64 EXERCISES. 
Fic. 9. 
(17). In the perspective group hG,( AO) what degenerate 
conics determine the identical, the involutoric, the two 
pseudo-transformations and a pair of inverse transformations 
of the group? 
(18). If we take on the line AA’, (Fig. 9), two points Q 
and @’ as the centers of perspective transformations T and 
T,, give a direct geometric proof that the resultant of T and 
T, is a perspective transformation whose center is also in 
AA’. 
(19). The group G,(O) of perspective transformations con- 
tains one parabolic subgroup; find the locus of Q for this 
parabolic perspective group. 
(20). Show that any system of parallel lines cutting / and 
1’ determines a projective transformation 7 whose invariant 
points are O and ~. 
(21). Find the relation between the value of k in the 
transformation of example (20) and the slope of the system 
of parallel lines. 
