; 





.:; -, 



(5) The surface U syium.-tn.al \\ith respect to each oo- 



This qiuulrio surface, whose equation in [35], i* called an 

 un-parted hyperboloid, or an hyperboloid of one sheet. It 

 may be conceived aa generated by a variable ellipse, which 

 has -s UJH.I, ami moves always perpendicula 



fixed liyjuTlxiUs \\hi.-li in turn an* j- i j--i..ii. ulur to each 

 other, ami have a common conjugate axi*. J I quation 

 can be readily obtaineil fi<>ni this dctinitiMn.* 



,ery equation of the fmin AJ* + Bp~ (V- Jf- 

 represents an un-parUnl \\\\* -rlMilma. If the two posi 

 coefficients are equal, i.*-., tf </ - A. the quadric is the simple 

 Ii\lH-rloi.iri . eq, 



230. The bi-parted hyperboloid: equation a ~ J-' 



ii the CM, 



S~"*~"i* =Sl 



following properties may be derived : 



i. m 



Art. 



