HEXAGON NOTATION. 



R. D. BOHANNAN. 



(1) Salmon, in the "Notes" at the end of his Conic Sections 

 designates by <| , \ the point of intersection of the Hnes ab, 



de; bv 



the Pascal line which contains the three 



(h) 



ab, cd, ef 

 de, fa, bc^ 



points indicated by the vertical columns; and by the following 

 a g-point and an h-point, respectively: 



ab, de, cf,l fab, ce, df' 



^ cd, fa, be, ^ (g) ; < cd, bf , ae > 



[ef, be, ad, J [ef, ac, bd^ 



The lines in (g) (h), taken in pairs, indicate the Pascal 

 lines which meet in a point, but the ItJies do ?wt give the hexagons. 

 In (h) only two Pascals are indicated, since ce, ac, do not meet 

 on the Pascal line, nor do df and bd. 



To get the hexagon indicated by the first and second lines 

 of (g) start with ab of the first line; look up the letter with b 

 in the second line, giving abe: then the letter with e in the 

 first line, abed; then that with d in the second line, abedc; then 

 that with f in the first line, getting, finally, abedcf. 



Treating the pairs of lines in (g), (h) in this way we get, 

 rather tediously, the hexagons: 



fabedcfl fabfdce^ 



■j cdafeb M g) ; i cdbfea 



[efcbadj [efdbac^ 



(2) I give here a notation which indicates the hexagons 

 by horizontal lines, as also their Pascal lines, when horizontal 

 lines are taken in pairs. The points (g), (h) above are: 



ab, ed, cf' (1) 



(h) 



\ cd, af , eb (2) (gO ; 

 [ef, cb, adj (3) 



ab, fd, eel (1) 



dc, ae, fb I (2) (h') 



ef, db, ac[ (3) 



[ba, ec, dfj (1'). 



In (g') line (2) is formed from line (1) by writing under each 

 segment of (1) its opposite segment in (1), reversing the hexagon 

 order of letters in {1): (3) from (2) as (2) from (1); (1) and (2) 

 give the Pascal line of (1); (2) and (3) that of (2); (3), (1) that 

 of (3). 



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