PEOFESSOR C. J. JOLY ON QUATERNIONS AND PROJECTIVE GEOMETRY. 279 
while corresponding sides intersect in the jDoints 
6Sca — cSah, cSah — aShc, aSbc ~ hSca .... (335). 
The point of concourse of lines of the linear complex in the plane [a6c], or, 
ih t.^)oSbc + (^3 — t^)bSca + — ycS«6 .... (331;), 
since this point is the intersection of the planes 
Sqf/t = 0 , Sqf]b = 0 , Sqf^c =0 .( 337 ). 
for which the united points are points of concourse. This point lies on the axis 
of perspective (335), and the ecpiation of that axis may be written in the form 
<l=^{f~t)fr^[abc-] .(338). 
The three lines of the complex which pass through the united points intersect the 
sides of the triangle (I) in a triangle (III) in perspective with (I), and through the 
vertices of this third triangle pass the polars of the united points with respect to 
the quadric SqfQq = 0, and the traces of these planes form a triangle (IV) likewise 
in perspective with (I). 
SECTION XIII. 
The System of Quadrics Sg 
q = 0, AND SOME Questions relating to 
Poles and Polars. 
81. General properties of the system.. 279 
82. The intersection of two quadrics of the system, and the analogies for confocal and 
coney die systems. 280 
83. The poles of tangent planes to two quadrics with respect to a third . ..280 
84. The condition that three c|uadrics may Ite polar cpiadrics of a cubic surface .... 281 
81. In this section we shall notice some properties of the system of quadrics 
= ^.(3d9). 
The self-conjugate function fin this homograjihic system may be supposed reduced 
to the type noticed in Art. 28, for by a linear transformation the symbolic quartic 
may be reduced in three ways to the form 
+ .(340). 
The system (339) is its own reciprocal, and it includes confocal and concyclic 
