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in such a way that the top part moves towards C (fig. 3), then in 
every position ? contains an oval, with BH for tangent at A and 
departing on / and ///. Every line through A in one of these planes 
has only one further point in common with #*. This contradicts 
the above obtained result that in every plane not containing one of 
the lines in «, A is point of inflexion with tangent in «a, for if the 
tangent be slightly tnrned round A, we obtain 0 or 2 points of 
intersection with #'*, different from A. 
A point as here described we call normal point of intersection 
of 3 lines situated in 1 plane. 
2. Above « AC is connected with AF (1), AD with AE (LIL) 
and AH with AB (V), below « AD with AH (11), AE with AF 
JV) and AB with AC (VI) (fig. 4). On none of the sectors 4/1, 
IV, V, and V/ can be situated a branch not having a as tangent 
plane, for let such a branch start on ///, then at once an infinite 
number of planes can be found in which 2 branches depart on 
lll and one on 4, Il, TV and VJ, each. This makes 6 in all, in 
other words it would mean degeneration. Hence in every plane 
Fig. 4. 
through A inside one of the angles FAM or HAD the line of inter- 
section with « is one of the two tangents at the double point 4. 
We consider an arbitrary plane @ through B£. In 8 a branch 
leaves A on J and another on //, both situated on the restoval. 
Let 8 turning round BE converge towards a, in such a way that 
the top part moves towards / (fig. 4), then these branches converge 
towards AF and AD respectively. If 8 turns the other way the 
branches converge towards AC and AH respectively. It follows that 
a position of ? exists in which the oval degenerates, hence a line 
