6830 



Spherical Trigonometry. Triangles 



6830 



Locus of vertex of spherical triangle of given 



base and area (Lexell's theorem). Barbier, E. 



Les Mondes 4 (1864) 42-. 

 Malfatti's problem for spherical triangle. 



Mertens, F. [1872] Crelle J. 76 (1873) 



92-. 

 Nine-points circle of spherical triangle. Cayley, 



. QJ. Mth. 27 (1895) 35-. 

 Perimeter, inner side of. Mobiits, A. F. Leip. 



B. 12 (1860) 51-. 

 Perpendiculars. Grunert, J. A. Grunert Arch. 



22 (1854) 478-. 

 Plane construction. Birkbeck, W. L. Thomson 



A. Ph. 1 (1821) 259-. 



and spherical triangles. Danione,D. Brug- 

 natelli G. 5 (1822) 1-. 



. , analogies. Domenico, D. Brug- 



natelli G. 4 (1821) 259-. 

 . , , and analytical treatment. 



Tralles, J. G. Berl. Ab. (1816-17) 65-. 



, comparison. Grunert, J. A. 

 Grunert Arch. 1 (1841) 110-. 



, , degree of approximation of 



results on taking one for the other. Valente 



do Couto, M. Lisb. Mm. Ac. Sc. 3 (pte. 2) 



(1814) 119-. 

 , problem, solution. Steiner, J. 



Crelle J. 28 (1844) 375-. 

 Problems. Meissel, E. Arch. Mth. Ps. 65 



(1880) 429-. 

 Rational spherical triangles. Bessell,F. Arch. 



Mth. Ps. 65 (1880) 363-. 

 Eelations. Moth, F. X. As. Nr. 6 (1828) 



217-. 



between two triangles, plane or spherical. 

 Bretschneider, C. A. Grunert Arch. 2 (1842) 

 132-. 



Right angled spherical triangles. Adams, Jas. 



Thomson A. Ph. 3 (1822) 422-. 

 . Grunert, J. A. GrunertArch.il 



(1848) 225-. 



, problems solved by spherical 

 5-gon. Prestel, M. A. F. GrunertArch.il 

 (1848) 56-. 



, properties. Dostor, G. Arch. 



Mth. Ps. 51 (1870) 109-. 

 triangles, spherical and plane, analogies. 



Lhuilier, S. Gergonne A. Mth. 1 (1810-11) 



197-. 

 , , . Buzengeiger, K. H. J. 



Lindenau Z. 3 (1817) 198- . 

 Small-circle spherical triangle. Hudson, E. C. 



QJ. Mth. 27 (1895) 378-. 



spherical triangle compared with plane. 

 Buzengeiger, K. H. J. Lindenau Z. 6 

 (1818) 264-. 



. Grunert, J. A. As. Nr. 52 



(1860) 49-. 

 triangles. Burg, A. Wien Jb. Pol. I. 7 



(1825) 86-. 

 . Grunert, J. A. Grunert Arch. 9 



(1847) 8-. 

 . Caldarera, F. Palermo At. 2 (1853) 



14 pp. 

 Solution. Unferdinger, F. Arch. Mth. Ps. 41 



(1864) 142-. 

 . Eagona, D. Mod. Ac. Sc. Mm. 5 (1887) 



53-. 



Solution of all triangles, spherical and plane, 



by one formula. Steffenelli, A. von. Munch. 



D. (1813) 343-. 

 , case (a, b, C). Mollweide, C. Lindenau Z. 



1 (1816) 459-. 

 , ( , , ). Sang, E. Edinb. N. Ph. 



J. 14 (1833) 311-. 

 .constructive. Steinheil, C. A. von. Munch. 



Sb. (1869) (II) 369-. 

 , given altitudes. Unferdinger, F. Wien 



Sb. 51 (1865) (Ab. 2) 97-. 

 , . Hunyady, E. von. Z. Mth. Ps. 12 



(1867) 91-. 

 , perpendiculars. Skrivan, G. Grunert 



Arch. 28 (1857) 471-. 

 , side, opposite angle, and one other 



element. Matzka, W. Grunert Arch. 11 



(1848) 300-. 

 , sides. Thomson, (Prof.) James. Edinb. 



J. Sc. 4 (1831) 124-. 

 , , in plane or spherical triangles. 



Bretschneider, C. A. Arch. Mth. Ps. 52 



(1871) 371-. 

 , (a, b, A) or (A, B, a). Lhuilier, S. 



Gergonne A. Mth. 2 (1811-12) 257-. 



by plane triangles on gnomonic projection. 

 Glotin, P. Bordeaux S. Sc. Mm. 3 (1880) 

 395-. 



, special cases. Saporetti, A. Bologna Ac. 



Sc. Mm. 7 (1897) 213-. 

 , and stereographic projection. Martinetti, V. 



Mil. I. Lomb. Rd. 24 (1891) 830-, 976-. 

 Spherical triangle, one side small, solution. 



Puissant, L. Par. EC. Pol. Cor. 2 (1809-13) 



236-. 

 , ABC, angles between OA and chord BC. 



Grunert, J. A. Grunert Arch. 26 (1856) 



113-. 

 with C = A + B. Unferdinger, F. Arch. 



Mth. Ps. 53 (1871) 344-. 

 Substitution of chords for sides. Nagel, A. 



Schlomilch Z. 1 (1856) 257-. 

 Surface. So-rnin, J. Toul. Mm. Ac. 5 (1855) 



351-. 

 Transversals bisecting sides. Schawen, P. von. 



Z. Mth. Ps. 27 (1882) 126-. 



joining mid-points of sides, and applications. 

 Unferdinger, F. Wien Sb. 52 (1866) (Ab. 2) 



323-. 



Unlimited spherical triangles. Chaurenet, W. 

 Gould As. J. 1 (1851) 39-, 41-. 



Substitution groups, Napier's rules in particular. 

 Pund, 0. [1897] Hamb. Mth. Gs. Mt. 3 

 (1900) 290-. 



Transformation of elliptic integrals, application 

 to spherical trigonometry. Russell, R. QJ. 

 Mth. 20 (1885) 378-. 



Transversals in spherical triangles and quadri- 

 laterals. Rogner, J. Arch. Mth. Ps. 45 

 (1866) 318-. 



Spheroidal triangle, small, reduction of angles 

 to angles of corresponding plane or spherical 

 triangle. Hansen, P. A. Leip. B. 21 (1869) 

 138- ; Leip. Ab. Mth. Ps. 9 (1871) 289-. 



471 



