6830 Formulae 



General demonstration. Harst, A, D. van der. 



N. Arch. Wisk. 17 (1890) 176- ; Fschr. Mth. 



(1890) 600. 

 Generalisation. Chauvenet, IF. Gould As. J. 



3 (1854) 50-, 137. 

 Interpretation of double sign in certain formulae. 



Spherical Trigonometry 6830 



Fundamental principle. Vincent, A. J. H. 



N. A. Mth. 1 (1842) 33-. 

 . Crova, (Prof.) . (vi Adds.) Perpi- 



gnan Bll. S. Ag. Pyr. Orient. 7 (1848) 255. 



. Foucaut, f C. N. A. Mth. 8 (1849) 58. 



. Patry, E. N. A. Mth. 17 (1858) 208-. 



Thomson, (Prof.) James. Ph. Mg. 10 (1837) Grea t c irc Delation betw^n spkerical 



18-. 



Walton, W. QJ. 



Lagrange's formulae, deduction from theorem 



in determinants. Studnicka, F. J. Prag 



Sb. (1875) 1-. 

 Napier's analogies. Gerono, G. C. N. A. Mth. 



2 (1843) 222-. 

 . Grunert, J. A. Grunert Arch. 3 (1843) 



104-. 



. Cortazar, J. N. A. Mth. 6 (1847) 218-. 



. Werner, O. Grunert Arch. 24 (1855)95-. 



Ptolemy and formulae of spherical trigono- 

 metry. Schubert, F. T. [1796] St Pet. Ac. 



Sc. N. Acta 12 (1801) 165-. 

 Significance in case of complex argument. 



Schilling, F. Gott. Nr. (1891) 188-. 

 Spherical excess. Grunert, J. A. Grunert 



Arch. 16 (1851) 483-. 

 , formulae, derivation. Werner, O. [1857] 



St Pet. Ac. Sc. Bll. 16 (1858) 11-. 

 , Lhuilier's formula. Gent, . Grunert \-~-j-v ~^J_ j ac j e 



Arch. 20 (1853) 358-. 16 (1898) 40-. 

 j Prouhet, E. N. A. Mth. 15 .' Lovett, E. O. N. Y. Am. Mth. 



(1856) 91-. g_ EH 4 (I 8 g 8 \ 552-. 

 . Ligowski, W. [1875] Arch. , graphic proof . Herschel, A. S. 



Mth. Ps. 58 (1876) 96-. Nt . 5 ( 1 87 2)24, 141-. 

 , .demonstration. Lobatto, R. (vm) , partly anticipated. De Morgan, 



Arch. Mth. Ps. 39 (1862) 240. j. Ph. Mg. 22 (1843) 350-. 

 of quadrilateral in small circle, and radius Orthogonal substitutions, elliptic functions, etc. 



tances from three points. 



Mth. 4 (1861) 328-. 

 Hexagon, rectangular skew, trigonometry. 



Burnside, W. Mess. Mth. 28 (1899) 92-. 

 Identity, case. Cayley, A. Mess. Mth. 1 



(1872) 145. 

 Mechanical solution of problems. Rambaut, 



A. A. Dubl. S. Sc. P. 5 (1886-87) 642-. 

 Method, new. Pessuti, G. Mod. S. It. Mm. 



15 (1811) 197-. 

 Mnemonics. Chasles, M., & Forestier, . 



N. A. Mth. 12 (1853) 312-. 

 Napier's rules of circular parts. Bowditch, N. 



Am. Ac. Mm. 3 (1809) 33-. 

 . Hemert, W. J. J. van, & 



Schroder, J. C. Amst. Mengelwerk 2 (1816) 



105-. 

 . Ivory, J. Tilloch Ph. Mg. 58 



(1821) 255-. 



Edinb. Mth. S. P. 



of small circle circumscribing quadrilateral. 

 Hart, H. Mess. Mth. 4 (1875) 181-. 



polygon, area. Quetelet, L. A. J. [1820-32] 

 Brux. Ac. Sc. Mm. 2 (1822) 105- ; Quetelet 

 Cor. Mth. 7 (1832) 278-. 



triangles. Bretschneider, C. A. Crelle J. 

 13 (1835) 85-, 145-. 



. Dienger, J. Grunert Arch. 7 (1846) 



225-. 



, cotangent formulae. Unferdinger, F. 

 Arch. Mth. Ps. 50 (1869) 107-. 



Supplements of angles, introduction. Grebe, 

 E. W. Grunert Arch. 39 (1862) 226-. 



ABC 



sin A + sin B + sin C = 4 cos 



generalisation. 

 (1852) 34-. 

 A A 



"2 ' 

 Arrest, H. d'. Leip. B. 



sin , cos , etc., geometric demonstration. 



Barbier, E. N. A. Mth. 4 (1865) 421-. 

 sin a cos B = cos b sin c - sin b cos c cos A. 

 Hertz, K. [1869] (xn) Eec. Mth. (Moscou) 

 4 (1869-70) (Pt. 2) 94-. 



tan - - tan - (cos A + i sin A) 



1 + tan - tan - (cos A + i sin A) 

 Cayley, A. L. Mth. S. P. 11 (1879-80) 48-. 



Study, E. Leip. Mth. Ps. Ab. 20 (1893) 85-. 

 Polar triangles, and polar trihedral angles. 

 Harst, A. D. van der. N. Arch. Wisk. 17 

 (1890) 188- ; Fschr. Mth. (1890) 600. 



in spherical trigonometry, history of. 

 Braunmuhl, A. von. Bb. Mth. (1898) 65-. 



Projection, stereographic, application to spheri- 

 cal trigonometry. Grunert, J. A. Grunert 

 Arch. 39 (1862) 318-. 



Quadratic binary forms, relation of system of 

 three, to spherical trigonometry. Stephanos, 

 C. Par. S. Mth. Bll. 10 (1882) 134-. 



Eational normal configurations M\ of S 6 . 

 Young, G. C. Tor. Ac. Sc. At. 34 (1898) 

 429- or 587-. 



Eesultants, concept. Meyer, F. Crelle J. Mth. 

 115 (1895) 209-. 



Simplification of spherical trigonometry. 

 Keogh, C., <& Lebesgue, V. A. N. A. Mth. 

 12 (1853) 304-. 



Spherical excess. Grunert, J. A. Grunert 

 Arch. 38 (1862) 220-. 



. Bacaloglo, E. Grunert Arch. 39 (1862) 



237-. 



, construction. Terquem, 0. N. A. Mth. 



5 (1846) 17-. 



, Gauss's theorem. Clausen, T. As. Nr. 

 20 (1843) 33-. 



oblong, area. Gudermann, C. Crelle J. 42 

 (1852) 280-. 



polygonometry. Raabe, J. L. Crelle J. 2 

 (1827) 9-. 



469 



