.-.,. j.:.:.] 





179 



( * metrical with respect to each coordi- 



nate i <*noe also with rv*j>ect to tho origin. 



through the origin and any other 

 os wholl us. 



surface is called a coos, and the origin U its 

 vertex. It may be conceived as generated by a straight line 

 h moves along a fixed ellipse as directrix, and pisses 

 i a fixed point in u straight line which is perpen 



o plane of the ellipse at iU center. 

 cry equation of tho form A^ + lty* CV - repre- 

 sents a cone. It tho two jMsitive coefficients are equal, it is 

 a cone of revolution, or circular cone (of. Art. 218, eq. (9)). 

 The reasoning of Art. 225, applied to the special equation 



.. form [ ;;i ] which represents a cone, gives an anal 

 proof of tho fact that every plane section of a cone U a 

 second degree c. ^ ; Appendix, Note D). 



233. The hyperboloid and its 

 asymptotic cone. The hv|>eruoloid 



and tho con*. 



are closely related. It is clear 

 that, since the equations diflVr 

 only in the constant terms, u it- 

 surf aces can have no tin. 



n ; while as the values 

 of y and M arc innvasfd ii. 



, the corresponding values 

 L from > equations be- r*>.m 



