358 GEOMETRY. 



obliquely : it will be then seen that the section, in 

 whatever direction it is taken, is a regular ellipsis ; 

 and this is the case, whether the cone be right or 

 oblique; except only in one case in the oblique cone, 

 which is when the section is taken in a particular 

 direction which is called sub-contrary to its base. 



48. When the section is made parallel to one of 

 the sides of the cone, as Fig. 32., the curve ABC, 

 which bounds the section, is called a parabola. 



49. When the section is taken parallel to the 

 axis, as Fig. 33., the curve is called an hyperbola. 



The curves which are formed by cutting a cone 

 in different directions are called conic sections, and 

 have various properties which are of great import- 

 ance in astronomy, gunnery, perspective, and 

 many other sciences. 



50. A sphere is a solid, terminated by a convex 

 surface, every point of which is at an equal distance 

 from a point within called the centre. Fig. 34. 



It may be conceived to be formed by making a 

 semicircle revolve round its diameter. This may 

 be illustrated by the process of forming a ball of 

 clay by the potter's wheel, a semicircular mould 

 being used for the purpose. The diameter of the 

 semicircle round which it revolves is called the 

 axis of the sphere. 



The ends of the axis are called poles. 



Any line passing through the centre of the 

 sphere, and terminated by the circumference, is a 

 diameter of the sphere. 



Every section of a sphere is a circle j every sec- 

 tion taken through the centre of the sphere, is 

 called a great circle, as A B, Fig. 34. ; every other 

 is a lesser circle, as C D. 



Any portion of a sphere cut off by a plane is 

 called a segment; and when the plane passes 



