7640 



Higher Algebraic Surfaces. Contacts 



7640 



# 2 3 x s + xJx-. + , 3 a; 2 , covariant theory. Brioschi, 



F. Mil. I. Lomb. Ed. 17 (1884) 401- ; Km. 



E. Ac. Line. T. 8 (1884) 164-. 

 (2y - Sb) (x 2 + i/ 2 ) + b 3 = 0. Almeida Lima, 



Joao d>. G. Teix. J. Sc. 6 (1885) 13-; 



Fschr. Mth. (1884) 644-. 

 ax 3 + 3by 2 z + 3cz*x = Q, concomitants. Walker, 



J. J. L. Mth. S. P. 20 (1889) 382-, 



Contacts, and Tangent Lines and Planes. 

 (See also 8450.) 



Contact of conies with surfaces. Spottiswoode, 

 W. Phil. Trans. 160 (1870) 289-. 



straight lines with surfaces. Salmon, G. 



QJ. Mth. 1 (1857) 329-. 



r"=a n sin nO. Iversen, I. M. N. Ts. Mth. 4 ,4. and 5-point. Gordan, P 



(B) (1893) 59-; Fschr. Mth. (1893-94) 1154. 



/>=2acosn0. Pirondini, G. Mathesis 14 

 (1894) 14-. 



p=R sinjtw, algebraic if /x is integral, other- 

 wise transcendental. Loria, G. Fschr. Mth. 

 (1899) 515. 



7640 Algebraic surfaces of degree 

 higher than the second. (See 

 also 8040.) 



(Miiller.) Petzval, J. Wien SB. 41 (1860) 



735-. 

 Cremona, L. Bologna Ac. Sc. Mm. 6 (1866) 



91- ; 7 (1867) 29-. 

 Backlund, A. V. Stockh. Ak. Hndl. 9 (1870) 



No. 9, 65 pp. 

 Mainardi, G. Em. At. N. Line. 26 (1873) 



384-. 

 Beltrami, E. Bologna Ac. Sc. Mm. 10 (1879) 



233-. 



Ocagne, M. d'. C. E. 99 (1884) 744-. 

 Asymptotes, curvature and singular points in 



surfaces of 2nd and 3rd degree. Beer, A. 



Grunert Arch. 17 (1851) 329-. 

 Asymptotic plane and cylinders of surface. 



Biehler, C. N. A. Mth. 8 (1889) 536-. 



planes and surfaces. Walton, W. Camb. 

 and Dubl. Mth. J. 3 (1848) 28-. 



straight lines, planes, cones, and cylinders. 

 Weddle, T. Ph. Mg. 31 (1847) 425-. 



Axes, 3 rectangular, cutting surface, theorems. 



Haillecourt, A. N. A. Mth. 12 (1853) 



398-. 

 Cones, algebraic, properties. Laguerre, E. 



[1870] (x) Par. S. Phlm. Bll. 7 (1871) 



139-. 

 , 3rd degree. Cayley, A. Ph. Mg. 18 (1859) 



439-. 

 , with degree, having vertices in straight line, 



and 2 plane intersection curves, theorem. 



Serret, P." N. A. Mth. 1 (1862) 21-. 

 Conical points on surfaces. Korteweg, . N. 



Arch. Wisk. 18 (1891) 153-. 

 Conjugate lines analogous to conjugate points. 



Walton, W. Camb. and Dubl. Mth. J. 9 



(1854) 238-. 

 Construction of surfaces from given points. 



Escherich, G. von. Wien Ak. Sb. 90 (1885) 



(Ab. 2) 1036-. 

 by means of reciprocal pencils of 



surfaces. Escherich, G. von. Wien Ak. Sb. 



85 (1882) (Ab. 2) 526-. 



plane sections. Cardinaal, J. 

 Amst. Ak. Vs. M. 6 (1889) 198-; Fschr. Mth. 

 (1889) 665-. 



Z. Mth. Ps. 12 (1867) 495-. 

 , various kinds. Clebsch, A. Crelle 



J. 58 (1861) 93-. 

 surfaces. Spottiswoode, W. Phil. Trans. 



162 (1872) 259-. 

 (Spottiswoode 's problems). Clifford, 



W. K. E. S. P. 21 (1873) 425. 

 . HalpJim, G. H. [1874] Par. S. 



Mth. Bll. 3 (1875) 28-. 



,2, having common generator, funda- 

 mental principle. Mansion, P. Brux. Ac. 



Bll. 3 (1882) 753-. 

 , , order of condition for. Roberts, 



S. QJ. Mth. 12 (1873) 229-. 

 , , , criteria. Plucker, J. 



Crelle J. 4 (1829) 349-. 

 Normals and tangents to algebraic surfaces 



and lines. Bardelli, G. Mil. I. Lomb. Ed. 



5 (1872) 167-. 

 Points where straight line has 5-point contact. 



Clebsch, E.F.A. [1863] (vn) Crelle J. 63 



(1864) 14-. 



Problem: if + -\ = 1 is a tangent plane, 



x l y l 2j 



and makes f(x, y, z) a maximum or minimum, 

 then /(a;, y, z) is constant, e. [Ellis, R. L.] 

 (vi Adds.) Camb. Mth. J. 4 (1845) 47-. 



Eotation surfaces, tangent planes, construction. 

 Matzek, F. Wien Sb. 58 (1868) (Ab. 2) 



Euled surfaces, 2, touching along generator, 

 condition. Ch., J. F. N. A. Mth. 2 (1863 

 262-. 



Skew surfaces, method of drawing tangents to. 

 Marchand, J. Par. S. Mth. Bll. 13 (1885) 



Surfaces, 3rd degree, contact of 4th order with 

 surface. Moutard, T. (x) Par. S. Phlm. 

 Bll. 2 (1865) 23-. 



Tangent planes. Reid, J. Mathematician 2 

 (1847) 187-. 



to algebraic surface through multiple 

 line of surface, number. Fouret,G. Palermo 

 Cir. Mt. Ed. 8 (1894) 202-. 



certain surfaces, arrangement. Weyr, 



E. [1878] Bordeaux S. Sc. Mm. 3 (1880) 

 191-. 



, higher, of algebraic surfaces. Totossy, 



B. Mth. Termt. Ets. 16 (1898) 127-. 



and normals to skew surfaces. Chasles, 

 M. Liouv. J. Mth. 2 (1837) 413-. 



at point on surfaces. Laisant, A. N. 



A. Mth. 7 (1868) 116-. 

 to skew surfaces. Monin, T. Prag Sb. 



(1888) (Mth.-Nt.) 210-. 



, theorems of Hachette and 

 Chasles. Goedseels, E. (xii) Mathesis 3 

 (1883) 49-. 



536 



