8810 



Curves on Surfaces. Loxodromes 



8810 



Latitude and longitude, formulae. Oriani, B. 



Mil. Effem. As. (1808) 3-. 

 Line-element of surface, certain forms. 



Massimi, P. Em. N. Line. At. 52 (1899) 93-. 

 Lines of equal slope on given surfaces. 



Schlamilch, 0. Schlomilch Z. 1 (1856) 250-. 



greatest slope. Stem, A. (xn) Ts. 

 Mth. 1 (1865) 123-. 



. Breton (de Champ), . C. B. 



70 (1870) 982-. 



, differential equation. Breton 

 (de Champ), . C. B. 64 (1867) 407-. 



, ridge lines and channels. 

 Boussinesq, J. C. B. 73 (1871) 1368- ; 75 

 (1872) 198-, 835-. 



shadow for some surfaces. Pirondini, G. 



G. Mt. 29 (1891) 356-. 

 striction. Larmor, J. QJ. Mth. 19 



(1883) 381-. 

 of hyperboloid. Monteiro, A. S. G. 



Teix. J. Sc. 3 (1881) 131-. 

 as curves generated by higher 



configurations. Schmid, T. [1881] Wien 



Ak. Sb. 84 (1882) (Ab. 2) 908-. 

 rational skew curves of 4th 



order. Migotti, A. [1879] Wien Ak. Sb. 



80 (1880) (Ab. 2) 1023-. 

 of one sheet. Bobek, K. Par. 



S. Mth. Bll. 11 (1883) 125-. 



and of hyperbolic 



paraboloids. Bauer, M. Z. Mth. Ps. 28 

 (1883) 274-. 



. ruled surfaces. Nicolaides, N. 



Les Mondes 9 (1866) 146-. 

 of 2nd and 3rd degrees. 



Adler, A. Wien Ak. Sb. 85 (1882) (Ab. 2) 



, etc. of skew surfaces. Enneper, A. 



Gott. Nr. (1867) 454-. 



Loxodromes. 



on conical surfaces. Enneper, A. Gott. Nr. 

 (1869) 459-. 



cylinder and cone. Grebe, E. W. Grunert 

 Arch. 2 (1842) 127-. 



ellipsoid and sphere. Plagemann, W. 

 Grunert Arch. 32 (1859) 1-. 



equation and properties. Fournier- Vannson, . 



N. A. Mth. 20 (1861) 31-, 225-. 

 and geodesies on tore. Puchta, A. Mh. Mth. 



Ps. 1 (1890) 443-. 



loxodromic figures. Friesach, K. Steierm. 

 Mt. (1878) 78-. 



on paraboloid of revolution. Boyman, J. B. 



Grunert Arch. 13 (1849) 375-. 

 projecting into logarithmic spirals, surfaces 



with. Molins, H. Toul. Ac. Sc. Mm. 7 



(Son. 2) (1885) 293-; 8 (1886) 426-. 

 properties. Arrest, H. d'. As. Nr. 36 (1853) 



351-. 

 on quadrics. Boyman, J. E. Grunert Arch. 



7 (1846) 337-. 

 and shortest paths on spheroid. Caluso, 



(I'abbe) T. V. de. Turin Mm. Ac. 4 (1788-89) 



325-; 5 (1790-91)100-. 



spherical catenary. Gudermann, C. Crelle 

 J. 11 (1834) 394-. 



on any surface. Legoux, A. Toul. Ac. Sc. 

 Mm. 1 (1889) 352-. 



surfaces. Dina, C. G. Mt. 19 (1881) 298-. 

 of revolution. Schubert, F. T. [1803] 



St Pet. Ac. Sc. N. Acta 15 (1806) 202-. 

 . Gergonne, J. D. Gergonne A. 



Mth. 8 (1817-18) 125-. 

 . Aoust, L. Liouv. J. Mth. 11 



(1846) 184-. 

 . Junge, A. Schlomilch Z. 5 



(1860) 296-. 

 . Laisant, C. A. N. A. Mth. 13 



(1874) 573-. 



, equations. Grunert, J. A. 

 Grunert Arch. 21 (1853) 304-. 



Loxodromic arc between two points on sphere. 

 Friesach, K. Steierm. Mt. (1880) 3-. 



and great circles on sphere, relation. 

 Friesach, K. Steierm. Mt. (1876) 97-. 



triangles. Grunert, J. A. Grunert Arch. 

 16 (1851) 23-. 



Maximum area on surface with given perimeter. 



Aelt, . N. A. Mth. 19 (1860) 100-. 

 Meridian curve of surface of revolution. Eesal, 



H.A. C. B. 85 (1877) 5-. 

 Motion of point on surface. Enneper, A. Gott. 



Nr. (1869) 62-. 

 Number of conditions for existence of an r-fold 



straight line on surface of nth order is 



Machovec, F. Casopis 16 (1887) 230-; Fschr. 



Mth. (1887) 780. 

 Orthodromic sailing. Glotin, P. [1876-79] 



Bordeaux S. Sc. Mm. 1 (1876) xlviii-; 2 



(1878) 189- ; 3 (1880) 377-. 

 Orthogonal lines on surface, and linear partial 



differential equations of 2nd order (elliptic 



type). Burgatti,P. A. Mt. 23 (1895) 225-. 

 Points on surfaces such that geodesies through 



them never cease to be shortest lines. Man- 



goldt, H. von. [1880] Crelle J. Mth. 91 



(1881) 23-. 

 Projection, quasi- stereographic, due to Gauss. 



Forsyth, A. E. QJ. Mth. 21 (1886) 376-. 

 Pseudo-spheres, Viviani's theorem. Torelli, G. 



G. Mt. 10 (1872) 128-. 

 Quadrable figures on surface of right cone. 



Magistrini, D. [1845] Bologna N. Cm. 8 



(1846) 427-. 

 Bibaucour's problem. GuicJuird, C. C. B. 



125 (1897) 1013-. 

 Bidge lines and channels. Barre" de Saint- 



Venant, . Par. S. Phlm. PV. (1852) 24-. 

 _ --- . Jordan, C. C. B. 74 (1872) 



1457- ; 75 (1872) 625-, 1023-. 

 ---- . Breton (de Champ), P. Liouv. 



J. Mth. 3 (1877) 99-. 

 ____ , geometrical characters. Breton 



[de Champ], P. C. B. 53 (1861) 808-. 

 --- lines connected with them. McCowan, 



J. Ph. Mg. 37 (1894) 227-. 

 Spherical catenaries. Gudermann, C. Crelle 



J. 33 (1846) 189-, 281-. 

 class-cubics with 3 single foci. Jeffery, H. M. 



B. A. Bp. (1878) 490-. 



639 



