. 



11 (1893) 330- ; Mth. Nt. B. Ung. 12 (1895) 



84-. 

 by Taylor's series. Crelle, A. L. Berl. Ab. 



(1843) 1-. 

 theorem. Graves, C. [1865] Ir. Ac. P. 9 



(1867) 297-. 



. Hermes, J. Arch. Mth. Ps. 8 (1890) 269-. 

 theorems. Catalan, E. C. Liege S. Sc. Mm. 



15 (1888) No. 1, 41-, 133-, 250-. 

 transformation of integral powers into. Trudi, 



N. [1873] Nap. Ac. At. 6 (1875) A T o. 4, 13 pp. 



Binomial theorem, alternative proof. Schuster, 



A. Metz Ac. Mm. 72 (1893) 163-. 

 , case. Catalan, E. Brux. Ac. Bll. 16 



(1888) 194. 

 , new form. Mendizdbal Tamborrel, J. de. 



Mex. S. "Alzate" Mm. 4 (1890) 117- ; Fschr. 



Mth. (1890) 256. 

 before Newton. Marre, A. N. A. Mth. 



5 (1846) 488-. 



for positive integral index. Bouvier, 

 L. C. Gergonne A. Mth. 14 (1823-24) 205-. 



. Garcet, . N. A. Mth. 19 



(1860) 32-. 

 as case of a general theorem. 



Grunert, J. A. Grunert Arch. 1 (1841) 67-. 

 , proofs. Woodcock, T. B. A. Ep. (1889) 



501-. 

 , property. Andre, H. d\ N. A. Mth. 5 



(1846) 121-. 

 Binomials. Hello, M. P. de. Lisb. Ac. Sc. 



Mm. (Cor.) 4 (Pte. 1) (1815) 41-. 

 Card dealing problem, Gergonne's. Dickson, 



L. E. N. Y. Am. Mth. S. Bll. 1 (1895) 



184-. 



game, question. Le Cointe, J. L. A. (vni) 

 A. Mt. 5 (1863) 108-. 



games of patience. Badoureau, A. [1881] 

 Bv. Sc. 2 (1882) 475-. 



, problem. Vachette, A. N. A. Mth. 5 



(1846) 394-. 



, (i.e. playing cards) and remark on 

 theory of substitutions. Petersen, J. P. C. 

 (xn) Ts. Mth. 1 (1871) 74-. 



trick. Gergonne, J. D. Gergonne A. Mth. 

 4 (1813-14) 276-. 



puzzle and a law of numbers. Steen, A. 

 (xn) Ts. Mth. 1 (1865) 49-; 2 (1866) 1-; 

 3 (1867) 1-; 6 (1870) 1-, 181- ; 3 (1873) 156-. 



. Hertzsprung, S. (xn) 



Ts. Mth. 3 (1867) 97-. 



. Lorenz, L. V. (xn) 



Ts. Mth. 1 (1871) 53-. 

 Cards. Theory of whist. Badoureau, . Ev. 



Sc. 36 (1885) 587-. 



Chess. 



Bishop's move. Cherriman, J. B. (xn) Cn. 

 E. S. P. & T. 1 (1883) (Sect. 3) 19. 



Chessboard geometry, and indeterminate equa- 

 tion ax + by c. Laquiere, E. M. Par. S. 

 Mth. Bll. 7 (1879) 85-. 



, theorem on polygons having vertices at 



VOL. I. 



Chess 1620 



centres of squares. Laisant, C. A. Par. S. 

 Mth. Bll. 6 (1878) 156-. 



Chessboard geometry, theorem on triangle 

 having vertices at centres of squares. 

 Lucas, E. [1877] Par. S. Mth. Bll. 6 

 (1878) 9-. 



problem. Lavernede, T. Gard Mm. Ac. 

 (1838-39) 151-. 



. "Entre chiens et loup." Lucas, E. 



Ev. Sc. 5 (1883) 555-. 



problems. Lucas, E. Ev. Sc. 17 (1879) 

 154- ; 18 (1880) 948-; 19 (1880) 36-, 375-; 

 1 (1881) 408-, 783- ; 2 (1882) 365-. 



. Perott, J. Par. S. Mth. Bll. 11 (1883) 



173-. 

 End games. Cunningham, (Lt.-Col.) A. B. A. 



Ep. (1894) 564. 

 Knight's move. Brewster, (Sir) D. Edinb. Ph. 



J. 9 (1823) 236-. 

 . Bouvard, A. Dijon Ac. Mm. (1830) 



23-. 

 . Roget, P. M. (vi Adds.) Ph. Mg. 16 



(1840) 305-. 

 . Moon, R. Camb. Mth. J. 3 (1843) 



233-. 



. Minding, E. F. A. [1847] St Pet. 

 Ac. Sc. Bll. 6 (1848) 209-. 



. Volpicelli, P. C. E. 31 (1850) 314-. 



. Clausen, T. Grunert Arch. 21 (1853) 



91-. 

 . Anon, (vi 883) N. A. Mth. 13 (1854) 



181-. 

 . Polignac, C. de. C. E. 52 (1861) 



840-. 



. Geynet, A. C. E. 60 (1865) 484. 



. Urusov, (Prince) S. S. (xu) [1865] 



Eec. Mth. (Moscou) 2 (1867) (Pt. 1) 189-. 

 _ _. Regnier, A. Les Mondes 32 (1873) 



507-. 

 . F rost t A. H. [1876] QJ. Mth. 14 



(1877) 123-. 

 . Flye Sainte-Marie, C. Par. S. Mth. 



Bll. 5 (1877) 144-. 

 . Polignac, C. (Prince) de. [1880] Par. 



S. Mth. Bll. 9 (1881) 17-. 



. Lucas, E. Ev. Sc. 6 (1883) 370-. 



. Gilbert, G. K. [1885] Smiths. Misc. 



Col. 33 (1888) Art. 2, 88. (Wash. Ph. S. Bll. 7 



(1885).) 

 . Hofmann, F. N. A. Mth. 5 (1886) 



224-. 

 . Jordan, C. Palermo Cir. Mt. Ed. 2 



(1888) 59-. 

 . Brunei, . Bordeaux S. Sc. Mm. 4 



(1894) liii. 



. Wolf, R. Ziir. Vjschr. 39 (1894) 147-. 



, generalisation of problem. Fitting, F. 



Z. Mth. Ps. 45 (1900) 137-. 



illustrating an electrical problem. 

 Brunei, . Bordeaux S. Sc. Mm. 2 (1891) 

 xxxiv-. 



, number of reentrant moves in half- 

 boards. Laquiere, E. M. [1880] Par. S. 

 Mth. Bll. 9 (1881) 11-. 



, regular solutions of Euler's problem. 

 Laquiere, E. M. Par. S. Mth. Bll. 8 (1880) 

 82-, 132-. 



81 F 



