Feb., 1916] 



Hexagon Notation 



137 



For (gi) of (4) it is g'j or g'o following: 



ab, cd, efl fa b c d e f] 



ed, af, cb \ (g'l) ; <^ a f c b e d ^ (g's). 



cf, eb, adj [a d c f e b , 



Of a pair of conjugate g-points, one is inside the conic; the 

 other outside; the line joining them is divided harmonically 

 by the conic (Steiner). 



The g-point on the Pascal of any hexagon is conjugate to 

 that of the hexagon. 



(6) To find three hexagons for which a given g-point is the 

 g-point. 



Write the conjugate g-point. 



(7) The two ordinary h-points of any hexagon and how to 

 write them. For any hexagon, as a b c d e f (1), write the 

 triangle of alternate letters: 



8.C, CC, C3-. 



Write under each letter its opposite letter in (1) giving, 



I ac, ce, ea ' /q-vN 

 \df, fb, bdj ^ -'■ 



The triangle, T, whose vertices are indicated by vertical 

 columns here, is in perspective with each of the triangles of 

 alternate sides of (1), giving for (1) two h-points. (T) may be 

 called the Pascal triangle of the given hexagon. 



To write the h-points of (/), wTite (1) forward and backwards 

 as in, 



a b c d e f (1) 

 a f e d c b (2) 



Group the alternate letters of (1), (2) in two groups, in 

 opposite directions, giving for (1) and (2) respectively: 



ace, fdb;aec, bdf, 



as the first lines of the desired h-points. Then complete as in 

 section (3) giving: 



ace, fdb] faec, bdf"] 



icea,, bf d [> (hi); ^ eca, fbd |^ (ho). 



eac, dbfj [cae, dfb^ 



We call these the two ordinary h-points of the corresponding 

 hexagon (1), to distinguish them from the unique h- point of the 

 same hexagon (see section (9) ). 



