Feb., 1916] Hexagon Notation 139 



This gives for a b c d e f , the unique h-point. 



ace, bfdl 

 < cea, dbf ^ (D) 

 [eac, fdb^ 



The geometric relation of a hexagon and its unique h-point 

 will appear later. (See section 40). 



(10) To write the unique hexagon of any given h-point. 



Set the fourth letter of any line between the first and second ; 

 the sixth between the second and third. 



That for (C) is a f c b e d; 

 That for (D) is a b c d e f. 



(11) Relation between the unique hexagon of an h-point and 

 its two ordinary hexagons. 



The two ordinary hexagons of (D) in (9) are, by (8), 



ad, cf, eb 

 da, fc, be 



and the unique hexagon is, in (10), a b c d e f, but these three 

 hexagons are those of the g-point. 



a b c d e f] 



<jafcbed!^ 

 [a d c f e b] 



(12) To write a g-point and two h-points on a straight line. 

 It follows at once from the definition of these points that the 



g-point and the two ordinary h-points of any hexagon are on a 

 straight line. 



(13) To write a g-point and three h-points on a line. (Salmon's 

 G-line). 



The hexagons of any g-point will give g', hi, ho on a line; 

 also g', h2, ha on a line; also g', ha, hi (See sec. (8), (11), (12) ). 



Therefore, g', hi, h2, hs are on a line, where g' is the conjugate 

 g-point of the given g-point. (See (5) ). 



Therefore, the g-point and three unique h-points of the hexagon 

 of a g-point are collinear. And what is the same thing and the 

 same line, the g-point and three pairs of ordinary h-points of the 

 hexagon of a g-point are a g-point and three h-points on a line. 



(14) The number of g-points. 



In forming g' in section (2) we reversed the hexagon order 

 of segments in each column. This can be done in only one way. 



