( 150 ) 



10. Hyperbolic paraboloid- of revolution third kind. 



One-sheeted, non rectilinear surface outside 7. Has a system of 

 distance lines in tangential planes to 7. 



TIL One plane of degeneration metrically real, 

 one ideal. 



IJ. Semi-hyperboloid of revolution. 



One-sheeted, non rectilinear surface. 



IV. Both planes of degeneration ideal. 



12. Elongated ellipsoid of revolution. 

 Closed surface. 



V. Planes o f d e g e n e r a t i o n c o n j ugate imaginary. 



13. Flattened ellipsoid of revolution. 

 Closed surface. 



VI. One plane of degeneration ideal, one touching 52. 



14. Elliptic paraboloid of revolution. 

 One-sheeted, non rectilinear surface. 



VII. Both planes of degeneration touching i2. 



15. Circular cylinder. 



One-sheeted, non rectilinear surface. The curve of intersection with 

 i2 is degenerated into a skew quadrilateral, the surface belongs also 

 io B. Both axes are equivalent, the ideal one bears a pencil of sections 

 along finite circles, the real one along distance lines. 



VIII. Planes of degeneration ideal, coinciding. 



16. Sphere. 



Closed surface, x' systems of finite circles. 



IX. Planes of degeneration touching 12, coin- 

 ciding. 



1 7 . Limiting-sphere. 



One-sheeted, non rectilinear surface, also belonging to C; oo^ systems 

 of circles, amongst which gd' systems of limiting circles. 



X. Planes of degeneration real, coinciding. 



18. Surface of distance. 



Locus of points at fixed distance on either side of a plane. Two- 

 sheeted, non rectilinear surface ; one inner domain, two outer domains. 

 Belongs also to B and C; oo' systems of circles, as well as of distance 

 lines, oo' systems of limiting circles. 



B. Cylinder-surfaces Proper. 

 Axis of revolution ideal (or indefinite), first systems of distance lines. 

 The surfaces 15 and 18. 

 XL Planesofdegenerationreal. 



19. Cone of revolution ivith ideal vertex and ideal axis. 



