73] CONSTRUCTION OF THE SURFACE OF THE SECOND ORDER &C. 427 
question to determine the analogue of Pascal’s theorem for surfaces of the second order. 
This of course admitted of being answered in a variety of different ways, according to 
the different ways of viewing the theorem of Pascal. Thus, M. Chasles, considering 
Pascal’s theorem as a property of a conic intersected by the three sides of a triangle, 
discovered the following very elegant analogous theorem for surfaces of the second order. 
“ The six edges of a tetrahedron may be considered as intersecting a surface of 
the second order in twelve points lying three and three upon four planes, each one of 
which contains three points lying on edges which pass through the same angle of the 
tetrahedron; these planes meet the faces opposite to these angles in four straight lines 
which are generating lines (of the same species) of a certain hyperboloid.” 
It is hardly necessary to remark that all the properties involved in the present 
memoir are such as to admit of being transformed by the theory of reciprocal polars. 
54—2