GEOMETRY. 359 



through the centre, it divides the sphere into two 

 equal parts, each of which is called a hemisphere. 



51. A conoid is a solid produced by the circum- 

 volution of a section of the cone about its axis ; 

 and consequently may be either an elliptical conoidy 

 a hyperbolical conoid y or ^ parabolical co7ioid. When 

 it is elliptical, it is generally called a spheroid. 

 These solids are also called ellipsoid^ hj/perboloid, 

 and paraboloid. 



52. A spheroid is a solid (Fig. 35.) generated 

 by the rotation of a semi-eliipsis about the trans- 

 verse or conjugate axis; and the centre of the 

 ellipsis is the centre of the spheroid. 



The line about which the ellipsis revolves, is 

 called the adis. If the spheroid be generated, 

 about the conjugate axis of the semi-ellipsis, it is 

 called ^prolate spheroid. 



If the spheroid be generated by the semi-ellipsis, 

 by revolving about the transverse axis, it is called 

 an oblong spheroid. 



Every section of a spheroid is an ellipsis, except 

 when it is perpendicular to that axis about which 

 it is generated ; in which case it is a circle. 



All sections of a spheroid parallel to each other 

 are similar figures. 



A frustum of a solid means a piece cut off from 

 the solid by a plane passed through it, usually 

 parallel to the base of the solid ; as the frustum of 

 a cone, a pyramid, &c. 



There is a lower and an upper frustum, according 

 as the piece spoken of does or does not contain the 

 base of the solid. 



53. Ratio is the proportion which one magnitude 

 bears to another of the same kind, with respect to 

 quantity j and is usually marked thus, A : B. 



A A 4 



