( 503 ) 
ray contains two pairs. They differ from PF, in this, that unlike the 
former they do not contain the tangential points of the double tangent 
as a pair. 
For M,=WM, we have a coincidence of the (2,2). From this is 
evident that the tangential points of the four tangents which can 
still be drawn from Mè, S or 7’ to C,, are every time connected 
with OQ, and O, by a conic (Q,, 6,, 7,). | 
In an analogous way as for /, we find by paying attention to 
the singular elements of the (2,2) on @,, 5, and r,, that the lines 
ST, and S,T, concur in R, the lines R,T, and R,T, in S the 
lines R,S, and R,S, in T. 
5. The polarcurve of the point (y,,7,,0) has as equation 
p I Yr Ya q 
yy (o,o? sl Laity” = b,@,°) zi (e‚°z, BE ORR zi b,x,°) =; 
or 
(ye, + Y, 24) (rara + 2,7) + (Oy, + by.) %,° = 0. 
By combination with the equation 
(wr, + #,7)? + Aber, = 0 
of the C, is evident that the points of intersection of the two curves 
lie on 7,2, J- 2,27 == 0 and on the curve 
syst + Yot.) by = (b,y, + bay.) (e,2, + #,?). 
Therefore the tangential points of the tangents out of a point of 
O,O, lie on a conic 1, 
For y,:y, = 6,:6,, ie. the point K=hk, we find the conic 
(biz, + bw) bc = 6,6, (a,x, + 2,7) through the points 1,2,3,4,5,6. 
Out of the equation 
YO, (@ 1%, aac © len 2.056, ti bale, Log) = 2a be} = 0 
is evident that the conics 4, form a pencil having as basis the points 
of intersection of z,7,-++2,2=0O with 6,—O0 (the points D,, D,) 
and two points of 6,7, = b,«, (the line A). 
One of the pairs of lines consists of the lines d and /; it contains 
the tangential points of the tangents out of H, two of which are 
united in d. 
The other two pairs of lines belong to two points of O,0,, for 
which the six tangential points lie every time on two lines passing 
through D, and D,. 
6. If (yx) is a point of d, thus 6,=0, then its polar curve with 
respect to C, is represented by 
2 (Yoe, + Yat, + 2y,2,) (t,2, + Lo) + Oyst Or = 0. 
