( 209 ) 

 (30), we find that the conic {D.^D.^B^^B^yBiBii) is represented by 



Jjj .Tj- — ^]2 -fl •';; — -■I 13 •''! -''3 + '' ^2 .^^3 = . . . (32) 



Here j/ is a new parameter dependent on Aj X^i whilst A ,/. denotes 

 the minor corresponding to o,t in the determinant formed by the 

 quantities «,x-. 



Of the biquadratic involution formed bv the points B (he qua- 

 druple r = is the only one, the points of which are collinear. 

 So the right lino T^gi /?23 has the equation 



^11 ^1-^12 •'•2-^13^3=0 (33) 



By remarking that the third diagonal point A of quadrangle 

 i?i B.^ Bi Bu is the pole of D(^^ D... with respect to the conic (32), 

 we easily find that the coordinates of A are determined bv 



yi 2/2 ^3 



(34) 



2^12^13 — ^11'' ^11^13 ^11^12 



Thus the locus of A is the right line 



A^.2.T.z=Ay^ir. (35) 



7. The relation 



"11 (-011^2" ^3" + 2^i.r2 3-3 ^ö„3a-i) = ((7iiJ-o:r3-f al2■''l^3 + «]3•^l•'■2)''4- 

 + •'"1" [(«11 «33— ai3-)-^2^ + 2 («11 «23— «12 «13) •'^2 ^3 + («11«22— ai2')^3-] • (36) 



proves that the tangents of r^ passing through D^ are represented by 



^22 .'•2- — 2^23^2-^3 + ^33^3^ = 0, .... (37) 



whilst their points of contact R^, 7?i are determined by the conic 



(*i EE «*h ^2 •''3 + «12 ^1 ''"3 + «13 '^1 -''a = . . ■ • (38) 

 Out of tlie equation 



Q., = «13 .rg 5-3 + f722 •'^l •'•3 + «23 •'''l ^2 = . . . . (39) 



