127] 
OF THE SECOND ORDER INTO ITSELF. 
137 
formation. In fact, the generating lines through P meeting the sections 6, </> in the 
points A, B respectively, and the remaining generating lines through A, B respectively 
meeting as before in the point Q, then P and Q will correspond to each other im 
properly, and in like manner P' and Q will correspond to each other improperly; i.e. 
P and P' will correspond to each other properly. The relation between P, P' may 
be expressed by saying that these points are opposite angles of the skew hexagon 
PAB'P'A'B lying upon the surface, and having the opposite angles A, A' in the 
section 6, and the opposite angles B, B' in the section <£. It is, however, clear from 
what precedes, that the points P, P' lie in a section passing through the points of 
intersection of 6, </>, and thus the proper transformation so obtained is not the general 
proper transformation. 
2 Stone Buildings, January 11, 1854.