Perspective Transformation is performed by a 4 by 4 matrix with elements in the final column:
Mpersp = 1 0 0 0
= 0 1 0 0
= 0 0 1 1/d
= 0 0 0 0
then [xyz1].Mpersp = [x,y,z,z/d] and as the w coordinate is effectively a scaling factor, items which are further away from the eye are 'shrunk' on the screen pixels. The red book gives a full description of the viewing transforms.