GEOMETRY. 357 



A cylinder is either right or oblique^ as the axis 

 is perpendicular to the base or inclined. 



Every section of a right cylinder taken at right 

 angles to its axis is a circle ; and every section 

 taken across the cylinder, but oblique to the axis, 

 is an ellipsis. 



As a circle may be considered to be a polygon of 

 an infinite number of sides, so a cylinder may be 

 conceived as a prism having such polygons for 

 bases. 



47. A cone is a solid, (Fig. 29. and 30.) having 

 for its base a circle, and its sides a convex surface, 

 and terminating in a point A called the vertex' or 

 apex of the cone. It may be conceived to be 

 generated by the revolution of a right-angled 

 triangle about its perpendicular. 



A line drawn from the vertex to the centre of 

 the base, is the axis of the cone. 



When this line is perpendicular to the base, the 

 cone is called an upright or right cone ; but when 

 it is inclined, it is called an oblique cone. 



If a cone be cut through the axis from the vertex 

 to the base, the section will be a triangle. 



If a right cone be cut by a plane at right angles 

 to the axis, the section will be a circle. 



If a cone be cut oblique to the axis, and quite 

 across from one side to the other, the section will 

 be an ellipsis, as Fig. 31. A section of a cylinder 

 made in the same manner, is also an ellipsis j and 

 this is easily conceived ; but it does not appear so 

 readily to most people, that the oblique section of 

 a cone is an ellipsis : they frequently imagine that 

 it will be wider at one end than the other, or what 

 is called an oval^ which is of the shape of an e^^. 

 But that this is a mistake, any one may convince 

 himselij by making a cone, and cutthig it acros:- 



A A 3 



