931 
through 4 carries 2 other points of F*. Evidently every line inside 
7 BAE can be taken as AM. 
Every point (# A) of CE is isolated on one side of a, hence BD 
is the only line of F° intersecting CE. 
In an arbitrary plane (Xe) through AM, A is double point with 
a tangent in a. Let 8 be the plane through the other tangent (A H) 
and CE. The resteurve in @ contains no line different from CE, as 
BD is the only line intersecting CH. Neither can the resteurve in 8 
contain an oval not passing through A, as no line through A carries 
2 other points of F*. An oval in 8 passing through A is also 
impossible as the above mentioned tangent AH would also be tangent 
to this oval, hence this oval would cross CE at a point different 
from A and this would be irreconcilable with the way in which 
the sectors meet along CEH. Hence 8 contains no points of F*, 
not situated on CE. It follows directly that 3 is tangent plane at A, 
hence A is a biplanar point. 
As 8 contains no points of F* not situated on CE, BD is not 
intersected by any line except CH. Above we found that CH has 
no line of intersection except BD, hence CE and BD are the only 
lines of F'*. It follows at once that neither counts double in any 
plane (Zea). It can also be easily shown that neither counts triple 
in any plane. Hence the total number of lines on F° is 3. In what 
follows we exclude points as here described, and we leave undecided 
whether they can occur. | 
2. Through A passes a line 6 of F', not situated in «. Let this 
line depart above « on /, then it leaves below a on JV, for if it 
started on ///, we could at once find an infinite number of planes 
in which 6 branches meet at A (2 on / and /// each and 1 on 
II and JV each) and this would mean an infinite number of dege- 
nerations. Besides it is evident that all branches leaving from A on 
II and //T touch a at that point. 
We consider the plane 8 through 6 and CZ. A reasoning analo- 
gous to that of p. 926 shows that in 3 a third line passes through 
A, again leaving on / and JV. Hence in 3 3 different lines pass 
through A, which case shall be treated in § 4. 
§ 4. On points through which pass 3 different lines of F’*, situated 
m one plane. 
Let A be a point throngh which 3 lines pass, situated in plane a. 
Six branches start from A in a. Along none of these the sectors 
meet from the same side of a, for in that case an infinite number 
