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lines ¢, and pay attention to the correspondence between the rays 
m, im’, connecting them with an arbitrary point M of g. 
Any ray m vears (v+3) points Q, is therefore associated to (n+3) 
(n—4) rays m’. The straight line MB contains (n-—3) (n—4) pairs 
(), Q’, represents therefore (n—3) (n—4) coincidences m= im’. The 
remaining coincidences pass through points Q—= Q’; their number 
amounts to 2 (n+-3) (m—4) — (n—8) (n—A4) or (n+ 9) (n—A4). 
The method followed here will, for the sake of brevity, be indicated 
as “process (M)” 
From the result found it ensues, that the locus of the tangents 
tz, which osculate in B, is a cone of order (n+9) (n—4). 
We arrive at the same result by paying attention to the tangents 
of gr, which meet in B. Since B is a sextuple point, the number 
of those tangents amounts to (#-+3) (n+2)— 6.7 =n? + òn — 
36 = (n+9) (n—4). 
§ 8. On a straight line ¢ passing through B an involution of 
order (7—2) is determined by the surfaces #”, which touch ¢ in 5, 
and therefore form a pencil. There are consequently 2 (#— 3) surfaces 
which touch ¢ moreover in another point. On a generatrix of the 
cone (¢,)° that second point of contact, R,,.is united with 5. The 
locus of the points A, has therefore in B a sextuple point and isa 
surface of order 2. 
The surface ®”, which touches ¢ in /,, intersects that straight 
line moreover in a group of (2—4) points S. If S coincides with 
B, tis one of the straight lines ¢32 considered above, the locus of 
S has therefore in B an (n+9)(n—4)-fold point and is a surface 
of order (2-+-9)(n—4) + 2(n—3)(n—-4) = (8n+3)(n—4). 
We now lay again through # a plane p; it intersects the surfaces 
(R,) and (S) along two curves of the orders 2n and (8n-+3)(n— 4). 
We again apply the process (J/) to the pairs of points (RS) and 
find for the number of coincidences R, = S 
2n (n —4) + (8n+-3) (n—4) — (2n—6)(rn—4) or (8n4+-9) (n—4). 
The straight lines t3, which have their point of contact R, in B, 
form therefore a cone of order (8n+9) (n —4). 
If the same process is applied to the pairs of points S,.S’, belonging 
to one and the same point Rk, a cone of order (2n-+-6)(n —4)(n—5) 
is found, of which the generatrices 222 have a point of contact in B. 
§ 4. A straight line ¢ passing through B is intersected by the 
net [®"| in the groups of an involution of the second rank ei: 
In each of the 3 (n—3) triple points (R,) t is osculated by a @; 
