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secants consecutively 63, bas 6;, bg and ej, then the five bisecants 
resting on aj are indicated by ¢)3, ¢14) ¢151 Co and 0,9, and ag meets 
the bisecants coz. Ca4s Co5, Cag and bj. 
It is easy to see that the remaining ten right lines of I, viz. 
A3, Ugs Az, Agy C345 359 C361 C459 Caos C56 have each one point in common 
with Z,. 
11. Let P be any point of the conic Q, meeting aj in P' and 
P". Now the axes p and p' must intersect each other on Q); so 
p will pass through the point O common to p' and p". 
Consequently the axes p lying in a plane @ pass through a point 
O of conic Q, determined by a. 
As 9 has been found to describe the line as if w revolves about 
a, O and @ are focus and focal plane in relation to a linear com- 
plex of rays of which aj and ag are conjugate lines, the axes p 
and the trisecants t being rays. 
12. The conics Q which cut 2; in P and P' forming a cubic 
surface, a right line / having @ points in common with ZR; meets 
the (8—@) conics Q through P and P'. 
So Bj is a (3—q@)-fold curve of the surface @, containing the 
conics Q, which pass through P and rest on /. As a trisecant can 
meet none of those conics in a point not on ;, @ is a surface of 
order 3 (8—@), 
Of the 3 (3—e) points common to «> and the /-secant m 
/?(3—a) lie on PR. The remaining (3 —a) (3— 2) points of inter- 
section determine as many conics Qs resting on / and on m and 
passing through P as well. 
From this we conclude again that all the conics Q cut by / 
and m will form a surface ¥, on which R; is a (3—a) (8—/?)-fold 
curve. Then however ® must be a surface of order 3 (3—a) (3—/). 
If we now notice that a y-secant n is cut by ¥ in (3—a) (3—/9) 
points lying on &;, thus in (B—u) (8—/?) (3—y)-points not lying 
on this curve, it is evident that three right lines having respectively 
a, 2 and y points common with R, determine (3—a) (3—/?) (3—7) 
conics Q2 resting on these lines. 
So any three bisecants meet one conic Q3 only. 
13. Let Cy be a conic having xo point in common with &;. 
The surface 1/3, with its double point P on Cy, cuts this curve 
still in four points P'; consequently C, is a fourfold curve of the 
locus = of the conics Q, each having two points in common with Cy. 
