Developable from the Equation (a, b, c, d, eYt, 1) 4 =0. 439 



equations of any generating line are d—0b=O, e—0 q a = O, 

 where is an arbitrary parameter. But considering the two 

 lines 



(<*-0,& = O, e-0?a = O), (d-0 <2 b=O i e-0 2 *a=O), 



the general equation of the quadric surface through these two 

 lines may be w T ritten 



A {d-0 l b) {d-0 2 b) 



+ B (e—0?a)(e-0fa) 



+ C (d-Ofi) {e-0 2 *a) + {d-0J>)(e-0 l *a) 



+ 0^0-{( d - i b ) {e-efa)-{d-OJ>){e-e x *a)\=Q, 



or, expanding and reducing, 



A{d*-{0 x + 2 )bd+0 1 2 b*\ 

 + B {* - tf* + 0*)ea + Q x *0*a*\ 

 + C{2de-{0*+0 2 *)ad-{0 1 + 2 )be + l 0c i {0 l + 02)ab\ 

 + T>{ {0 l +0 2 )ad- be- l i ab\=O, 



which, if #,, 0<2 are the roots of the equation 0^—^0+1=0, 



o 



and therefore x + 2 = |, 0A=h and 6*+0*=s* £ is 

 + B(e 2 + ^ + fl 2 ) 



+ D( 3^~ be—ab) = 0. 



9 15 



And putting A = 6, B = 9, C= ^, D = — — , this is 



9 ('a 2 



17 

 + 9 



ae + e q ) 





+ e(b* 



"J' 



bd+d*\ 





+ ^Uab + 2de 



^ 17 A 1 



be\ 



15/ , 



+ - 2 -r 





-I ad + 



be\ = 0, 



