947 
A line A,C is cut at right angles by two lines A,A,; it contains 
therefore two points H, which as a rule lie neither on a, nor in 
C. It has appeared above, that there are three rays 4,C on each 
of which one of the points H lies in C; the pairs of points H form 
consequently a curve H, with triple point C. 
Finally the plane Co, contains a conic which is the locus of the 
orthocentre of a triangle A,D,D, (where D, is intersection of a, 
and Ca,). 
We may conclude, that the orthocentres of the triangles A,A,A, 
lie on a surface H° with double lines a,,a,,a, and triple point C. 
From this it ensues, that there are nine singular planes in which 
the four points A,, A,, A,, A, form an orthocentrical group. 
Any straight line of such a plane is apparently singular. 
