148 



The Ohio Journal of Science [Vol. XVI, No. 4,. 



(2) 



(F). 



give, when used as the leading lines of a set like (Ai) in (45), 

 the same I-line; (2) will lead to the line gi, gv, ge, g5 on the 

 Pascals of (Ai) in (45). 



ah, ef, cd' 



ab, cd, fe 



ab, fe, dc 

 [ab, dc, ef 



But (Ai) and (F) belong to different Veronese groups. 



Thus the six stars of the I-lines in the six Veronese groups 

 are linked by having one line in common between each pair; 

 each star has one line in common with each of the five other 

 stars. See (48), which shows that all the stars could not be 

 five pointed. 



(48) Numerical table for the I-lines of g-points. 



Selecting any g-point as 



ab, cd, ef] 

 ed, af, cb j> (1) 

 cf, eb, adj 



the collinear groups of I-lines through (1) have for initial lines 

 of their g-points: 



ab, cd, ef (1)1 fed, af, cb (1)] fcf, eb, ad (1) 



ab, ef, dc (2) I led, ch, fa (5) I I cf , ad, be (8) I 



ab, dc, fe (3) | ' ] ed, fa, be (6) [ ' 1 cf, be, da (9) ( 



ab, fe, cd (4)J [ed, be, af (7)J [cf, da, eb (10)J 



Denote by 2 the g-point on the Pascal of hexagon (2), etc. 

 and write the above lines thus: 



1 



(a) The vertical columns are I-lines through 1. 



(b) The line joining 2 and 5 meets that joining 3 and at 

 10' (the conjugate of 10); and so, in general, the line joining 

 any two points in a horizontal line meets the line joining any 

 other two, in another horizontal line and in the columns of the 

 first two, in the conjugate of the point not in these columns- 

 nor lines (2, 8 meets 4, 10 at 6'; 7, 10 meets 6, 9 at 2', and so on).. 



