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We think it meet, to deal first with the following very simple 
problem: 
There being given three circles 
a, ft, y, to determine the .incident 
circle X. 
(Two circles, are said to be 
incident if they intersect in two 
real or imaginary points). 
There being given three couples 
of points a,b,c, to determine the 
incident couple 1 
(Two couples of points are said 
to be incident if the pencils of#- 
spheres they determine have an 
element in common, in which case 
they lie on a circle). 
One easily recognizes in these propositions the transformed ones 
of the following: 
To determine the transversal line I To determine the transversal 
l> to three given straight lines a,b,c. | plane to three given planes a,ft,y. 
The very simple solution of these may be represented symbolically 
thus: 
(bc) = A 
(c a) = B 
(ab)= r 
a/b/f= l 
Heading these symbols as follows 
S-sphere A through b a 
0/y = A 
Y/a = B 
ct/p= C 
A B C = X 
couple of points l, intersection 
of the three spheres A, B, r, 
^-sphere A orthogonal to ft and ) 
a „ £ 
the three 
circle X 
^-spheres A,B,Ci 
we have obtained a solution which we think to be the most natural 
one, even apart from our correspondence. 
e now pass to the construction of the Segre configuration in 
our space Z7. 
We transform directly the theorems relative to this construction, 
they having been originally thought as theorems in S„ 
There bemg given four elements: 
couples of points a, b, c, d | circles «, ft y, <f 
we can determine the incident element to every three of them, so 
that there be formed a double four 
« fS y <f 
a' ft y'd' 
