GEOMETRIC THEORY. 3) 
Fic. 6. 
generate, and each must consist of linear segments terminat- 
ing at O. Every transformation of this kind is a perspective 
transformation. The point Q from which the projecting 
lines are drawn may be any point in the plane; Q may there- 
fore have ~* different positions; and we see that there are 
co* perspective transformations, each of which leaves the 
point O invariant. These ’ perspective transformations 
form the two-parameter group G,(O). This subgroup con- 
tains all the perspective transformations in the general pro- 
jective group and no others. 
THEOREM 32. All the perspective transformations contained in 
the general projective group form a two-parameter subgroup G.(0O); 
this subgroup contains no transformation which is not perspective. 
69. Subgroups of the Perspective Group. We now proceed 
to the consideration of the one-parameter subgroups which 
compose the two-parameter perspective group. Each of 
