32 ROYAL SOCIETY OF CANADA 
Hence the curve through the five points À, B, C, D, E is unique, 
und does not depend on the particular pair selected as radiant points. 
Next let the curve through A, B, C, D E be constructed, and on it 
select any five points. Take any two of these as radiant points and 
suppose the curve constructed. This must be the curve first constructed, 
since only one curve can pass through the second five points, and the 
original curve does this. 
An analogous proof applies to the uniqueness of the sheaf of rays of 
the second order, whatever five rays of the sheaf be selected as the base 
of the construction and whichever of these be taken as the base lines. 
The following is the figure correlative to the preceding : 

A Le Les ° a 
= 
\ “, 
y 
ee TS NT 4 
rs Sai Wie 
4 
uw 
! 
The five rays which form the base of the construction are u, u,, À A,, 
BB, ana CC. Then u, u, being the base lines, and S, S, the radiant 
points, C B, or u, is the perspective axis. Hence, given a point D on u, 
we construct at once the corresponding point D, on u,, and the new 
ray D D, is reached. 
