7240 



Quadric Surfaces. Generators. Hyperboloid 



7240 



Focals, theory, and quadrics. Amiot,B. Liouv. 



J. Mth. 10 (1845) 109-. 

 Foci. Bobillier, . Quetelet Cor. Mth. 4 



(1828) 157-. 



. Beccaro, T. del. Tortolini A. 2 (1859) 30-. 

 . Haillecourt, A, N. A. Mth. 17 (1878) 



457-. 



of contours, general method of determining. 

 Pelz, C. Wien Ak. Sb. 75 (1877) (Ab. 2) 

 175-, 320 ; 77 (1878) (Ab. 2) 259-. 



curve of intersection of two quadrics. 



Catalan, E. C. N. A. Mth. 6 (1847) 421-. 



and directrices. Crosnier, . N. A. Mth. 

 13 (1874) 266-. 



. Lemonnier, H. N. A. Mth. 14 



(1875) 216-. 



, synthetic treatment. Hicks, W. M. 

 [1873] Mess. Mth. 3 (1874) 122-. 



of quadrics and rotation surfaces, determina- 

 tion. Lemonnier, H. N. A. Mth. 13 (1874) 

 318-. 



Locus of foci of central sections of quadric. 



Painvin, L. N. A. Mth. 5 (1866) 553-. 

 (Painvin). Boklen, 0. 



N. A. Mth. 18 (1899) 370-. 



questions. Azzarelli, M. Em. N. Line. At. 

 27 (1874) 405-. 



Paraboloid, focal properties. Staude, 0. Leip. 



Mth. Ps. B. 47 (1895) 483-. 

 , , algebraic basis. Staude, O. Leip. 



Mth. Ps. B. 49 (1897) 172-. 

 , pseudo-focus. Jung, G. Mil. I. Lomb. 



Ed. 15 (1882) 407-. 

 Plane section, foci, determination. Painvin, L. 



N. A. Mth. 3 (1864) 481-. 

 , , . Saltel, L. N. A. Mth. 9 (1870) 



463-. 

 Surfaces without foci. Chasles, M. Liouv. J. 



Mth. 1 (1836) 187-. 

 Umbilical lines. Titeica, G. 



fill. 6 (1897)] 401-. 



projection. Ascione, E. [1900] Nap. Ac. 

 At. 10 (1901) No. 2, 33 pp. 



Umbilici. Servais, C. Brux. Ac. Bll. 17 

 (1889) 366-. 



of ellipsoids. Stegmann, F. Grunert Arch. 

 8 (1846) 49-. 



. Verdam, G. J. [1851] Amst. Ts. 



Ws. Nt. Wet. 5 (1852) 42-. 



Formulae relative to quadrics. Spottiswoode, 

 W. Crelle J. 42 (1852) 169-. 



Function at* + bu~ + ctu, geometrical interpre- 

 tation, and applications. Weddle, T. Camb. 

 and Dubl. Mth. J. 9 (1854) 67-. 



Generation and Generators of Quadrics. 



Generation. Dupin, C. Par. EC. Pol. Cor. 1 



(1804-08) 144-. 



. Salmon, G. Ir. Ac. P. 3 (1847) 536-. 

 . Dienger, J. Grunert Arch. 16 (1851) 430-. 

 . Azzarelli, M. Em. N. Line. At. 37 (1884) 



205-. 

 by conies. Lentheric, . N. A. Mth. 6 



(1847) 5-. 



Generation and discussion. Amiot [Amyot], B. 



Liouv. J. Mth. 8 (1843) 161-. 

 (Amyot). Cauchy, A. L. C. E. 16 



(1843) 783-. 

 ( ). Chasles, M. C. E. 16 (1843) 



828-. 

 (priority question). Amyot, B. C. E. 



16 (1843) 938-. 

 ( ). Poncelet, J. V. C. E. 16 



(1843) 947-. 

 ( ). Chasles, M. C. E. 16 (1843) 



1105-. 

 , double, by movement of circle. Braxxeur, 



J. B. Liege Mm. S. Sc. 1 (1843) 157-. 



by homographic plane pencils. Jacobi, 

 C. G. J. Crelle J. 73 (1871) 179-. 



, Jacobi's method. Hermes, O. [1870] Crelle 



J. 73 (1871) 209-. 

 , . Sturm, R. Crelle J. Mth. 122 



(1900) 263-. 

 , mechanical. Pliicker, J. Crelle J. 34 



(1847) 357-. 

 , modular and umbilical, theory. Tillol, . 



Toul. Mm. Ac. 2 (1864) 80-. 

 , Salmon's and MacCullagh's methods. 



Neicson, H. B. A. Mth. 6 (1891-92) 198-. 

 Generator, condition that 2 quadrics should 



have one common. Bourlet, C. N. A. Mth. 



13 (1894) 434-. 

 Generators. Hachette, J. N. P. Crelle J. 1 



(1826) 339-. 

 Hyperboloid, generation, method. Olivier, T. 



Par. S. Phlm. N. Bll. (1833) 139-. 

 , orthogonal, mode of generation. Ruth, F. 



[1879] Wien Ak. Sb. 80 (1880) (Ab. 2) 



257-. 



of 1 sheet and hyperbolic paraboloid, recti- 

 linear generators. Gerono, G. C. N. A. 

 Mth. 15 (1856) 388-. 



[Bucarest S. Sc. , . Seidelin, . Mth. 



Ts. 6 (1864) 38-. 



Quadrics as generated by project! ve system of 

 spheres. Rollner, F. Z. Mth. Ps. 24 (1879) 

 116-. 



Homographic transformation of quadric into 



itself. Cayley,A. Ph. Mg. 6 (1853) 326- ; 



7 (1854) 208-. 

 Homographics, undevelopable uni-quadric. 



Gardiner, M. E. S. P. 16 (1868) 389-. 

 Homography and application to quadrics. 



Schoute, P. H. [1870] Arch. Neerl. 6 (1871) 



348-. 

 Homothetic conies on two quadrics. Jarolimek, 



V. Prag Ceske Ak. Fr. Jos. Ez. (Trida 2) 7 



(1898) Art. 20, 5 pp. ; Fschr. Mth. (1898) 



470. 

 Hyperbolas, rectangular, lying on quadric 



surface. Rupp, 0. [1882] Wien Ak. Sb. 86 



(1883) (Ab. 2) 909-. 



Hyperboloid and Hyperbolic Paraboloid. 



Conjugate diameters. Chasles, M. Quetelet 



Cor. Mth. 5 (1829) 137-. 

 Hyberboloid. Marrecas Ferreira, L. F. G. 



Teix. J. Sc. 7 (1886) 49-. 



506 



