6820 



Stereometry. Spheres 



6820 



Spheres touching tetrahedron edges. Miiller, 



J. H. T. [1854] Wien SB. 20 (1856) 



225-. 

 faces. King, L. Arch. Mth. Ps. 61 



(1877) 361-. 

 ,5 in contact, radii. Baur,C.W. Schlomilch 



Z. 5 (1860) 365-. 

 , 16 touching 4, and circles touching 3 circles, 



centres. Steplian, E. Par. S. Phlm. Bll. 2 



(1865) 133-. 

 , , , radii. Mention, 



J. N. A. Mth. 18 (1859) 438-. 

 , , on sphere. Casey, 



J. [1866] Ir. Ac. P. 9 (1867) 396-. 

 , , geometric property. Schubert, H. 



Z. Mth. Ps. 14 (1869) 506-. 

 , , metrical relations of radii. 



Schubert, H. Z. Mth. Ps. 14 (1869) 513-. 

 Steiner's series of spheres touching two spheres. 



Vahlen, K. T. Z. Mth. Ps. 41 (1896) 



153-. 



Coordinates in spherical geometry. Lupton, W. 



Ph. Mg. 14 (1857) 35-. 

 Cylinders and spheres, cylindrically pierced. 



Fuss, N. [1800] St Pet. Ac. Sc. N. Acta 14 



(1805) 213-. 

 , mensuration problems. Ferroni, P. 



Mod. S. It. Mm. 10 (1803) 649-. 

 Diameters of sphere, number. Hessel, J. F. C. 



Grunert Arch. 24 (1855) 1-. 

 Division of sphere, equal, by concentric spheres. 



Davidson, G. [1873] Calif. Ac. P. 5 (1873- 



74) 5-, 98-. 



, problem. Brinkley, J. [1801] Ir. 



Ac. T. 8 (1802) 513-. 



, solutions, new. Hess, E. D. Nf. 



Tbl. (*1878) 38. 



Dodecahedron and icosahedron in sphere, rela- 

 tion between. Flaugergues, H. Gergonne 



A. Mth. 2 (1811-12) 357-. 

 Ellipse, spherical, properties. Strebor. [Pseud. 



of Roberts, W.] N. A. Mth. 7 (1848) 135-, 



451- ; 9 (1850) 308-. 

 Ellipsoids and spheres, theorems. Kilbinger, G. 



Ens. Mth. 2 (1900) 196-. 

 Equal spheres, number touching given equal 



Inscribed regular polyhedra, volume. Bax, D. 



Leijd. A. Ac. (1815-17) 20 pp. 

 --- , . Serooskerken, R. C. van T. Leijd. 



A. Ac. (1815-17) 12 pp. 



solids. Kumps, H. J. Louvain A. Ac. 4 

 (1822) 51 pp. 



Intercepts on axes of coordinates of sphere or 



cone, proof of theorem of Steiner. Bermann, 



O. Arch. Mth. Ps. 53 (1871) 129-. 

 Intersections of circles, and intersections of 



spheres. Alvord, B. Am. J. Mth. 5 (1882) 



25-. 

 --- , ---- (Alvord). Kretkowski, 



W. Krk. Ak. (Mt.-Prz.) Pam. 13 (1887) 81- ; 



Fschr. Mth. (1887) 563. 

 --- , ---- , theorems. Miqiiel, A. 



Liouv. J. Mth. 3 (1838) 517-. 

 --- or spheres at given angles. Pellet, A. 



As. Fr. C. B. (1889) (Pt. 2) 161-. 

 Isodromes on a sphere. Reveille, J. Bv. Mar. 



et Col. 100 (1889) 546-. 

 Lexell's theorem concerning " parallelograms " 



and triangles on a sphere, proof. Lebesgue, 



V. A. N. A. Mth. 14 (1855) 24-. 

 Maximum, property. Bonnet, O. N. A. Mth. 



12 (1853) 433-. 

 Multiplication of matrices, theorem proved by. 



Chrystal, G. Edinb. Mth. S. P. 2 (1884) 



45-. 

 Osculating surfaces of moving sphere of variable 



radius. Starkov, A. N. Bs. S. Nt. Mm. 



(Mth.) 4 (*1883). 

 Pentahedron and quadrilateral, circum- and in- 



scribed. Jeffery, H. M. QJ. Mth. 25 (1891) 



336-. 

 Perspective of spheres, problem. Bergh, J. G. 



van den. Leijd. A. Ac. (1818-19) 24 pp. 

 Plane and sphere, Ceva's theorem. Spitzer, S. 



[1848] Haidinger B. 5 (1849) 21-. 



4 points, mutual distances. Scott, R. F. [1873] 



Mess. Mth. 3 (1874) 58-. 



on sphere, arcs joining two and two. 

 Berard, . Gergonne A. Mth. 6 (1815-16) 

 253-. 



5 points lie on sphere, condition. Luchter- 

 handt, A. R. Crelle J. 23 (1842) 375-. 



----- , . Enneper, A. Z. Mth. Ps. 



sphere. Bender, C. [1869] Arch. Mth/Ps. -- --- , , f rom barycentric principle. 



55 (1874) 303-. 

 Excentric sector. Hoppe, R. Arch. Mth. Ps. 



65 (1880) 176-. 

 Figures, which by inversion and reflection, fill 



up whole spherical surface. Hoist, E. B. 



(xn) Ts. Mth. 5 (1875) 87-. 

 Frustum of sphere, surface. Escher, P. 



Grunert Arch. 32 (1859) 188-. 

 Gergonne' s method, application to sphere. 



Barbarin, P. As. Fr. C. B. (1895) (Pt. 2) 



43-. 

 Hemisphere penetrated by indefinite number of 



equal cylinders. Knight, T. Phil. Trans. 



(1812) 310-. 

 Homocentric spheres of Eudoxus, Calippus and 



Aristotle. Schiaparelli, G. V. [1874] Z. 



Mth. Ps. 22 (1877) (Suppl.) 101-. 

 In-quadrilateral. Collite, J. N. A. Mth. 8 



(1849) 435-. 



Mdbius, A. F. Crelle J. 26 (1843) 26-. 

 Polygons, angles, theorem. Lebesgue, V. A. 



N. A. Mth. 9 (1850) 327-. 

 , convex, plane and spherical, angles. John, 



C. N. A. Mth. 5 (1846) 674-. 

 Poristic polygons on sphere. Enneper, A. Z. 



Mth. Ps. 14 (1869) 147-. 

 . Stall, . Z. Mth. Ps. 29 (1884) 



91-. 

 Pothenot's problem extended. Grunert, J. A. 



Grunert Arch. 1 (1841) 238-. 

 to space. Plath, C. W. Grunert 



Arch. 35 (1860) 241-. 1 

 sphere. Grunert, J. A. Grunert 



Arch. 7 (1846) 104- ; 47 (1867) 194-. 

 . Friesach, K. Steierm. Mt. 



(1876) 85-. 

 , graphical solution. Bauern/eind, C. M. 



Munch. Sb. (1871) 124-. 



459 



