to movement in three dimensions 165 



is evidently one which leaves unaltered the fundamental quadric S 

 whose equation was taken to be xy — zt — 0. 



The result then is: if we apply to the figure for which the co- 

 ordinates {x) have been used the transformation /x, by {Xy) = /x {x), 

 this being a transformation leaving the arbitrary quadric S un- 

 altered, the relation between the figure {x-^, and the figure (x'), 

 which arose from {x) by {x') = '^ {x), which is expressed by 



is that the figure {x') arises from the figure {x-^ by an axis-range 

 perspectivity. The axis of this is an arbitrary " line in two planes " 

 of a certain developable determined by the arbitrary quadric and 

 the original transformation ^. 



