Two bisecants meet a trisecant ¢ in each of its points whilst 
each plane through ¢ contains a chord. All these bisecants form a 
cubie scroll 43 with double director t. The single director u is evidently 
a unisecant of R;. On the scroll 4 determined by u of course t 
is a part of the above mentioned double curve. 
Each of the double points of the involution determined on u, by 
the generators of 4; procures coinciding chords; consequently u is 
the section of two double tangent planes. 
6. A conic Q having five points in common with &; is not 
intersected by a trisecant in a point not lying on R;, for in its 
points of intersection with 2; it has ten points in common with 75. 
The surface J” formed by the conics @, the planes of which pass 
through the line c¢, is intersected by each trisecant in three points; 
so I’ is a cubic surface. 
The right line ¢ meets five trisecants lying on J’, hence also five 
bisecants belonging to this surface. As c is intersected by the 
conic Q of J in an involution, there are two conics Q, touching 
it. When ce becomes a unisecant then its point S on KR; is a double 
point of 43. Besides ce still five right lines of F3 pass through 5, 
two of which are trisecants; the remaining three must be bisecants 
completed to degenerated conics Q, by the other trisecants resting on c. 
If c becomes a chord, J’; has two double points, each of which 
supports two bisecants belonging to I’, and two trisecants also 
lying on the surface. If finally c is a trisecant, 13 becomes the 
above mentioned surface dz. 
So: All conics QQ intersecting two times a given right line form 
a cubic surface. 
7. The conics Q. passing through any given point P form a 
cubic surface II, with double point P. 
For only one conic Q, passes through P and the point S on Z5, 
as PS is a single line on the cubic surface 43 determined by PS, 
From this ensues that R; is a single curve of the surface 1/3, so 
that this is intersected by a trisecant in three points. And as a 
right line through P has in general with only one conie Q3 two 
points in common, one of which is lying in P, P is a double 
point of Js. 
On this surface lie the five bisecants meeting in P, moreover the 
five trisecants by which they are completed to conics. The quadratic 
cone determined by these five chords intersects 1/3 in a right line 
p, on which the mentioned trisecants rest; so p has no point in 
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