( 205 J 
are intersected by this plane, will meet each other on the line of 
intersection Z of the planes (a; bg) and (az 64). In like manner the 
line of intersection m (fig. 2) of the planes (0; a2) and (b3 a4) passes 
through the point of intersection O of P,P, and Ps P,. 
Fig 2. 
If we now indicate the two skew quadrilaterals according to the 
vertices in the way pointed out in fig. 2 by Q; Q Q; Q, and Lj Ry R; Ry 
and if Pio, Paas Qi3, 2y3 represent the points separating O harmoni- 
cally from the pairs of points (Pj, Pa), (Pas Ps) (Qs Qs), Lln, Ps), it 
is easy to see that 
(Qo Pra Qis)s (Qs Psa Qis)s (Re Pie Mis), (Ry Poa Ais) 
are four triplets of points on a right line, 
(Pig Pas Qo Qs Gis)» (Pig Poa Po Ra Mh) 
two quintuples of points in a plane and that 
Pis Pq Qo Qs Qis Ry By Ly 
are eight points of a same space. We now choose the five-cell of 
which O is a vertex, the four lines PP», Ps Ps, Q Gs, Lj Rs are the 
edges passing through this point and the space just found is the 
side-space situated opposite O, as five-cell of coordinates; this has 
the five points O, Pio, Paas Qis, Liz as vertices. By assuming the 
point of intersection of the four spaces 
(Pi Pas Qis Rs), (Pa Pig Qis fs), (Q Piz Pas Bj), (Zj Pig Pas Qis) 
