6820 



Stereometry. Spheres ; Contacts 



6820 



Circle cutting given circles at given angles. 



Kretkowski, W. Krk. Ak. (Mt.-Prz.) Pam. 



13 (1887) 97-; Fschr. Mth. (1887) 564. 

 Circles described about eight small circles. 



Jeffery, H. M. QJ. Mth. 24 (1889) 198-. 



passing through two points and meeting a 

 line, locus of centres. Schiffner, F. Arch. 

 Mth. Ps. 5 (1887) 442-. 



of sphere, geometry. Schumacher, F. Z. 

 Mth. Ps. 34 (1889) 257-. 



and spheres with common radical axis and 



centre. Study, E. Crelle J. Mth. 94 (1883) 



233-. 

 Condition that 4 spheres or 3 circles go through 



same point. Steen, A. (xn) Ts. Mth. 2 



(1872) 56-. 

 Cone circumscribing sphere, maximum volume 



or surface. Snell, E. S. Camb. (M.) Mth. 



M. 1 (1859) 236-. 



, minimum volume. Snell, E. S. 

 Silliman J. 5 (1848) 227-. 



and sphere, intersection. Chasles, M. 

 Quetelet Cor. Mth. 5 (1829) 44-. 



--- , theorems. Miller, W. J. Mess. Mth. 

 2 (1863) 11-. 



with vertex on sphere, intersection with 

 sphere. Reiss, M. Quetelet Cor. Mth. 4 

 (1828) 355-. 



Cones and cylinders, intersection by spheres, 



theorems. Baltzer, R. Crelle J. 54 (1857) 



162-. 

 Construction, graphical, from 4 conditions. 



Gaultier, L. Par. EC. Pol. J. 16" cah. 



(1813) 124-. 

 Constructions, geometrical, on sphere. Bar- 



barin, E. Mathesis 19 (1899) 57-, 81-. 



, , -- . Bonnesen, T. N. Ts. Mth. 10 

 (B) (1899) 1-, 25- ; Fschr. Mth. (1900) 508. 



Contacts. 



Circle touching 3 circles on sphere. Olivier, T. 



Par. S. Phlm. N. Bll. 3 (1813) 312. 

 ------ . Gergonne, J. D. Gergonne 



A. Mth. 4 (1813-14) 349-. 



. Trzaska, W. Par. T. 



Nauk Sc. Pam. 1 (*1871) 123- ; Bll. Sc. 



Mth. As. 6 (*1874) 153-. 



, solution. Breton, Ph. 

 [1864] (xn) Isere S. Bll. 7 (Livr. 3 & 4) 

 (1867) 458. 



-- 4 spheres. Barbier, E. C. E. 60 (1865) 



1076-. 

 Circles, contact on sphere. Neumann, F. E. 



Oken Isis (1826) 349-, 466-. 



, --- . Fournier-Vannson, . N. A. 

 Mth. 14 (1855) 55-. 



and spheres, contacts. Alvord, B. Smiths. 

 Ct. 8 (1856) 16 pp. 



-- , . Coaklay, G. W. Camb. (M.) 

 Mth. M. 2 (1860) 116-. 



, spheres, cylinders and cones, contacts. 

 Durrande, J. B. 



(1820-21) 1-. 



touching each its predecessor and two 

 fixed circles. Gudermann, C. Crelle J. 39 

 (1850) 42-. 



Gergonne A. Mth. 11 



Sphere touching 3 or 4 spheres. Dupin, C. 



Par. EC. Pol. Cor. 2 (1809-13) 420-. 

 4 spheres. Euler, L. [1779] St Pet. 



Ac. Sc. Mm. 2 (1810) 17-. 

 . Poisson, S. D. Par. S. Phlm. 



Bll. 3 (1812) 141-. 

 . Tucci, F. P. Nap. At. S. Pont. 



2 (1812) 257-. 



. Frangais, J. F. Gergonne A. 



Mth. 3 (1812-13) 158-. 



. Gergonne, J. D. [1814] Tor. 



Mm. Ac. 22 (1816) 20*-. 

 . Hacliette, J. N. P. Par. EC. Pol. 



Cor. 3 (1814-16) 21-; Par. EC. Pol. J. 



17" cah. (1815) 129-. 

 . Binet, J. P. M. Par. EC. Pol. 



J. 17 e cah. (1815) 113-. 

 . Bohnenberger, G. C. Lindenau 



Z. 6 (1818) 270-. 

 . Dandelin, G. P. Quetelet Cor. 



Mth. 2 (1826) 13-. 

 . Trebert, A. N. A. Mth. 3 (1844) 



101-. 

 . Serret,J.A. Crelle J. 37 (1848) 



51-. 

 . Barbier, E. C. K. 60 (1865) 



1151-. 

 . Frischauf, J. Wien Sb. 52 



(1866) (Ab. 2) 222-. 

 , Apollonian problem. Flauti, V. 



Nap. At. Ac. 1 (1819) 369-. 

 , . Hunyady, J. [1877] (xn) 



Mag. Tud. Ak. Etk. (Mth.) 5 (1879) (No. 5) 



16pp. 

 , circle touching 3 circles on plane or 



sphere, and cone touching 3 cones. Poncelet, 



J. D. Gergonne A. Mth. 11 (1820-21) 



317-. 

 ,2 constructions and associated 



theorem. Walker, G. F. Mess. Mth. 11 



(1882) 173-. 



, magnitude. Fenwick, S. Mathe- 

 matician 1 (1845) 27-. 

 in mutual contact. Rutherford, W. 



Mathematician 1 (1845) 21-. 

 Spheres, contact. Hachette, J. N. P. Par. 



EC. Pol. Cor. 1 (1804-08) 17-. 

 , , problems. Flauti, V. [1809] Nap. At. 



Ac. 1 (1819) 21-. 

 , , theorems. Orr, W. McF. Camb. Ph. 



S. P. 9 (1898) 271-. 



touching central sphere of same diameter, 

 maximum number. Tandel, C. Quetelet 

 Cor. Mth. 2 (1826) 310-. 



given sphere. Hoppe, R. Arch. Mth. 



Ps. 1 (1884) 148-. 

 4 planes. Catalan, E. C. N. A. Mth. 



6 (1847) 253-; 9 (1850) 352-. 



, and circles touching 3 lines. 



R., L. P. F. (vi Adds.) Gergonne A. Mth. 



19 (1828-29) 211-. 

 , , radii. Steiner, J. 



Gergonne A. Mth. 19 (1828-29) 85-. 

 , radii. Loky, B. Orv.-Termt. 



Ets. (Termt. Szak) (1895) 265-. 

 skew quadrilateral. Vogt, H. Crelle J. 



Mth. 92 (1882) 328-. 



458 



