6830 



Formula of Plane Trigonometry 



Extension to system of 3 non-intersecting 



straight lines. Grunert, J. A. Grunert 



Arch. 35 (1860) 1-. 

 Formulae deduced from definite integrals. 



Girault, C. Caen Ac. Mm. (1856) 19-. 

 regular polygons in-, or circum-scribed 



to circle. Kroutil, J. Casopis 19 (1890) 



70-; Fschr. Mth. (1891) 265. 

 a=bcosC + ccosB. Egidi, G. Em. 



N. Line. At. 43 (1890) 147-. 

 Fundamental formulae (Legendre). Osorio, 



R. G. Coimbra I. 3 (1855) 234-. 

 Half angles. Redl, F. Ens. Mth. 2 (1900) 



201-. 



Hero's polygon formulae, are they trigono- 

 metrical? Schmidt, W. Bb. Mth. 1 (1900) 



319-. 

 Multiple angles from equation of circle. 



Rudberg, F. Stockh. Ak. Hndl. (1823) 



229-. 

 Ozanam's formula for approximate solution of 



triangle. Brocard, H. Mathesis 9 (1889) 



161-. 

 . . Mansion, P. Mathesis 9 



(1889) 162-, 181-, 265-. 

 , ascribed to W. Snell. Le 



Paige, . Mathesis 10 (1890) 34-. 

 Quadrilaterals, area, given sum of 2 opposite 



angles. Anglin, A. H. H. QJ. Mth. 19 



(1883) 138-. 

 , , Lefevre's formula. Verhulst, P. F. 



Quetelet Cor. Mth. 6 (1830) 120-. 

 Series derived from sin 2 x + cos 2 a; = l. Lemon- 



nier, H. N. A. Mth. 4 (1845) 606-. 



6830 



Wallis's formula, and Stirling's, proved by 

 hyperbola. Mansion, . Brux. S. Sc. A. 

 23 (1899) (Pt. 1) 1-. 



(2 cos x) m , formulae. Anon. (vr558) Gergonne 

 A. Mth. 16 (1825-26) 254-. 



1 - cos n(f>, factorisation, and series for 



. jr etc. Huguenin, U. (vn) Amst. N. 



Ws. Ntk. Vh. 1 (1844) 1-. 

 Cos n x in sines or cosines of multiples of x. 

 Dirksen, E. H. Berl. B. (1845) 261-. 



Cos- in terms of cos a, note on equation. 

 A. N. A. Mth. 4 (1845) 52-, 



Guilmin, 

 122- . 



for tangent, cotangent, etc. Herschel, (Sir) 

 J. F. W. Nicholson J. 31 (r ' ' 



x n - 2 cos na + , factorisation. Airy, (Sir) 



G. B. [1868] Camb. Ph. S. T. 11 (pt. 2) 

 (1869) 426-. 



x n + - 2 cos n a , factorisation. Adams, (Prof.) 



J. C. [1868] Camb. Ph. S. T. 11 (pt. 2) 

 (1869) 444-. 



360 

 Cos , when rational. Hessel,J.F.C. Arch. 



Mth. Ps. 48 (1868) 81-. 

 Cos n<f> in powers of cos <f>. Heine, E. Mth. A. 



2 (1870) 187-. 

 Cos ma, sin ma as functions of sin a or cos a, 



demonstration. Desboves, A. N. A. Mth. 



14 (1875) 385-. 



x n - 2 cos n6 4 , factorisation. Ferrers, N. M. 



- cos - g cos 20 + etc. = log ( 

 Blissard, J. 



(1812) 133. 



etc. 



Mess. Mth. 5 (1876) 6. 



Cos 2 a + cos 2 ft + cos 2 -y + 2 cos a cos cos y - 1 = 0. 

 Zahradnlk, K. Arch. Mth. Ps. 62 (1878) 



Mess. Mth. 1 (1862) 124-. 330 ~' . 



Substitution of 1-* for A, etc. Dostor, G. = &>BC + ccoBB, substitution of (J+-) 



for 2cosJ5, etc. Cayley, A. (xn) 

 Un. Cir. [1] (1882) 241. 



N. A. Mth. 19 (1880) 362-. 

 Sums and products. Wiegers, C. Grunert 



Arch. 33 (1859) 338-. 

 System connecting sines and cosines of A, B, C 



and their differences. Glaisher, J. W. L. 



[1880] Mess. Mth. 10 (1881) 73-. 

 Systems, complete, in plane trigonometry. 



Meyer, W. F. D. Mth. Vr. Jbr. 5 (1901) 



(Heft 1) 61-. 

 Triangle, altitude. Dufour, C. [1877] Laus. 



S. Vd. Bll. 15 (1878) (PV.) 49-. 

 , area. Wallace, (Prof.) W. Camb. Mth. J. 



2 (1841) 35-. 

 , . Baker, M. [1885] A. Mth. 1 (1884-85) 



134- ; 2 (1885-86) 11-. 

 , , geometric derivation of formulae. 



Hultman, F. W. Ts. Mt. Fys. 2 (1869) 



, formulae, examination question. Gerono, 



G. C. N. A. Mth. 16 (1857) 76-. 

 Triangles, right angled, sides. Slop de Caden- 



berg, G. Mod. S. It. Mm. 13 (1807) 285-. 

 , , . AzzarelU, M. Em. At. N. 



Line. 26 (1873) 43-. 

 Wallis's formula, deduction. Herschel, (Sir) 



J. F. W. Nicholson J. 32 (1812) 13. 



J. H. 





Cos , quadratic radical expression for. Steg- 



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

 Cos n in terms of cosines of multiples of 6. 



Candida, G. Par. S. Phlm. Bll. 1 (1899) 



5-. 

 Sin nA and other formulae. Cagnoli, A . Verona 



Mm. S. It. 7 (1794) 1-. 

 Sin n 0, cos n and sinn0, cosnO, extension to 



hyperbolic areas. Brinkley, J. [1797] Ir. 



Ac. T. 7 (1800) 27-. 

 Sin (A B) and cos (A B) deduced from 



Ptolemy's theorem. Mollweide, C. Zach 



M. Cor. 26 (1812) 601-. 

 , method of obtaining formulas. 



Strong, T. Silliman J. 1 (1818) 424-. 

 . Thibault, . N. A. Mth. 2 (1843) 



309-. 

 , construction. Midy, . N. A. Mth. 



3 (1844) 374-. 

 . Arndl, F. Grunert Arch. 6 (1845) 



95-. 

 . Bianchi, G. Palomba Eac. 1 (1845) 



325-. 



464 



