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complex, there must be a closer defiuition of the conies. This is 

 also evident from the following. All cones P- of the complex belong 

 to zero systems of a special kind. The line connecting P and A 

 defines such a special linear complex of rays ; it consists of all rays 

 intersecting PA. All these systems have the point A in common; 

 the net of rays through A contains the rays common to these 

 systems and finally the screws common to all consist of the pencil 

 {A, a) and the pencil through A perpendicular to «. Hence it 

 follows : 



All zero systems in which the screws of the cones of the complex 

 are situated have in common the pencil through A perpendicular to 

 a, to which in .^i a point O on K'^d corresponds (compare Sturm, 

 III p. 276). 



In a similar manner is proved that the pencil of screws common 

 to all zero systems of the curves of the complex is the pencil of 

 parallel screws lying in «, to which pencil a point C„ in -^i on 

 K^u corresponds. 



9. Now a construction will be deduced to find the points Q 

 and Cu. It is evidently sufficient if we consider the point of inter- 

 section of a plane, in which one of the conies Pj^ or tii^ is lying, 

 with K'^j and K\ ; specially that point of intersection which is not 

 at the same time a point of F^" or n^^, for which we can choose 

 in ^ a special cone or conic. 



Let us take P on the nodal line d in the point where the 

 generatrices with maximum and minimum pitchy and A meet. Cone P =2 

 breaks up into two planes through d] one plane is perpendicular to 

 ff, in which a pencil of screws lies with P as vertex, all screws 

 having a pitch equal to that of k; the second is perpendicular to 

 I; which also contains a pencil of screws having a pitch equal 

 to that of (/. To each of these pencils a right line corresponds in 

 ^i; the first belongs to the cone T^^t; the second to the cone T'^g ; 

 further a screw of the degenerated cone P~ coinciding with </, the 

 corresponding plane of ^i passes through J^d T,, 7),; so it intersects 

 K^d still in a point, the point Q that was to be found. 



10. From the preceding we easily deduce the construction of the 

 point C'u. Let us bring plane n through (/ and k. The parabola 

 71^ breaks up into two pencils of parallel screws consisting of 

 rays perpendicular to g and of rays perpendicular to k, the first 

 having the pitch k^ the second the pitch ƒ/. So the corresponding 

 plane in .^i passes through two generatrices of the cones 2-^- and 



